ML Math and Statistics Refresher

Compute expectations, variances, and covariances from a specified probability model.

Apply conditional probability and Bayes’ theorem to update beliefs from observed evidence.

Construct a likelihood and derive a maximum-likelihood estimate for a simple probabilistic model.

Interpret a confidence interval in terms of repeated sampling without treating it as a posterior probability.

Design train, validation, and test partitions appropriate to independent, grouped, or time-ordered observations.

Implement a preprocessing-and-model pipeline for cross-validated hyperparameter selection, fitting imputation, encoding, and scaling only within each training fold and reserving the test set for final evaluation.

Derive the ordinary least-squares estimator from the mean-squared-error objective.

Fit a linear regression model and use residual diagnostics to assess its main assumptions.

Fit and compare ridge and lasso models, explaining how feature scaling and penalty strength affect coefficients and model complexity.

Derive logistic-regression log loss from a Bernoulli likelihood and interpret fitted logits, odds, and class probabilities.

Calculate a candidate decision-tree split using squared-error or Gini-impurity reduction.

Control decision-tree overfitting using depth, leaf-size, and pruning constraints.

Explain how bootstrap aggregation and feature subsampling reduce variance in a random forest.

Explain gradient boosting as functional gradient descent by relating fitted base learners to negative loss gradients, or pseudo-residuals.

Choose among linear models, random forests, and gradient-boosted trees based on their inductive biases.

Diagnose underfitting and overfitting by comparing training and validation learning curves.

Select confusion-matrix and ranking metrics for class imbalance and asymmetric costs, including when precision-recall AUC is more informative than ROC-AUC.

Choose a classification threshold using the relative costs of false positives and false negatives.

Assess probabilistic calibration using reliability diagrams and the Brier score.

Use bootstrap confidence intervals to quantify uncertainty in a model-performance estimate.

Fit k-means on scaled and unscaled data and diagnose sensitivity to initialization, distance, and cluster geometry.

Apply DBSCAN and explain how its neighborhood parameters, feature scaling, and density assumptions determine clusters and noise labels.

Perform principal component analysis and choose a retained dimension using explained variance.

Evaluate a clustering using silhouette scores, stability checks, and domain usefulness.

Compute permutation feature importance and analyze its behavior when predictors are correlated.

Compute SHAP values for a small example and explain how local attributions can be summarized into global importance.

Distinguish predictive feature attributions from causal effects when interpreting model explanations.

Translate a product objective into a prediction unit, target, observation window, decision, and action.

Identify target leakage, selection bias, and proxy-label risk in a proposed ML dataset.

Define a simple baseline and quantify the incremental value required from an ML model.

Design a randomized online evaluation that connects model-quality metrics to product outcomes and operational guardrails.

Specify monitoring for input drift, prediction drift, calibration, and delayed ground-truth performance.

Critique an end-to-end conventional-ML proposal for framing, data validity, evaluation, deployment, and product value.