problemset/

Problem Set

349 hands-on problems across 5 study modules.

Mathematics & Statistics Linear algebra, calculus, probability, and statistical foundations Data Science Data processing, analysis, and experiments Classical ML Supervised and unsupervised models, trees, ensembles, and evaluation Deep Learning Neural networks, layers, activations, losses, and optimization Transformers & LLMs Attention, transformer blocks, language modeling, and NLP

Compute a Stable L2 Norm Linear algebra Beginner

Normalize a Vector Linear algebra Beginner

Cosine Similarity Linear algebra Beginner

Matrix-Vector Product Linear algebra Beginner

Matrix Transpose Linear algebra Intermediate

Frobenius Norm Linear algebra Intermediate

Gram Matrix Linear algebra Intermediate

Solve a 2×2 Linear System Linear algebra Intermediate

Power Iteration Eigenvalues Advanced

Low-Rank Reconstruction SVD Advanced

Finite Difference Derivative Calculus Advanced

Gradient of a Quadratic Calculus Advanced

Jacobian by Finite Differences Calculus Beginner

Hessian Diagonal Calculus Beginner

Directional Derivative Calculus Beginner

Monte Carlo Expectation Probability Beginner

Bernoulli Mean and Variance Probability Intermediate

Conditional Probability Table Probability Intermediate

Bayes Posterior Bayesian inference Intermediate

MLE of Gaussian Mean Estimation Intermediate

MAP Bernoulli Estimate Bayesian inference Advanced

Entropy of a Distribution Information theory Advanced

Mean Imputation Data cleaning Advanced

Median Imputation Data cleaning Advanced

One-Hot Encode Categories Data cleaning Beginner

Min-Max Scaling Data cleaning Beginner

Z-Score Scaling Data cleaning Beginner

Robust Scaling Data cleaning Beginner

IQR Outlier Flagging EDA Intermediate

Correlation Matrix EDA Intermediate

Stratified Split Sampling Intermediate

Bootstrap Mean Sampling Intermediate

Two-Sample Difference in Means Hypothesis testing Advanced

Welch t Statistic Hypothesis testing Advanced

Confidence Interval for Mean Confidence intervals Advanced

A/B Conversion Rate A/B Testing Advanced

Pooled Proportion Test Statistic A/B Testing Beginner

Sample Size for Proportion Experiment design Beginner

Leakage Detector Data leakage Beginner

Group Aggregation Data wrangling Beginner

Winsorize Values EDA Intermediate

Time-Series Lag Feature Time series Intermediate

Rolling Mean Time series Intermediate

Inferential Regression Slope Regression for inference Intermediate

Linear Regression Prediction Linear regression Advanced

Linear Regression Normal Equation Linear regression Advanced

Mean Squared Error Metrics Advanced

Mean Absolute Error Metrics Advanced

Logistic Sigmoid Logistic regression Beginner

Binary Cross-Entropy Logistic regression Beginner

Logistic Gradient Logistic regression Beginner

Ridge Objective Regularization Beginner

Lasso Soft Threshold Regularization Intermediate

Elastic-Net Penalty Regularization Intermediate

Linear SVM Hinge Loss SVM Intermediate

SVM Subgradient Step SVM Intermediate

KNN Classification Knn Advanced

KNN Regression Knn Advanced

Precision Recall Metrics Advanced

F1 Score Metrics Advanced

Confusion Matrix Metrics Beginner

ROC Curve Points Metrics Beginner

K-Fold Indices Cross validation Beginner

K-Fold Splits (Index-Based) Cross validation Beginner

Bias-Variance Decomposition Bias variance Intermediate

Polynomial Features Feature engineering Intermediate

Standardize Then Train Feature engineering Intermediate

Calibration Bins Model evaluation Intermediate

Gini Impurity Decision trees Advanced

Entropy Impurity Decision trees Advanced

Best Binary Split Decision trees Advanced

Decision Stump Decision trees Advanced

Tree Leaf Majority Decision trees Beginner

Bootstrap Sample Bagging Beginner

Random Feature Subset Random forest Beginner

Random Forest Vote Random forest Beginner

Bagging Regression Mean Bagging Intermediate

AdaBoost Weight Update Boosting Intermediate

AdaBoost Alpha Boosting Intermediate

Gradient Boosting Residual Gradient boosting Intermediate

Gradient Boosting Update Gradient boosting Advanced

XGBoost-Style Leaf Weight Regularized boosting Advanced

XGBoost Split Gain Regularized boosting Advanced

Feature Importance from Splits Feature importance Advanced

Out-of-Bag Mask Out of bag Beginner

OOB Accuracy Out of bag Beginner

Stacked Predictions Stacking Beginner

Blended Prediction Blending Beginner

K-Means Assignment K Means clustering Intermediate

K-Means Centroid Update K Means clustering Intermediate

K-Means One Iteration K Means clustering Intermediate

K-Means Inertia Clustering evaluation Intermediate

Hierarchical Single-Link Distance Hierarchical clustering Advanced

Complete-Link Distance Hierarchical clustering Advanced

DBSCAN Core Point Dbscan Advanced

DBSCAN Region Query Dbscan Advanced

Gaussian Log Likelihood Gaussian mixture Beginner

GMM Responsibility Gaussian mixture Beginner

PCA Centering PCA Beginner

PCA Covariance PCA Beginner