Data Science Foundations

Probability Fundamentals

Master conditional probability, Bayes' theorem and the base-rate fallacy, random variables, expectation and variance, the six distributions data scientists actually meet, the Law of Large Numbers and Central Limit Theorem, and the classic interview puzzles.

Descriptive Statistics & Exploratory Data Analysis

Learn to describe centre, spread and shape, choose the right plot for the question, detect outliers and missing-data mechanisms, run data quality checks that catch leakage and unit errors, avoid Simpson's paradox, and follow a repeatable EDA checklist in pandas.

SQL for Data Analysis

Master analytical PostgreSQL: query evaluation order, join fan-out traps, CTEs, window functions with frames, date bucketing, cohort retention, funnels, sessionisation, NULL pitfalls, CASE pivots, deduplication and the classic SQL interview questions.

Hypothesis Testing & Statistical Inference

Learn hypothesis testing from first principles: p-values and their misreadings, Type I/II errors and power, z, t, Welch, paired, chi-square and proportion tests, non-parametric alternatives, confidence intervals, effect sizes, multiple-comparison corrections, bootstrap and sample-size formulas.

A/B Testing & Online Experimentation

Learn to design trustworthy online experiments: pick metrics and randomisation units, size a test with power and MDE, catch SRM and peeking, cut variance with CUPED, and read lifts, segments and holdouts correctly.

Linear Regression

Learn how ordinary least squares fits a line, how to read coefficients (dummies, interactions, log transforms), the Gauss-Markov assumptions and how to diagnose violations, R-squared traps, standard errors and confidence intervals, VIF, leverage and Cook's distance.

Logistic Regression & Linear Classifiers

Master logistic regression: sigmoid and log-odds, odds-ratio interpretation with worked numbers, maximum likelihood and log-loss, linear decision boundaries, cost-aware thresholds, calibration, class imbalance handling, multiclass softmax, and how it compares to SVMs, naive Bayes and trees.

Regularization: L1, L2 and Elastic Net

Learn how Ridge (L2), Lasso (L1) and Elastic Net penalties shrink or zero out coefficients, why lasso does feature selection and ridge does not, how to pick lambda, and how the same idea shows up in logistic regression, neural nets and gradient boosting.

Bias–Variance Trade-off & Cross-Validation

Master the bias-variance decomposition, learning and validation curves, k-fold, stratified, group and time-series cross-validation, nested CV for honest tuning, and the data-leakage traps that make validation scores lie.

Model Evaluation Metrics

Master the confusion matrix and its derived metrics, ROC vs precision-recall curves, log loss, calibration and ECE, cost-based threshold selection, regression and ranking metrics like NDCG, multiclass averaging, and how to tell real metric gains from noise.

Feature Engineering

Learn the feature engineering toolkit data scientists are tested on: scaling and transforms per model family, categorical encodings including leakage-safe target encoding, missing-value strategies, cyclical time features, point-in-time aggregations, feature selection, and sklearn pipelines that prevent training/serving skew.

Decision Trees

Learn how decision trees partition feature space using impurity measures, how recursive binary splitting works, which hyperparameters control overfitting, and how feature importance is calculated — the foundation for understanding gradient boosting models like LightGBM and XGBoost.

LightGBM

Understand how LightGBM builds sequential ensembles of trees, why leaf-wise growth outperforms level-wise, what every key hyperparameter controls, why a slow learning rate with more trees generalizes better, and how to diagnose and fix overfitting through regularization.

Clustering & Dimensionality Reduction

Learn k-means, hierarchical clustering, DBSCAN and Gaussian mixtures, how to choose k and evaluate clusters without labels, and how PCA, t-SNE and UMAP compress high-dimensional data — with a worked PCA example and interview traps.

Time Series Fundamentals

Master time series forecasting: trend and seasonal decomposition, stationarity and differencing, ACF/PACF, exponential smoothing and ARIMA/SARIMA, lag-feature gradient boosting, temporal backtesting with MAE, MAPE, sMAPE and MASE, prediction intervals, and the leakage traps interviewers probe.

Causal Inference Basics

Learn potential outcomes, confounding and colliders, and the observational toolkit — regression adjustment, matching, IPW, difference-in-differences, regression discontinuity, instrumental variables and synthetic control — with worked examples and failure modes.