Overview

Onsite

ML Concepts:

  • Underfitting and Overfitting: Understanding these concepts is crucial in machine learning.
  • Logistic Regression: A key algorithm used for binary classification tasks.
  • Decision Tree: A simple, interpretable model used for classification and regression tasks.
  • XGBoost: A powerful gradient boosting algorithm often used for structured data.

How to Address Data Imbalance:

  • Techniques to handle imbalanced datasets, which can skew model performance.

Data Mining and Product Design:

  • ML Design: How to make job recommendations based on a personal profile and job description.

Distance Calculation:

  • Finding the Smallest Point: Calculating the distance to a series of coordinates and determining the median point.

Hiring Manager (Behavioral Questions):

  • General behavioral questions related to background, experience, and project discussions.

I received an SR position offer from the company at the end of 2020 but didn’t take it because I had better offers from other companies for real SR positions. This year, the company’s stock price dropped significantly, so I decided to try for a staff position instead.

Overview:

I noticed that the MLE question bank seems to have only a few core questions, but the difficulty is adjusted depending on the role level. I encountered several familiar, though slightly different, questions during the coding round.

First Round (TPS):

  1. Coding:
    Given ( f(x) ), find the maximum/minimum.
    This question was very similar to one I had during the store interview last year, but the key difference was that the x at the SR level was discrete, while at the staff level, it was continuous, making it more challenging. The solution from last year couldn’t be applied. I followed GD’s ideas, but the process didn’t feel smooth. However, the main focus seemed to be on communication.

  2. ML Design:
    How to improve personalized job recommendations?
    This was an ML design essay. It wasn’t difficult if you have experience with similar tasks, as it mainly involved discussing ideas.

VO1: Host Manager Behavioral Questions (BQ):

  • Topics included:
    • Why LinkedIn?
    • Project deep dives.
  • The main goal was to assess whether my scope had reached the staff level. I received a score of 31 in this round.

VO2: Data Mining and Product Design:

  • Design Task: Design LinkedIn’s feed ranking system.
    This round was not difficult because it was mostly a discussion about feed ranking and product design. I was given a score of 32.

VO3: Data Coding:

  • First Question:
    Given a sorted array A of doubles, compute a new sorted array B, where each element is obtained by applying the function ( f(x) ) to elements in A.
    This question felt very similar to the TPS question but required careful thought. In reality, it was the same as my TPS question from last year.

  • Second Question:
    Given a stream of arbitrary objects (e.g., numbers spanning a large range), return one precise sample.

The Chinese interviewer in the data mining round was very relaxed. He asked many questions about basic ML and deep learning concepts, such as:

  • What is MLE?
  • How to differentiate between log-loss?

I admitted that I had forgotten some of the details, but he didn’t make a big deal out of it and gave me a score of 32.

Final Feedback:

The recruiter called me to discuss the feedback and mentioned that a score of 30 was considered a passing score, so my scores would be considered a “weak yes.” After that, three groups were arranged for team matching.

In the past, LinkedIn staff members gave higher scores, equivalent to 55 for senior roles, but now it seems everyone gives around 500+, and the company doesn’t seem to have the same advantage it once had.

I want to give back by sharing the latest interview experience of an ML engineer at L company.

Background:
I have a PhD in physics from a less-known school and am planning to change careers after graduation. My background includes just a few research projects during my PhD that barely make up for useful ML experience (such as simple KNN). Companies in the Bay Area are very tolerant of applicants from different backgrounds. As long as they have relevant projects, even if they are academic, they will give you an interview. I asked a friend who works there to recommend me, and I received a call from HR about a week later.

In the first round of the HR interview, they asked about my resume, relevant background, related projects, and proficiency in various languages and packages. It took half an hour and wasn’t difficult if you can articulate well.

Second round (phone interview):
It took one hour. The first half-hour focused on basic ML knowledge. They asked me to pick an ML algorithm I was familiar with, explain the parameters, the type of data it’s suitable for, whether it’s a linear classifier, how to train it, what overfitting is, and how to prevent overfitting. The questions were very detailed and basic but not difficult if you prepare for 1-2 algorithms carefully.

The second half-hour was for coding, which was simple. The task was to find the range of a certain number in a sorted array with repeating elements (essentially the original binary search problem). I used a binary tree + recursion to solve it.

After the phone interview, I received an onsite notification a week later. The onsite was in Sunnyvale and lasted a whole day, with 6 rounds, each lasting one hour. The questions were comprehensive and well-structured.

1. First round (ML technical interview):
It was very similar to the phone interview. The interviewer picked a project from my resume and asked detailed questions like how I implemented it, why I chose that method, whether there was overfitting, how to judge overfitting, and how to solve it. They also asked about my results and how to justify them (such as hypothesis testing). The questions were broad but basic, requiring thorough preparation.

2. Second round (Algorithm coding interview):
There were two coding questions. For ML track roles, the algorithm requirements aren’t as strict as for general SWEs. The questions were at an easy level on LeetCode. The first one was about finding the number of islands, which I solved quickly using DFS. The second was about finding the highest level of a tree. I hadn’t practiced much, so I didn’t finish it, which caused some trouble.

3. Third round (Lunch break):
Yes, eating counts! It was easy to handle—just praise the interviewer as much as possible.

4. Fourth round (Product design):
I was asked to design a friend recommendation algorithm. Since I’m good at networking, I did well in this round. I mentioned two ways to recommend friends.

5. Fifth round:
One of the questions was how to generate 1-hot or 0-hot vectors corresponding to 1-6 bits. Another question was to quickly find the median, which was interesting. I used the partition method from quicksort to find it in O(n) time.

A week later, I received feedback saying I was weak in coding. The new interview involved inserting and finding elements in a binary search tree. Thanks to my previous onsite experience, I prepared thoroughly and wrote the code quickly. However, the interviewer said I didn’t communicate well and ended up failing me, even though the task was very basic.

In conclusion, this LinkedIn interview tested fundamental knowledge but was quite comprehensive. It’s actually very friendly to people from non-traditional backgrounds.

1. Basic ML Concepts:

  • What is overfitting/underfitting?
  • What is the bias/variance tradeoff?
  • What are the general preventive measures for overfitting?
  • What is the difference between Generative and Discriminative models?
  • Given a set of ground truths and 2 models, how do you determine which model is better?

2. Regularization:

  • L1 vs L2: Which one is which and what are their differences?
  • Explanation of Lasso/Ridge (What are the priors for each?)
  • Derivation of Lasso/Ridge
  • Why is L1 sparser than L2?
  • Why does regularization work?
  • Why do we use L1/L2 and not L3/L4?

3. Metrics:

  • Precision and recall trade-off
  • What metric to use when labels are imbalanced?
  • What metric should be used for classification problems and why?
  • Explanation of confusion matrix and AUC (e.g., the probability of ranking a randomly selected positive sample higher)
  • What are the true positive rate and false positive rate?
  • What is ROC?
  • What is Log-loss, and when should it be used?

There are also scene-related questions such as:

  • What metric to use in ranking design?
  • What metric to use for recommendation systems? (These are not in the scope of this discussion)

4. Loss and Optimization:

  • Is Logistic Regression with MSE as the loss a convex problem? Explain and write the MSE formula.
  • When to use MSE?
  • What is the relationship between the Linear Regression least squares method and Maximum Likelihood Estimation (MLE)?
  • What are relative entropy/cross-entropy and KL divergence? What is their intuition?
  • Logistic Regression loss and its derivation
  • SVM loss function
  • Multiclass Logistic Regression
  • Why is cross-entropy used as a cost function?
  • What is the optimization goal when splitting a Decision Tree node?

5. Basic Concepts of Deep Learning (DL):

  • Why does DNN need a bias term? What is the intuition behind it?
  • What is Backpropagation?
  • What are gradient vanishing and gradient exploding? How to solve them?
  • Can neural network initialization start with all weights initialized to 0?
  • What is the difference between DNN and Logistic Regression?
  • Why do you think DNN has better fitting ability than Logistic Regression?
  • How to do hyperparameter tuning in DL (random search, grid search)?
  • What are the ways to prevent overfitting in Deep Learning?
  • What is Dropout? Why does it work? What is the process of Dropout (difference between training and testing)?
  • What is BatchNorm? Why does it work? What is the process of BatchNorm (difference between training and testing)?
  • What are common activation functions (Sigmoid, Tanh, ReLU, Leaky ReLU) and their advantages and disadvantages?
  • Why do we need non-linear activation functions?

6. Optimizers:

  • Differences between different optimizers (SGD, RMSprop, Momentum, Adagrad, Adam)
  • The advantages and disadvantages of SGD
  • The impact of batch size
  • The impact of a learning rate that is too large or too small on the model
  • The problem of plateau and saddle points
  • When does transfer learning make sense?

It is not easy to organize all this, so I hope that some replies will encourage the author to slowly organize the remaining topics (Next, there may be ML model classes, CNN vision classes, RNN/NLP classes, data processing classes).

Everyone is welcome to reply with their answers below the post. If you have any questions, you are also welcome to reply and discuss.

Interview Details:

1. Machine Learning Basic Concepts:

  • Overfitting/Underfitting: Explanation of these concepts.
  • Bias/Variance Tradeoff: What it means.
  • Overfitting Prevention: Common techniques used to avoid overfitting.
  • Generative vs. Discriminative Models: Differences between the two.
  • Model Comparison: Given two models and a set of ground truths, how do you determine which model is better?

2. Regularization:

  • L1 vs. L2: What they are and their differences.
  • Lasso/Ridge: Explanation and derivation of both, and why L1 tends to be sparser than L2.
  • Why Regularization Works: Why we use L1/L2 regularization instead of L3 or L4.

3. Metrics:

  • Precision and Recall Trade-off: What it is and when to use specific metrics, especially for imbalanced labels.
  • Confusion Matrix & AUC: Explanation of these concepts, including ROC, true positive rate, false positive rate, and log-loss.

4. Loss and Optimization:

  • MSE in Logistic Regression: Why it is a convex problem and its formula.
  • Linear Regression and MLE: Relationship between the two.
  • Cross Entropy/KL-Divergence: Intuition and uses of these concepts.
  • SVM and Logistic Regression: Loss functions of each.

5. Decision Trees:

  • Node Split Optimization: How decision trees split nodes and what they optimize for.

6. Deep Learning (DL) Basics:

  • Bias Term: Why bias terms are needed in neural networks.
  • Backpropagation: How it works and the problems of vanishing/exploding gradients.
  • Neural Network Initialization: Why weights shouldn’t be initialized to zero.
  • DNN vs. Logistic Regression: Differences in representational power and why DNNs are better at fitting complex patterns.

7. Hyperparameter Tuning:

  • Random Search vs. Grid Search: Differences and when to use each.
  • Overfitting in DL: Preventive measures, including Dropout and Batch Normalization.

8. Common Activation Functions:

  • Sigmoid, Tanh, ReLU, Leaky ReLU: Strengths and weaknesses of each.
  • Non-Linear Activation: Why it’s needed.

9. Optimizers:

  • SGD, RMSprop, Momentum, Adagrad, Adam: Differences between these optimizers and when to use each.
  • Batch Size: Effect of batch size on model performance and learning rate tuning.

10. Transfer Learning:

  • When It Makes Sense: Scenarios where transfer learning is effective.

11. Random Forests and Boosting:

  • Random Forests vs. Boosting Trees: Differences between the two models.
  • Bagging vs. Boosting: Key differences and when to use each method.
  • Why Random Forest Samples 63% of Data: Explanation of why each tree in a random forest samples approximately 63% of the data (related to the concept of bootstrapping).

12. Model Robustness:

  • Handling Outliers: Which classifiers/models are more robust to outliers.
  • Dealing with Missing Values: Which classifiers/models are less influenced by missing data and why.

13. Metrics for Specific Tasks:

  • Ranking Metrics: Which metrics to use for ranking systems.
  • Recommendation System Metrics: When building recommendation systems, what metrics to prioritize (not covered in detail but mentioned as context-specific).

14. SVMs and Decision Trees:

  • SVM Loss Function: Detailed explanation of the loss function used by Support Vector Machines (SVMs).
  • Decision Tree Split Criterion: Criteria used by decision trees to split nodes (e.g., Gini impurity, information gain).

15. Neural Network Training Issues:

  • Vanishing/Exploding Gradients: Explanation of what causes these problems in deep neural networks and methods to mitigate them (e.g., using ReLU, proper weight initialization, Batch Normalization).
  • Plateaus and Saddle Points: Problems with optimization in deep learning, particularly with large models.

16. Cross-Entropy and Logistic Regression:

  • Why Use Cross-Entropy for Cost Function: Explanation of why cross-entropy is commonly used in classification problems, particularly in logistic regression and deep learning models.

17. Backpropagation and Gradient Descent:

  • Backpropagation Process: Explanation of how gradients are propagated through layers in a neural network.
  • Gradient Descent Variants: Differences between standard gradient descent, mini-batch, and stochastic gradient descent.

This concludes the core interview topics discussed, which included essential machine learning and deep learning concepts, coding problems, and model-specific questions.

1. Coding Problem:
You are given a sorted array A and a quadratic function in the form of ( ax^2 + bx + c ). The function is applied to each value in array A, resulting in a new array B. Then, you are required to output the sorted sequence of B in O(N) time.

After the interview, I found out that this was the LeetCode problem #360, and I had never done this question before.

2. Machine Learning (ML) Discussion:
ML is a very broad field, and the interview covered various basic ML concepts. For example:

  • They asked me to talk about the ML model I am most familiar with and explain it in detail.
  • Then, they asked if I know the tree-based model and to explain that as well.
  • My resume mentioned Long Short-Term Memory (LSTM), so they asked me to explain that, too.
  • Finally, they asked about the advantages and disadvantages of each model, and when to use a particular model and why.

The on-site interview experience has been posted here:

Host Manager Interview:

First half-hour: Resume discussion, some behavioral questions (e.g., why you changed jobs, leadership roles, and specific responsibilities in your projects). Second half-hour: Small ML design task: hashtag recommendation.

Resume discussion, project details will go into depth. ML basics: Tree-based models, handling imbalanced data. Coding problem: Classic biased 0/1 to unbiased 0/6. Other interviews have mentioned it, so I won’t repeat it.

Coding and Algorithms: Module 1
Design a data structure that supports the following operations with O(1) complexity:

  1. increase(key) - Increases the frequency of the key by 1.
  2. decrease(key) - Decreases the frequency of the key.
  3. get_max_key() - Gets the most frequent key so far.
  4. get_min_key()

Coding and Algorithms: Module 2

  1. Determine the longest reply string of a string.
  2. Given a list of points on a 2D plane, implement a function: 
    def get_nearest_k_point(self, center): 
 # center is a given point

Host Leader
Chatted about projects and praised each other.

Eng Lunch
Ambassador chatted about projects and meta.

Chinese brother
Was very good and gave me some guidance on employment planning. 23333

Concurrency
Classic delayed task scheduler design.

Data Structures & Algorithms
Design a key-value store with the constraint that there are only 100k files on a machine. The interfaces you can use are:

  1. create_a_file
  2. delete_a_file
  3. append_something_to_a_file

Complex Systems

First round

K means

When dealing with the K-means algorithm, certain scenarios can present unique challenges. Here’s how to handle each of the situations you’ve mentioned:

1. Data is less than the number of clusters (K > N)

  • Issue: The number of data points (N) is less than the number of clusters (K).
  • Solution: This situation is problematic because K-means aims to partition the data into K clusters, but you can’t have more clusters than data points.
    • Adjust K: Reduce the number of clusters ( K ) to be equal to or less than the number of data points ( N ).
    • Alternative Approaches: Consider different clustering algorithms that don’t require a predefined number of clusters, such as hierarchical clustering.

2. Data is repeated

  • Issue: Repeated data points might lead to certain clusters having multiple identical centroids, which can make the algorithm ineffective.
  • Solution:
    • Remove Duplicates: If the duplication doesn’t add value, consider deduplicating the data before clustering.
    • Weighting: If duplicates represent important aspects of the data (like frequency), consider weighted clustering algorithms where repeated points have more influence on cluster centroids.
    • Cluster Initialization: Ensure that the initial centroids are distinct and not simply duplicates of data points.

3. Data is empty or K is negative

  • Issue: If the data is empty or ( K ) is negative, the algorithm cannot function properly.
  • Solution:
    • Empty Data: If the dataset is empty, K-means cannot run. Ensure that there is valid data before running the algorithm. Implement checks to avoid passing empty data to the algorithm.
    • Negative K: ( K ) must be a positive integer, as it represents the number of clusters. Implement a validation check to ensure ( K ) is a positive integer before starting the algorithm. If ( K ) is negative, prompt the user to provide a valid ( K ) value.

Summary:

  1. K > N: Reduce ( K ) to be less than or equal to ( N ).
  2. Repeated Data: Remove duplicates or adjust for their presence through weighting or distinct centroid initialization.
  3. Empty Data / Negative K: Implement validation checks to ensure non-empty data and a positive integer ( K ).
  • These strategies will help ensure that the K-means algorithm is applied effectively and avoid common pitfalls.

Statistical Questions

Twyman’s Law is an adage in the field of data analysis and statistics that states:

“Any figure that looks interesting or different is usually wrong.”

Explanation:

Twyman’s Law is a cautionary principle that suggests when you come across a data point, trend, or figure that stands out as surprising, unusual, or interesting, it is often an indicator that something might be wrong with the data, the analysis, or the interpretation. The law implies that anomalies in data are frequently the result of errors rather than meaningful insights.

Applications:

  • Data Analysis: When analyzing data, if a particular result seems too good to be true, or if it deviates significantly from expectations, Twyman’s Law suggests that the first step should be to check for possible errors or misinterpretations.
  • Statistics: In statistical analysis, an unexpected result might be due to a mistake in data collection, data entry, the use of incorrect statistical methods, or an overlooked variable.
  • Scientific Research: Twyman’s Law serves as a reminder for researchers to be skeptical of surprising findings and to rigorously verify them before drawing conclusions.

Implication:

Twyman’s Law encourages a healthy skepticism and the practice of validating data, especially when results appear unexpected or counterintuitive. It underscores the importance of thoroughness in data analysis, where a surprising result is often a signal to double-check the work before accepting or promoting the finding.

Origin:

Twyman’s Law is named after Tony Twyman, a media researcher and consultant, though it has become a widely recognized principle in various fields involving data and statistics.

In essence, Twyman’s Law is a reminder that interesting or unusual data points should prompt further investigation to rule out errors before being considered significant findings.

  • Fisher’s Inequality is a fundamental result in the design of experiments and combinatorial design theory, specifically related to balanced incomplete block designs (BIBDs).

Key Concepts:

  1. Balanced Incomplete Block Design (BIBD): In a BIBD, a set of (v) elements (called treatments) is arranged into (b) blocks, each containing exactly (k) elements, such that each element appears in exactly (r) blocks. Additionally, each pair of elements appears together in exactly (\lambda) blocks.

  2. Parameters: The design is described by the parameters ((v, b, r, k, \lambda)).

    • (v): Number of treatments or elements.
    • (b): Number of blocks.
    • (r): Number of blocks in which each treatment appears.
    • (k): Number of treatments in each block.
    • (\lambda): Number of blocks in which each pair of treatments appears together.

Fisher’s Inequality:

Fisher’s Inequality states that for any balanced incomplete block design, the number of blocks (b) must be at least as large as the number of treatments (v). In mathematical terms:

[ b \geq v ]

Significance:

Fisher’s Inequality provides a fundamental limit on the design of experiments. It implies that in any BIBD, there must be at least as many blocks as there are treatments. This result is crucial in the study of combinatorial designs and helps in the construction and analysis of experimental designs.

Example:

Consider a BIBD where (v = 4), (k = 3), and (\lambda = 2). Fisher’s Inequality tells us that the number of blocks (b) must be at least 4. If we construct such a design, we find that (b = 4) and (r = 3), meaning that each treatment appears in exactly 3 of the 4 blocks, satisfying Fisher’s Inequality.

Fisher’s Inequality is named after the statistician Ronald A. Fisher, who made significant contributions to the field of experimental design.

Simpson’s Paradox and the two-sample proportion test are important concepts in statistics, particularly when analyzing and interpreting data. Let’s break down each concept and see how they relate to one another.

1. Simpson’s Paradox

What is it?

Simpson’s Paradox occurs when a trend that appears in different groups of data disappears or reverses when the groups are combined. This paradox shows the importance of considering the context and structure of the data before drawing conclusions.

Example:

Suppose you have data from two hospitals on the success rate of a certain surgery:

  • Hospital A:
    • Group 1: 90% success rate (out of 100 surgeries)
    • Group 2: 80% success rate (out of 200 surgeries)
  • Hospital B:
    • Group 1: 95% success rate (out of 20 surgeries)
    • Group 2: 85% success rate (out of 180 surgeries)

When you look at the combined data, it might seem that Hospital B has a higher overall success rate, but when you break it down by groups, Hospital A might have a higher success rate in each group. This reversal of the trend when aggregating data is Simpson’s Paradox.

Implication:

Simpson’s Paradox suggests that when comparing proportions or rates across different groups, one must be careful about combining the groups without considering the underlying factors. It highlights the importance of stratifying the data and analyzing it within its context.

2. Two-Sample Proportion Test

What is it?

A two-sample proportion test is used to determine whether the proportions of a certain outcome are the same in two different populations.

Hypotheses:

  • Null Hypothesis (( H_0 )): The proportions in both populations are equal (( p_1 = p_2 )).
  • Alternative Hypothesis (( H_1 )): The proportions in both populations are not equal (( p_1 \neq p_2 )).

Test Statistic:

The test statistic for a two-sample proportion test is usually based on the standard normal distribution (Z-distribution) and is calculated as follows:

[ Z = \frac{\hat{p_1} - \hat{p_2}}{\sqrt{\hat{p}(1 - \hat{p}) \left( \frac{1}{n_1} + \frac{1}{n_2} \right)}} ]

where:

  • ( \hat{p_1} ) and ( \hat{p_2} ) are the sample proportions.
  • ( n_1 ) and ( n_2 ) are the sample sizes.
  • ( \hat{p} ) is the pooled sample proportion, calculated as:

[ \hat{p} = \frac{x_1 + x_2}{n_1 + n_2} ]

( x_1 ) and ( x_2 ) are the number of successes in the two samples.

Decision:

  • Compare the calculated Z-value to the critical value from the Z-distribution table (e.g., 1.96 for a 95% confidence level).
  • If the absolute Z-value is greater than the critical value, reject the null hypothesis, indicating a significant difference between the two proportions.

How Simpson’s Paradox Relates to the Two-Sample Proportion Test

  • Impact of Simpson’s Paradox: When conducting a two-sample proportion test, it’s important to ensure that the data isn’t subject to Simpson’s Paradox. If it is, the aggregated data might suggest a misleading conclusion. The test might show a significant difference or no difference between proportions when, in fact, the opposite is true when analyzing subgroups separately.

  • Mitigation: To avoid Simpson’s Paradox, analyze the data separately for different subgroups before combining them. Consider stratifying the data and performing separate proportion tests for each stratum.

Summary

  • Simpson’s Paradox cautions against combining data across groups without understanding the underlying patterns, as it can lead to misleading conclusions.
  • Two-Sample Proportion Test is used to compare proportions between two groups, but care must be taken to account for potential confounding variables that could lead to paradoxical results.

ML

Variance, bias, and regularization are key concepts in machine learning and statistics, particularly when dealing with model performance and generalization. Here’s how these concepts are related and how they impact model training:

1. Bias-Variance Tradeoff

Bias:

  • Definition: Bias refers to the error introduced by approximating a real-world problem, which may be complex, by a simplified model. High bias usually occurs when a model is too simple, leading to underfitting.
  • Example: A linear model trying to fit a non-linear dataset will likely have high bias, as it cannot capture the underlying structure of the data.

Variance:

  • Definition: Variance refers to the model’s sensitivity to small fluctuations in the training data. High variance occurs when a model is too complex and captures the noise in the training data, leading to overfitting.
  • Example: A deep neural network with many parameters might fit the training data very well but perform poorly on unseen data because it has learned the noise in the training set rather than the true underlying pattern.

Tradeoff:

  • Balance: The bias-variance tradeoff is the balance between underfitting (high bias) and overfitting (high variance). Ideally, you want to find a model that captures the underlying patterns without being too sensitive to noise.

2. Regularization

What is Regularization?

  • Definition: Regularization is a technique used to reduce variance (overfitting) by penalizing model complexity. It adds a penalty term to the loss function, discouraging the model from fitting the noise in the training data.

Types of Regularization:

  • L1 Regularization (Lasso):
    • Adds a penalty equal to the absolute value of the magnitude of coefficients.
    • Encourages sparsity in the model (i.e., some coefficients may become exactly zero, leading to feature selection).
    • Regularization Term: ( \lambda \sum w_i )
  • L2 Regularization (Ridge):
    • Adds a penalty equal to the square of the magnitude of coefficients.
    • Leads to smaller, more evenly distributed coefficients, reducing model complexity.
    • Regularization Term: ( \lambda \sum w_i^2 )
  • Elastic Net:
    • A combination of L1 and L2 regularization.
    • Useful when you want both feature selection and complexity reduction.

Impact on Bias and Variance:

  • Increasing Regularization: Tends to increase bias (as the model becomes simpler) and decrease variance (as the model is less sensitive to noise).
  • Decreasing Regularization: Tends to decrease bias (allowing the model to fit the training data better) but may increase variance (risking overfitting).

3. Relationship Between Variance, Bias, and Regularization

  • Bias-Variance Decomposition: The error of a model can be decomposed into three components: bias, variance, and irreducible error (noise in the data that no model can learn).

    • Total Error = Bias² + Variance + Irreducible Error

  • Role of Regularization:

    • Reducing Overfitting: By adding regularization, you can reduce the variance component of the error, leading to better generalization on unseen data.
    • Potential Underfitting: However, too much regularization can increase bias, leading to underfitting.

4. Practical Considerations

  • Model Selection: The choice of regularization technique and the strength of regularization (e.g., the value of ( \lambda )) is often determined through cross-validation, where you evaluate how well different models generalize to unseen data.
  • Complexity Control: Regularization is a powerful tool to control the complexity of the model, ensuring that it performs well not just on the training data but also on new, unseen data.

Summary

  • Bias: Error due to oversimplification; leads to underfitting.
  • Variance: Error due to model sensitivity to training data; leads to overfitting.
  • Regularization: Technique to reduce overfitting by penalizing model complexity; balances the bias-variance tradeoff.

Code

It seems like the message got jumbled together, but I understand that you’re asking for help with a coding problem related to simulating the outcome of rolling a ( M )-sided die using the inverse CDF method. The message also includes references to hidden content and scoring, which seem unrelated to the actual coding problem.

Inverse CDF Simulation: Rolling an M-sided Die

To simulate rolling an ( M )-sided die using the inverse CDF (Cumulative Distribution Function) method, you can follow these steps:

  1. Define the CDF:
    • For an ( M )-sided die, each side has an equal probability of ( \frac{1}{M} ). The CDF for the die is a step function that increases by ( \frac{1}{M} ) for each side.
    • The CDF ( F(x) ) for side ( i ) (where ( i ) ranges from 1 to ( M )) is given by: [ F(x) = \frac{i}{M} \text{ for } x = i ]
  2. Inverse CDF:
    • To use the inverse CDF method, generate a random number ( u ) uniformly distributed in the interval [0, 1].
    • Determine the smallest integer ( i ) such that ( F(i) \geq u ). The result is the side ( i ) of the die.
  3. Implement the Simulation:
    • You can implement this in Python as follows:
import random

def roll_die_inverse_cdf(M):
    # Generate a uniform random number between 0 and 1
    u = random.uniform(0, 1)
    
    # Calculate the side of the die based on the inverse CDF
    for i in range(1, M + 1):
        if u <= i / M:
            return i

# Example: Rolling a 7-sided die 10 times
M = 7
rolls = [roll_die_inverse_cdf(M) for _ in range(10)]
print("Roll results:", rolls)

Explanation:

  • random.uniform(0, 1): Generates a random number between 0 and 1.
  • for i in range(1, M + 1): Loops through each side of the die.
  • if u <= i / M: Checks if the random number falls within the interval for side ( i ).

Example Output:

If you run the example with a 7-sided die, you might get something like:

Roll results: [3, 1, 7, 5, 6, 2, 7, 4, 2, 5]

This represents 10 rolls of a 7-sided die.

Additional Request (Rice!):

The mention of rice seems metaphorical, but if it’s literal and part of a game or task you’re working on, it’s unrelated to the coding aspect. If you need further clarification on that, feel free to ask!

Behavioral

2 Quick behavioral questions:

a. Have you ever made technical or product-related suggestions that were adopted?

b. As a TL (Team Lead), what have you done to remove yourself from the critical path?

c. Decisions you have made to improve the technical level of your products.

  1. Retain best cache similar to:

System Designs

Here is the refined version of your LinkedIn feed ranking system with improved headings and formatting:

Design LinkedIn’s Feed Ranking System

Designing LinkedIn’s feed ranking system involves multiple stages, including identifying user engagement signals, defining inputs and outputs, selecting data and features, choosing the appropriate model, and evaluating system performance. Here’s a comprehensive plan to design a feed ranking system similar to those used by other social networks, such as LinkedIn, Facebook, or Twitter.

1. System Overview

The LinkedIn feed ranking system will aim to increase user engagement by ranking posts according to their relevance to individual users. The system will prioritize content that drives engagement (e.g., likes, shares, comments) and align with the business goals of promoting sponsored content when necessary.

2. Input and Output of the Model

  • Input:
    • User Profile Data: Includes demographic information, current job, location, network connections, and past interactions with content.
    • Post Data: Content, timestamp, engagement signals (e.g., likes, shares), and type of media (text, image, video).
    • User-Post Interaction Data: Historical data showing user interactions with similar types of posts (e.g., clicks, likes, shares).
    • Contextual Data: Time of day, device used, and session length.
  • Output:
    • A ranked list of posts displayed in the user’s feed, ordered by predicted engagement score.

3. Data and Features

User Data:

  • Demographics: Age, location, job title, industry.
  • Network Connections: Size of the user’s network and their closeness to other users.
  • Behavioral Data: Previous interactions with posts, connections, or companies (e.g., liking, sharing, commenting).

Post Data:

  • Content Type: Text, image, video, or a combination of these.
  • Engagement Data: Number of likes, shares, comments, and reactions a post has received.
  • Post Metadata: Timestamp, hashtags, mentions, and linked users or companies.

User-Post Interaction Data:

  • Previous Engagements: How the user engaged with similar posts in the past (e.g., dwell time, clicks, likes).
  • Affinity Data: The relationship between the user and the post author, such as mutual connections or shared work experiences.

4. Model Selection

a. Pointwise Learning to Rank (LTR):

This method predicts engagement scores for individual user-post pairs and ranks posts based on the score. This can be implemented with a binary classifier (engage or not).

  • Pros: Simple and effective for ranking individual posts.
  • Cons: Does not capture user-to-user relationships (social context).

b. Pairwise Learning to Rank:

Instead of assigning scores to individual posts, this method compares pairs of posts and learns to rank the more relevant post higher.

  • Pros: Optimizes the relative ranking of posts, which aligns better with the task of showing the most relevant content first.
  • Cons: Computationally more expensive than pointwise ranking.

c. Deep Learning Models (Neural Networks):

  • Multi-task Deep Neural Networks (MTL): This can simultaneously predict multiple types of engagement (e.g., likes, comments, shares).
  • Pros: Can learn rich interactions between users and content using deep embeddings.
  • Cons: Requires large amounts of data and computational power to train.

d. Graph Neural Networks (GNNs):

  • Models the relationships between users and content as a graph where edges represent interactions between users and posts.
  • Pros: Can incorporate social context (e.g., mutual connections, interactions) into the ranking system.
  • Cons: Complex to implement and requires significant computational resources.

5. Loss Function

a. Binary Cross-Entropy Loss:

Used for predicting binary outcomes (e.g., will the user engage with the post or not). This loss function is appropriate when the task is a classification of engagement likelihood.

b. Pairwise Ranking Loss:

Used to ensure that relevant posts are ranked higher than less relevant ones in pairwise ranking systems. The goal is to minimize incorrect pairwise rankings.

c. Multi-Task Loss:

In the case of multi-task models, a combination of losses is used for different engagement metrics (e.g., click, like, share). The total loss is computed as a weighted sum of individual losses: [ L_{total} = \alpha_1 L_{click} + \alpha_2 L_{like} + \alpha_3 L_{share} ] where (\alpha) are weights assigned to each task.

6. Optimization Algorithm

  • Adam Optimizer: Preferred for deep learning models, especially for its ability to handle sparse gradients and large datasets.
  • RMSProp: Could be used for models where balancing learning rates is crucial, especially in the presence of noise.
  • SGD (Stochastic Gradient Descent): Useful for simpler models like logistic regression but may need advanced techniques like momentum to ensure convergence.

7. Evaluation Metrics

Offline Metrics:

  • Precision@K and Recall@K: These metrics measure how many of the top-K ranked posts are relevant or lead to engagement.
  • NDCG (Normalized Discounted Cumulative Gain): Evaluates the ranking quality, taking into account the position of the relevant posts in the ranked list.
  • AUC-ROC: Used to evaluate the classification performance of predicting engagements like likes, shares, or clicks.

Online Metrics:

  • Click-Through Rate (CTR): Percentage of impressions that lead to user clicks.
  • Engagement Rate: Percentage of posts that receive user reactions (e.g., likes, shares, comments).
  • Dwell Time: Measures how much time users spend viewing each post, a key indicator of engagement.
  • Time Spent on Feed: Total time users spend interacting with the feed, which indicates the system’s success in delivering engaging content.

8. Serving/Deployment Flow

  • Data Preparation Pipeline:
    • Data Preprocessing: Clean and preprocess user interaction data, post metadata, and user profiles.
    • Embedding Layer Preparation: Convert text-based information such as post content and user biographies into embeddings (e.g., using pre-trained models like BERT).
  • Prediction Pipeline:
    • Retrieval Service: Fetch posts that a user hasn’t seen yet.
    • Ranking Service: Rank posts by computing engagement scores using the trained ranking model.
    • Re-Ranking Service: Apply business rules (e.g., boost sponsored content, prioritize posts from close connections).
  • Online Inference:
    • Deploy models to the cloud for real-time inference using platforms such as AWS, GCP, or Azure.
    • Use A/B testing to evaluate new ranking models by serving different versions of the ranking algorithm to user segments.

9. Scalability and Real-Time Requirements

a. Distributed Training:

To handle large volumes of data, the system will use distributed training on platforms like TensorFlow or PyTorch. Parallelizing the training across multiple GPUs or machines will help scale up the training process for larger datasets.

b. Serving Architecture:

The model will be deployed using scalable infrastructure, such as Kubernetes or Amazon SageMaker, to serve real-time predictions. The model needs to rank posts in milliseconds to meet real-time requirements for the user experience.

c. Continuous Learning:

The system will be updated regularly with new data from user interactions (e.g., clicks, likes) to fine-tune the model and improve its ranking accuracy over time. Continuous learning pipelines can be established to periodically retrain the model.

Conclusion

By combining deep learning, multi-task learning, and ranking techniques, the LinkedIn feed ranking system can deliver personalized and relevant content to users in real-time. The system is designed to optimize user engagement through continuous feedback, efficient data pipelines, and scalable infrastructure. Handling challenges like real-time performance and cold starts ensures a seamless experience that keeps users engaged with the LinkedIn platform.

Designing a friend recommendation algorithm, commonly referred to as the “People You May Know” (PYMK) feature, involves leveraging user data, social connections, and behavioral patterns to suggest potential connections. Here’s how we can design such an algorithm, including the use of graph-based methods, collaborative filtering, and content-based approaches.

1. System Overview

The goal of the “People You May Know” (PYMK) algorithm is to recommend new connections (friends or professional contacts) to users. The system will suggest users who are likely to connect based on shared attributes (e.g., mutual friends, workplace, or school) and past interactions.

2. Input and Output of the Model

  • Input:
    • User Profile Data: Information such as education, work experience, skills, location, and network size.
    • Connection Data: User connections (friends, colleagues) and strength of those relationships (frequency of interactions, closeness).
    • Behavioral Data: Interaction history with other users (profile views, connection requests, comments, likes, etc.).
    • Social Graph Data: The social connections graph where nodes are users and edges represent friendships or interactions.
  • Output:
    • A ranked list of potential connections (other users) relevant to the target user.

3. Data and Features

a. User Features:

  • Demographic Data: Age, gender, location, education, job title.
  • Work and Education History: Companies worked for, schools attended, time spent in each institution.
  • Skills and Interests: Endorsements, skills listed, groups joined.

b. Connection Features:

  • Mutual Connections: Number of mutual friends or colleagues with another user.
  • Connection Strength: Frequency of interactions with mutual connections (e.g., messaging, liking posts).
  • Interaction Data: How frequently the user interacts with specific profiles (profile views, comments).

c. Graph Features:

  • One-Hop and Two-Hop Neighborhood: How closely connected the user is to the potential recommendation. One-hop represents direct connections, while two-hop represents mutual friends or shared colleagues.
  • Transitivity: If two users share many mutual connections, there is a high probability they may connect as well.
  • Closeness Centrality: How central a user is in the social network graph. Users with high centrality might be suggested to others more frequently.

4. Model Selection

a. Graph-Based Models (Graph Neural Networks, GNNs)

Since user connections form a natural graph, GNNs can be highly effective. GNNs allow us to predict whether two users will form a connection by leveraging both user features and the structural information from the social graph.

  • Graph Neural Networks (GNNs): Use a GNN to propagate features across the social network graph, allowing the model to learn relationships between users based on their connections.
    • Pros: Captures complex social structures and relationships. Can effectively model mutual friends, shared work experiences, and network effects.
    • Cons: Computationally expensive for large networks, especially with multi-hop neighborhoods.

b. Collaborative Filtering

  • User-User Collaborative Filtering: Identify similar users based on shared connections or behavior (e.g., users who connected with the same individuals in the past). Recommend connections that similar users have formed.
    • Pros: Works well when users have significant interaction data.
    • Cons: Struggles with new users (cold start problem).

c. Content-Based Filtering

  • Profile-Based Matching: Use user profile information (e.g., job title, education, location) to recommend users with similar attributes.
    • Pros: Effective for cold-start users who have not yet established connections on the platform.
    • Cons: Limited by profile information and does not capture social connections or behaviors.

d. Hybrid Models

  • Combination of GNN and Collaborative Filtering: Use a hybrid model that combines the graph-based approach (for understanding user connections) and collaborative filtering (for behavioral data).
    • Pros: Balances the strengths of both approaches, handling new users and leveraging existing connection patterns.
    • Cons: Complexity in implementing and tuning multiple models.

5. Model Architecture

The model will combine the following components to create a robust friend recommendation system:

a. Embedding Layers

  • User Embedding: Represent users as dense vectors based on their features (e.g., age, location, work history).
  • Interaction Embedding: Capture historical interactions between users and connections. This could involve collaborative filtering to embed users based on their shared connections and behaviors.

b. Graph-Based Layer (for GNNs)

  • Graph Convolutional Layers: Process the social network graph to propagate features between users based on the structure of the network. For example, the features of a user’s neighbors (connections) can be propagated to the user, helping the model learn important relationships.
  • Multi-Hop Neighborhoods: Consider one-hop and two-hop neighborhoods to capture both direct and indirect relationships between users.

c. Interaction Layer

  • User-User Interaction Modeling: Combine the user embeddings and graph embeddings to predict the probability that two users will connect. Interaction features, such as mutual friends, shared groups, and message exchanges, are incorporated here.

d. Output Layer

  • Ranking Output: The final layer ranks potential friends by their predicted relevance to the user. The top-N recommendations are shown to the user.

6. Loss Function

a. Binary Cross-Entropy Loss

If the task is framed as a classification problem (predict whether two users will connect or not), binary cross-entropy is an appropriate loss function: [ L_{binary} = -\left[ y \cdot \log(p) + (1 - y) \cdot \log(1 - p) \right] ] Where ( y ) is the actual label (whether the users connected), and ( p ) is the predicted probability of forming a connection.

b. Pairwise Ranking Loss

For ranking potential connections, we can use pairwise ranking loss. The goal is to rank relevant users (likely to connect) higher than less relevant users: [ L_{ranking} = \max(0, 1 - (s_{i} - s_{j})) ] Where ( s_{i} ) and ( s_{j} ) are the scores for two users, and the objective is to rank the higher-relevant user above the lower-relevant user.

7. Handling Cold Starts

a. New User Cold Start

  • Profile-Based Recommendations: For new users, leverage content-based filtering using profile attributes (e.g., job, education, location). Recommend users with similar profiles or in the same industry.
  • Popular Users or Influencers: Recommend connections with highly connected users (e.g., influencers or people with many followers), as they are more likely to accept connection requests from new users.
  • Mutual Connections: If a new user has imported their contacts or is connected to even one user, recommend mutual friends.

b. New User Cold Start in GNN

  • Feature Propagation: Even if the user has no connections, the GNN can propagate features from their immediate neighborhood (e.g., location, job role) and infer likely connections based on users in the same subgraph.

8. Optimization Algorithm

  • Adam Optimizer: Standard optimizer for neural networks that handles sparse gradients and large datasets well.
  • SGD (Stochastic Gradient Descent): Could be used for simpler models but may need momentum for faster convergence.

9. Evaluation Metrics

a. Offline Metrics

  • Precision@K and Recall@K: Measure how many of the top-K recommended connections are relevant (i.e., users actually send or accept connection requests).
  • ROC-AUC: Measure how well the model distinguishes between relevant and non-relevant connections.
  • NDCG (Normalized Discounted Cumulative Gain): Evaluate the ranking of potential connections.

b. Online Metrics

  • Connection Acceptance Rate: Percentage of recommended users who form connections.
  • Profile Views: Number of times users view the profiles of their recommended connections.
  • Engagement Metrics: Dwell time and actions taken on the recommended users (e.g., follow, message, comment).

10. Serving and Real-Time Deployment

a. Real-Time Recommendation Engine

  • Graph Querying Service: Efficiently query the social graph to retrieve mutual connections and compute interaction scores.
  • Prediction Pipeline: For each user, the model fetches features (e.g., user profile, connection strength), applies the trained model, and outputs ranked recommendations.

b. Re-Ranking with Business Logic

  • Boost Certain Recommendations: For example, prioritize high-profile users or connections from the same company for professional networking.

c. Continuous Learning

  • Online Learning: As users accept or reject connection recommendations, update the model in near real-time to refine future predictions.
  • A/B Testing: Experiment with different model architectures or ranking criteria to optimize the recommendation engine.

Conclusion

The friend recommendation algorithm leverages a combination of graph-based learning, collaborative filtering, and content-based matching to recommend potential connections. By focusing on both the social structure of the network and user behavior, the system can deliver highly relevant and timely connection recommendations, improving the user experience and engagement on LinkedIn or other social networks.

Job Recommendations Based on Personal Profile and Job Description

Designing a job recommendation system for LinkedIn based on personal profiles and job descriptions can follow several stages similar to social network recommendation systems like “People You May Know” or news feeds from the documents provided【8†source】【9†source】. Here’s a comprehensive plan:

1. System Overview

The system will recommend jobs to users based on their personal profile, skills, job experience, and interests while matching them with job descriptions posted by companies. The goal is to increase engagement with the platform and improve job matching accuracy.

2. Input and Output of the Model

  • Input:
    • User Profile: Attributes such as education, work experience, skills, certifications, location preferences, current job role, and previous interactions with job posts (e.g., clicks, saved jobs).
    • Job Description: Information extracted from job postings, such as required skills, role description, location, company profile, and job title.
    • User-Job Interactions: Historical data showing user interactions with job postings (e.g., views, applications, saves).
  • Output:
    • A ranked list of job postings for each user, tailored based on their personal profile and past engagement.

3. Data and Features

User Data:

  • Demographic Features: Age, location, current job, industry, education.
  • Behavioral Data: Clicks on job posts, applications, job saves, profile views.
  • Skillset Data: Extracted from profile descriptions and user-uploaded resumes.

Job Description Data:

  • Textual Data: Job title, description, and requirements, extracted using NLP techniques.
  • Company Data: Industry, size, and location.
  • Required Skills: Compared against the user’s skills, work experience, and interests.

User-Job Interaction Data:

  • Previous Interactions: How users have engaged with specific types of jobs (e.g., clicks, saves, and applications).
  • Engagement Signals: How frequently users interact with job descriptions from specific industries or companies.

4. Model Selection

a. Collaborative Filtering (CF):

  • Pros: Works well when there is a lot of user-job interaction data.
  • Cons: Cold start problem with new users or jobs.

b. Content-Based Filtering (CBF):

  • Pros: Leverages job descriptions and user profile information, suitable for cold starts.
  • Cons: Limited by the information in user profiles, may not explore outside the user’s historical preferences.

c. Hybrid Models:

  • Combine collaborative and content-based filtering, allowing the system to overcome the cold-start problem while providing relevant recommendations based on both user preferences and job descriptions.

d. Deep Learning Models (Neural Networks):

  • Multi-task DNN (used for personalized news feeds【8†source】): Predict multiple job-interaction behaviors, such as clicks, applications, or saves, all in a single model.
  • Pros: Effective with unstructured data like job descriptions or resumes.
  • Cons: Requires significant computational resources and large amounts of data.

e. Graph Neural Networks (GNN):

  • Suitable for handling user-job interaction data as a graph, where nodes are users and jobs, and edges represent user interactions.
  • Pros: Can model complex relationships, like mutual connections (e.g., social connections in LinkedIn) between users and jobs.
  • Cons: Computationally intensive and requires careful graph construction【9†source】.

5. Loss Function

For training the recommendation model:

  • Binary Cross-Entropy: If we are predicting binary outcomes such as whether a user applies to or saves a job.
  • Ranking Loss (Pairwise Ranking): Optimizes the ranking of relevant jobs over non-relevant ones.
  • Mean Squared Error (MSE): For predicting continuous values like click-through rate (CTR) or dwell time on job posts.

6. Optimization Algorithm

  • Adam Optimizer: Common in deep learning for efficient gradient-based optimization.
  • SGD (Stochastic Gradient Descent): Could also be used for simpler models like collaborative filtering but may require fine-tuning for convergence.

7. Evaluation Metrics

Offline Metrics:

  • Precision@K and Recall@K: Measure how many of the top-K recommended jobs are relevant to the user.
  • NDCG (Normalized Discounted Cumulative Gain): Measures the ranking quality of the recommendations.
  • AUC-ROC: Useful for evaluating the binary classification model if predicting actions like “apply” or “save.”

Online Metrics:

  • Click-Through Rate (CTR): Measures the effectiveness of job recommendations based on the number of clicks on suggested jobs.
  • Application Rate: Number of applications made to recommended jobs.
  • Time Spent: How much time users spend interacting with recommended job posts, a proxy for engagement.

8. Serving/Deployment Flow

  • Data Preparation Pipeline:
    • Clean, preprocess, and extract features from both job descriptions and user profiles.
    • Convert text-based information into embeddings (e.g., using BERT or TF-IDF for job descriptions).
  • Prediction Pipeline:
    • Retrieval Service: Retrieve unseen job postings relevant to the user’s profile.
    • Ranking Service: Rank job posts using the engagement score predicted by the model.
    • Re-Ranking Service: Apply business logic, such as promoting premium job postings or factoring in sponsored jobs【8†source】【9†source】.
  • Online Inference:
    • Deploy models using cloud services like AWS, GCP, or Azure.
    • Use A/B testing for online evaluation to compare the recommendation system with existing systems.

Conclusion

This system combines personal profile data and job descriptions to recommend the most relevant jobs using hybrid ML models, leveraging collaborative filtering, content-based filtering, and deep learning approaches. It also ensures a real-time user experience with job recommendations tailored to individual user preferences and past behaviors.

Digging Deeper Into the Model

Let’s dive deeper into the key steps involved in model design, selection, architecture, training, and deployment, with a focus on advanced aspects like model architecture, loss function, optimization techniques, and addressing challenges such as cold starts, scalability, and real-time inference.

1. Model Design and Architecture

The core model will combine multiple methods to balance user-job relevance, past behavior, job content, and interaction patterns. We’ll use a hybrid approach, incorporating content-based features, collaborative filtering, and deep neural networks (DNNs) for ranking.

a. Embedding Layers

The system will transform both user profile and job description into dense vectors (embeddings) that represent the key features.

  • User Embedding: Capture user features such as education, experience, skills, and interaction history. This embedding can be learned using a multi-dimensional embedding layer.
  • Job Embedding: Transform job descriptions, company profiles, and required skills into an embedding. Pre-trained models like BERT or GloVe can represent the job description text in vector form.
  • Interaction Embedding: Capture historical user-job interactions (e.g., clicks, applications) through a collaborative filtering mechanism or matrix factorization.

b. Multi-Task Learning

The model must handle different objectives, such as predicting user engagement (click, save, apply). A multi-task learning (MTL) approach allows the model to predict multiple outcomes simultaneously. For instance:

  • Click Prediction
  • Job Save Prediction
  • Job Application Prediction

c. Neural Network Layers

After embedding user profiles and job descriptions, the model can pass these embeddings through several fully connected layers (DNNs). The network will:

  • Combine user embeddings and job embeddings using interaction layers (e.g., dot product or concatenation).
  • Add interaction features between users and jobs (previous engagement or dwell time).

d. Ranking Layer

The model must rank the jobs for each user. A Pointwise Ranking approach can predict the engagement score for a user-job pair, or a Pairwise Ranking approach can rank two jobs based on relevance. The output is a ranking score, representing the relevance of each job to the user.

2. Cold Start Problem

a. User Cold Start

For users without prior engagement data, content-based filtering and the user profile embedding can recommend jobs based on job descriptions.

  • Solution: Use latent factor models or deep content-based models to compare the embeddings of the user profile with job embeddings (skills and descriptions).

b. Job Cold Start

For new jobs without interaction data, content-based features (job descriptions and required skills) will play a primary role.

  • Solution: Use BERT-like models to process and embed job descriptions, matching them with users based on similar skills and past behavior.

3. Loss Function

To train the model effectively, we need to select appropriate loss functions for both classification and ranking.

a. Binary Cross-Entropy Loss

For each prediction task (click, save, apply), the binary cross-entropy loss can be used.

b. Pairwise Ranking Loss

For ranking tasks, pairwise ranking loss (e.g., Hinge Loss) ensures relevant jobs are ranked higher than less relevant ones.

c. Multi-Task Loss

For multiple tasks (clicks, saves, applies), a weighted sum of individual task losses can be used to balance the importance of each task.

4.

Optimization Algorithm Given the deep nature of the model, standard optimization algorithms such as Adam Optimizer or RMSProp are effective for large datasets with non-stationary objectives.

5. Evaluation

a. Offline Evaluation

  • Precision@K / Recall@K: Measure the precision and recall of the top-K job recommendations.
  • NDCG (Normalized Discounted Cumulative Gain): A ranking quality measure.
  • AUC-ROC: Evaluate the binary classification tasks (click/save/apply) using the area under the curve metric.

b. Online Evaluation

  • Click-through Rate (CTR): Percentage of recommended jobs clicked by the user.
  • Conversion Rate: Percentage of recommended jobs applied for by the user.
  • User Engagement Metrics: Time spent interacting with recommended jobs and return engagement.

6. Serving and Real-Time Deployment

a. Serving Architecture

The deployment pipeline will serve recommendations in real-time, including:

  • Data Pipeline: Periodically update user features, job descriptions, and interaction data.
  • Inference Engine: Compute the job recommendation list in real-time when the user visits the platform.

b. Ranking and Re-ranking

After initial ranking, re-ranking can apply business rules (e.g., boosting premium job postings or jobs from certain geographies).

c. A/B Testing and Continuous Learning

  • A/B Testing: Experiment with new models and algorithms by testing on different user segments.
  • Online Learning: Use feedback loops to fine-tune the model in near real-time.

7. Scalability and Distributed Computing

The system must scale efficiently:

  • Distributed Training: Use frameworks like TensorFlow or PyTorch to parallelize training across a cluster.
  • Serving at Scale: Implement model parallelism and distributed serving architectures (e.g., Kubernetes) for real-time recommendations to millions of users.

Conclusion

By incorporating advanced techniques like multi-task learning, content-based filtering, and ranking models, while addressing challenges like cold starts and scalability, the job recommendation system will deliver highly personalized job recommendations. This will drive user engagement and improve the job-seeking experience on LinkedIn.

Designing a system to recommend users for a newly created page or company on LinkedIn is a more nuanced problem that requires considering various factors like user interests, professional background, and company attributes. The goal is to maximize engagement by connecting the right users to the new page or company in a meaningful way. Here is a detailed breakdown of how you can design such a system:

System Overview

The system’s objective is to recommend a newly created company or page to relevant users who are likely to follow, engage, or be interested in the company based on their profiles, activities, and interactions. The recommendation should enhance both user engagement and visibility for the new company page.

1. Input and Output of the Model

  • Input:
    • Company/Page Data: Information about the newly created page, such as industry, location, description, services, and job roles.
    • User Profile Data: User attributes such as job title, industry, education, skills, location, and current/past companies.
    • User-Company Interaction Data: Historical data showing user interactions with companies (e.g., follows, likes, job applications).
    • User Behavioral Data: Data on how users engage with other companies’ content (views, likes, follows, comments, or shared posts).
    • Connection Data: Information on the user’s professional network (e.g., colleagues or peers who follow similar companies).
  • Output:
    • A ranked list of users who are most likely to follow or engage with the new company or page.

2. Data and Features

a. Company/Page Data

  • Industry: The sector in which the company operates (e.g., IT, finance, healthcare).
  • Location: Company headquarters or operational locations, which are important for regionally focused recommendations.
  • Keywords/Services: Extracted using NLP from the company’s description, capturing its domain, services, or specialties.
  • Size of Company: A large, well-known company may appeal to more users than a small startup.
  • Similar Companies: The system should understand which other companies are similar to the new one in terms of size, industry, or job roles.

b. User Data

  • Professional Profile: Job title, skills, industry, education, and work experience.
  • Past Company Interactions: Companies the user has previously followed, interacted with, or applied to.
  • Network Information: Connections the user has within the same industry or company.
  • Skills and Interests: Skills listed in the user’s profile that match the company’s services or offerings.

c. Interaction Data

  • Behavioral Data: Historical data showing how users engage with similar companies or pages (e.g., likes, follows, comments, posts).
  • Engagement with Industry-Specific Content: Users who frequently engage with content in the company’s domain are more likely to be interested.

3. Model Selection

a. Collaborative Filtering

  • User-Company Collaborative Filtering: Based on the past behavior of users, recommend the new company to users who have followed or engaged with similar companies or industries.
    • Pros: Effective when there is sufficient historical user-company interaction data.
    • Cons: Cold start problem when users or companies are new, with little interaction data.

b. Content-Based Filtering

  • User-Profile to Company Matching: Use the user’s profile data (job title, skills, location, and industry) and match it with the company’s metadata (e.g., industry, services, location).
    • Pros: Works well for cold-start companies with no interaction data.
    • Cons: Limited by the quality and completeness of user and company profiles.

c. Graph-Based Approaches (GNNs)

  • Graph Neural Networks (GNNs): Build a social graph where nodes represent users and companies, and edges represent interactions such as follows, views, or likes. For a new company, find users that are indirectly connected through mutual connections, interests, or behaviors.
    • Pros: Can capture complex relationships between users and companies by considering mutual connections and interests.
    • Cons: Computationally intensive and requires careful graph construction.

d. Hybrid Model

  • Combining Collaborative Filtering, Content-Based Filtering, and Graph Networks: Use a hybrid approach that leverages the strengths of both collaborative filtering and content-based approaches, while also considering social connections through a graph-based system.
    • Pros: Balances cold-start issues and provides better user-to-company matching by utilizing multiple data sources.
    • Cons: Complex to implement and requires tuning across multiple systems.

4. Model Architecture

a. Embedding Layers

  • User Embedding: Transform user profiles, behavior, and interaction data into dense vectors using an embedding layer. Capture important features like job role, industry, and skills.
  • Company Embedding: Similarly, represent the new company/page using an embedding layer that captures its industry, services, and keywords.
  • Interaction Embedding: For collaborative filtering, represent user-company interactions as dense vectors to learn relationships between users and companies they are likely to engage with.

b. Graph-Based Layer (if using GNNs)

  • Node Embeddings: Represent users and companies as nodes, where features are propagated between neighbors (mutual connections, similar users, etc.).
  • Multi-Hop Propagation: Utilize one-hop and two-hop neighbors to propagate information, allowing the model to predict connections based on indirect relationships.

c. Fully Connected Layers

After embeddings, use fully connected layers to combine user and company representations, refining the prediction of whether the user will engage with the new company.

d. Output Layer

The output layer will generate a ranked list of users with probabilities indicating their likelihood of following or engaging with the new company page.

5. Handling Cold Starts

a. Cold Start for New Companies

  • Content-Based Recommendations: When a new company is created with no interactions, recommend it to users based on similarities in company metadata (industry, location) and user profiles (job title, skills, interests).
  • Popular Users or Influencers: Recommend the new company to users who are highly active or influential in the industry to quickly gain traction.
  • Seed Recommendations: Show the new company to a small sample of relevant users (based on profile matching) to collect early interaction data and refine future recommendations.

b. Cold Start for New Users

  • Profile-Based Recommendations: For new users, leverage their profile (job title, location, education) to recommend companies from similar industries.
  • Collaborative Recommendations: Suggest companies based on what users with similar profiles or behaviors follow or engage with.

6. Loss Function

a. Binary Cross-Entropy Loss

Use binary cross-entropy loss for predicting whether a user will engage with a company (e.g., follow, like): [ L_{binary} = -\left[ y \cdot \log(p) + (1 - y) \cdot \log(1 - p) \right] ] Where ( y ) is the actual label (followed or not), and ( p ) is the predicted probability.

b. Pairwise Ranking Loss

Use a pairwise ranking loss for ranking users based on their likelihood of engaging with the new company. This ensures that more relevant users are ranked higher.

7. Optimization Algorithm

  • Adam Optimizer: Effective for deep learning models with embeddings, especially for handling large datasets.
  • SGD with Momentum: Could be useful for simpler models or for tuning collaborative filtering algorithms.

8. Evaluation Metrics

a. Offline Metrics

  • Precision@K and Recall@K: Measure the proportion of top-K recommended users that actually followed or engaged with the new company.
  • AUC-ROC: Evaluate the classification performance of the system in predicting whether users will engage with the company.
  • NDCG (Normalized Discounted Cumulative Gain): Measures how well the ranking of users aligns with the probability of engaging with the company.

b. Online Metrics

  • Follow Rate: Measure the percentage of users who follow the new company after being recommended.
  • Engagement Rate: Measure how often recommended users engage with the company’s posts (e.g., likes, comments, shares).
  • Click-Through Rate (CTR): Track how often users click on the company’s page after seeing it in their recommendations.

9. Serving and Real-Time Deployment

a. Real-Time Recommendation Engine

  • Data Pipeline: Continuously update user profiles and company data as new interactions are recorded.
  • Prediction Pipeline: Fetch relevant users in real-time and generate a ranked list of recommendations for the new company.
  • Re-Ranking: Apply business rules, such as boosting sponsored companies or companies with premium features.

b. A/B Testing

  • Experiment with Recommendation Algorithms: Run A/B tests to determine which recommendation approach (content-based, collaborative filtering, or hybrid) performs best for new companies.

c. Continuous Learning

  • Feedback Loop: Use user interactions (follows, clicks, engagement) to fine-tune the recommendation model, ensuring that it continuously improves over time.

Conclusion

Designing a system to recommend users for a newly created page or company on LinkedIn requires a hybrid approach that combines content-based filtering, collaborative filtering, and graph-based techniques. Handling cold starts for new companies and users is key to delivering timely and relevant recommendations. By leveraging user data, behavioral patterns, and social connections, the system can effectively recommend relevant users to a new company page, maximizing engagement and driving growth for both users and the company.

Data Mining

This round has 2 parts: the first part is about your and your past project. You will want to demonstrate the impact of your project, how you come up with your solution, data, features and modeling technique. The second part will be a discussion about how you can use ML to implement some LinkedIn features. For example, you might be asked to implement job recommendations, People you may know or feed ranking.

What is the Bias-Variance Tradeoff?

The bias-variance tradeoff is a fundamental concept in machine learning that describes the balance between two types of errors when building models:

  • Bias refers to the error introduced by approximating a real-world problem, which may be complex, by a much simpler model. High bias can cause an algorithm to miss relevant relations between features and target outputs (underfitting).

  • Variance refers to the error introduced by sensitivity to small fluctuations in the training set. High variance can cause overfitting, where the model learns noise in the training data as if it were true signal.

The tradeoff involves finding the right balance between bias and variance to minimize the total error. As you make your model more complex to reduce bias, variance tends to increase, and vice versa.

Why Do You Need to Create a Validation Set?

A validation set is a subset of data not used during training but utilized to evaluate the model’s performance while tuning hyperparameters. The reasons for creating a validation set include:

  • Hyperparameter Tuning: To adjust model parameters (e.g., learning rate, regularization strength) in order to improve performance without overfitting to the training data.

  • Model Selection: To compare different models or architectures and select the one that performs best on unseen data.

  • Prevent Overfitting: To monitor the model’s ability to generalize to new data and avoid overfitting to the training set.

What Are Common Methods to Generate a Validation Set?

  • Hold-Out Method: Randomly split the dataset into training, validation, and test sets (e.g., 70% training, 15% validation, 15% testing).

  • K-Fold Cross-Validation: Divide the dataset into k equal parts, train the model k times each time using a different fold as the validation set and the remaining folds as the training set.

  • Stratified Sampling: Ensure that each set has the same class distribution, which is especially important in imbalanced datasets.

  • Leave-One-Out Cross-Validation: A special case of k-fold where k equals the number of samples in the dataset.

What Are Some Methods to Control Overfitting in Neural Networks?

  • Regularization Techniques: Such as L1 and L2 regularization to penalize large weights.

  • Early Stopping: Stop training when performance on a validation set starts to degrade.

  • Dropout: Randomly deactivate a subset of neurons during training to prevent co-adaptation.

  • Data Augmentation: Increase the size and diversity of the training dataset through transformations.

  • Batch Normalization: Normalize the inputs of each layer to stabilize learning.

  • Model Simplification: Reduce the complexity of the network by decreasing the number of layers or neurons.

How Does L2 Regularization Help in Controlling Overfitting?

L2 regularization adds a penalty term to the loss function proportional to the square of the magnitude of the weights:

  • Penalty on Large Weights: By discouraging large weights, the model becomes simpler and less likely to overfit.

  • Smoothes the Model: Encourages the distribution of weights to be more uniform, leading to smoother predictions.

  • Mathematical Formulation: [ L_{\text{total}} = L_{\text{original}} + \lambda \sum_{i} w_{i}^{2} ] where ( \lambda ) is the regularization strength and ( w_{i} ) are the weights.

What Is Early Stopping?

Early stopping is a regularization technique where training is halted when the model’s performance on a validation set begins to degrade. Key aspects include:

  • Prevents Overfitting: Stops the training process before the model starts to learn noise.

  • Monitors Generalization Error: Uses validation loss to gauge when to stop training.

  • Implementation: Set a patience parameter that specifies how many epochs to wait after the last improvement before stopping.

What Is Weight Clipping and Gradient Clipping?

  • Weight Clipping:
    • Definition: Restricts the weights to a specified range by clipping them during training.
    • Purpose: Prevents weights from growing too large, which can lead to overfitting or numerical instability.
  • Gradient Clipping:
    • Definition: Limits the magnitude of gradients during backpropagation.
    • Purpose: Addresses the problem of exploding gradients, especially in recurrent neural networks.

What Is Dropout?

Dropout is a regularization technique where, during each training iteration, a subset of neurons is randomly “dropped out” or ignored. Details include:

  • Random Deactivation: Neurons are randomly deactivated with a certain probability (dropout rate).

  • Prevents Co-Adaptation: Forces the network to learn redundant representations, enhancing robustness.

  • During Inference: All neurons are active, but their outputs are scaled by the dropout rate to account for the reduced capacity during training.

How Do These Methods Help to Control Overfitting?

  • Regularization (L1, L2): Penalizes large weights to simplify the model.

  • Early Stopping: Stops training before the model overfits the training data.

  • Dropout: Reduces complex co-adaptations of neurons, promoting independence.

  • Weight and Gradient Clipping: Maintains numerical stability and prevents extreme weight values.

  • Data Augmentation: Provides more diverse training examples, helping the model generalize better.

  • Model Simplification: Reduces the capacity of the network, making it less likely to overfit.

How Is Dropout Implemented?

  • During Training:
    • Apply a Mask: For each mini-batch, create a binary mask where each neuron is kept with probability ( p ) and dropped with probability ( 1 - p ).
    • Modify Outputs: Multiply the outputs of the neurons by the mask to deactivate certain neurons.
    • Scaling (Inverted Dropout): Some implementations scale the activations by ( 1/p ) during training so that no scaling is needed during inference.
  • During Inference:
    • Use Entire Network: All neurons are active; the learned weights are utilized without dropout.
    • Scaling Outputs: If activations were not scaled during training, scale them now to account for dropout.
  • Framework Implementation:
    • Libraries: Most deep learning libraries like TensorFlow and PyTorch have built-in dropout layers.
    • Configuration: Specify the dropout rate (e.g., Dropout(p=0.5)), and the framework handles the rest.

Reservoir Sampling and Its Variants

Reservoir Sampling:

Reservoir sampling is an efficient algorithm for randomly selecting a sample of k items from a large or unknown-size data stream, ensuring each item has an equal probability of being chosen. It’s especially useful when the data stream is too large to store in memory.

Algorithm for Sampling One Item (k=1):

  1. Initialize:
    • Create an empty reservoir.
  2. Process the Data Stream:
    • For the first item, add it to the reservoir.
    • For each subsequent item at position i (starting from i = 2):
      • Generate a random number j between 1 and i.
      • If j equals 1, replace the item in the reservoir with the current item.
  3. Result:
    • After processing all items, the reservoir contains one item randomly selected from the stream.

Algorithm for Sampling k Items:

  1. Initialize:
    • Fill the reservoir array with the first k items from the stream.
  2. Process the Data Stream:
    • For each item at position i (starting from i = k + 1):
      • Generate a random number j between 1 and i.
      • If j is less than or equal to k, replace the j-th item in the reservoir with the current item.
  3. Result:
    • The reservoir now contains k items, each selected with equal probability from the stream.

Variants of Reservoir Sampling:

  • Weighted Reservoir Sampling:
    • Purpose: Samples items when each has an associated weight, giving higher-weighted items a higher chance of selection.
    • Algorithm: Modifies the selection probability based on item weights, often using a priority queue or adjusted probabilities.
  • Distributed Reservoir Sampling:
    • Purpose: Applies reservoir sampling across multiple data streams or distributed systems.
    • Algorithm: Merges samples from different nodes or partitions using a coordinated approach to maintain overall randomness.
  • Time-Biased Reservoir Sampling:
    • Purpose: Gives preference to more recent items in the data stream.
    • Algorithm: Adjusts selection probabilities to favor newer items, useful in applications where recent data is more relevant.
  • Priority Sampling:
    • Purpose: Ensures that items with higher priority (not necessarily weight) have a higher chance of being included.
    • Algorithm: Assigns a random priority score to each item and selects items based on these scores.

Importance of Probability and Statistics:

Beyond coding proficiency, a solid understanding of probability and statistics is crucial in various aspects of computer science and software development:

  • Algorithm Design and Analysis:
    • Helps in understanding the behavior and efficiency of algorithms like reservoir sampling.
    • Essential for randomized algorithms and probabilistic data structures.
  • Machine Learning and Data Science:
    • Fundamental for building models, interpreting data, and making predictions.
    • Key to understanding concepts like distributions, hypothesis testing, and statistical significance.
  • System Performance and Reliability:
    • Aids in modeling system performance, conducting capacity planning, and analyzing failure rates.
    • Important for optimization and ensuring system robustness.
  • Decision Making:
    • Enables informed decisions based on data analysis and statistical evidence.
    • Useful in A/B testing, user behavior analysis, and product feature evaluation.

Conclusion:

Refreshing knowledge on reservoir sampling and its variants equips you with efficient techniques for handling large-scale data and real-time processing tasks. Emphasizing probability and statistics enhances your problem-solving toolkit, enabling you to tackle a broader range of challenges beyond standard coding questions. This combined expertise is highly valuable in technical interviews and real-world applications where data-driven decision-making is paramount.