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.

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

Use residual diagnostics to assess the main assumptions of a linear regression model.

Compare how ridge and lasso regularization alter fitted coefficients and model complexity.

Derive logistic-regression log loss from a Bernoulli likelihood.

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

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 sequential correction of prediction errors.

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

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

Use cross-validation to estimate generalization performance and tune hyperparameters.

Detect data leakage and prevent it by fitting preprocessing steps only within training folds.

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

Select classification metrics that reflect class imbalance and asymmetric business costs.

Compare ROC-AUC and precision-recall AUC for a specified classification problem.

Assess probabilistic calibration using reliability diagrams and the Brier score.

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

Predict how feature scaling and distance choice affect distance-based unsupervised methods.

Fit k-means clustering and diagnose sensitivity to initialization and cluster geometry.

Apply DBSCAN to identify dense clusters and label low-density observations as noise.

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

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

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.

Use permutation importance and SHAP values to explain model behaviour without making causal claims.

Design an online evaluation that connects model-quality metrics to product outcomes.

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.