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: