Notation: TP, FP, FN, TN from the confusion matrix at a threshold; P = TP + FN positives; N = FP + TN negatives.
Threshold metrics
| Metric | Formula | Use | Misleads when |
|---|---|---|---|
| Accuracy | (TP + TN) / (P + N) | balanced classes, equal costs | classes are imbalanced |
| Balanced accuracy | (TPR + TNR) / 2 | imbalanced, both classes matter | costs are very asymmetric |
| Precision (PPV) | TP / (TP + FP) | cost of acting on false alarms | few predicted positives (noisy) |
| Recall (TPR, sensitivity) | TP / P | cost of missing positives | used alone (flag everything = 1.0) |
| Specificity (TNR) | TN / N | screening negatives | - |
| FPR | FP / N | false-decline / false-alarm rate | - |
| F1 | 2PR / (P + R) | quick single number when costs unknown | costs differ; TN matter |
| F-beta | (1+β²)PR / (β²P + R) | recall β times as important as precision | β chosen arbitrarily |
| MCC | (TP·TN − FP·FN) / sqrt((TP+FP)(TP+FN)(TN+FP)(TN+FN)) | one balanced number, uses all four cells | you need an interpretable business number |
| Cohen's kappa | (p_o − p_e) / (1 − p_e) | agreement beyond chance | prevalence extreme (kappa paradox) |
Ranking metrics (threshold-free)
ROC-AUC
Probability that a random positive scores above a random negative. 0.5 = random, 1.0 = perfect. Insensitive to prevalence, which is both its strength (comparable across datasets) and its weakness (at 0.1% prevalence an AUC of 0.95 can still mean precision of 2% at useful recall).
PR-AUC / average precision
Area under precision-recall; average_precision_score computes the step-wise sum
Σ (R_k − R_{k−1}) P_k. Random = prevalence (not 0.5). Focuses on the top of the ranking, where rare-event
decisions are made. Do not use trapezoidal interpolation of the PR curve (auc(recall, precision)): it is
optimistic.
Partial AUC
ROC-AUC restricted to FPR ≤ x (roc_auc_score(..., max_fpr=0.05), McClish-standardised). Use when only a low
false-positive region is operationally relevant (fraud, screening).
Precision@K, recall@K, lift@K
Sort by score, take K. Lift = precision@K / prevalence. The right metric for capacity-bound actions.
Probability metrics
| Metric | Formula | Notes |
|---|---|---|
| Log loss | −mean(y log p + (1−y) log(1−p)) | proper scoring rule; punishes confident mistakes; baseline = entropy of the prior |
| Brier | mean((p − y)²) | proper scoring rule; bounded; decomposes into calibration + refinement |
| ECE | Σ_bins (n_b/n) · | mean p_b − frac positive_b |
A model can have excellent AUC and terrible calibration (any monotone transform keeps AUC). Calibrate with
CalibratedClassifierCV(method="isotonic" | "sigmoid") on held-out data when probabilities are consumed.
Resampling (SMOTE, undersampling) and class_weight distort probabilities; recalibrate afterwards.
Multiclass averaging
| Average | Computes | Use |
|---|---|---|
| micro | pool all TP/FP/FN over classes | equals accuracy for single-label multiclass |
| macro | unweighted mean of per-class metric | every class equally important |
| weighted | mean weighted by class support | frequency = importance |
Report the per-class table (classification_report) whenever classes differ in importance.
Multiclass ROC-AUC: roc_auc_score(y, P, multi_class="ovr", average="macro") or "ovo" (insensitive to
imbalance).
Confusion-matrix costs
predicted 0 predicted 1
actual 0 0 (TN) C_fp
actual 1 C_fn C_tp (often negative = benefit)Expected cost per row = (FP·C_fp + FN·C_fn + TP·C_tp) / n. For calibrated p, predict 1 when
p·(C_fn − C_tp) > (1−p)·C_fp, i.e. p > C_fp / (C_fp + C_fn − C_tp).
scikit-learn calls
from sklearn.metrics import (accuracy_score, average_precision_score, balanced_accuracy_score, brier_score_loss,
classification_report, confusion_matrix, f1_score, fbeta_score, log_loss,
matthews_corrcoef, precision_recall_curve, roc_auc_score, top_k_accuracy_score)
from sklearn.calibration import calibration_curve
roc_auc_score(y, p)
average_precision_score(y, p)
roc_auc_score(y, p, max_fpr=0.05)
log_loss(y, p); brier_score_loss(y, p)
frac_pos, mean_pred = calibration_curve(y, p, n_bins=10, strategy="quantile")
fbeta_score(y, p >= t, beta=2)
top_k_accuracy_score(y_multi, P, k=3)TunedThresholdClassifierCV (scikit-learn >= 1.5) selects a threshold by cross-validation for a chosen
scorer, including a custom cost scorer built with make_scorer.
Common mistakes
- Reporting accuracy or F1 at 0.5 for an imbalanced problem.
- Comparing PR-AUC across datasets with different prevalence (normalise by prevalence: lift).
- Choosing the threshold on the test set and reporting the test metric at it.
- Averaging per-fold precision when folds have very different predicted-positive counts (pool instead).
- Treating AUC differences of 0.005 as meaningful without a paired test.
anomaly-detection-model-builder
Build and evaluate anomaly detection for tabular, sensor and transaction data with few or no labels: define the anomaly type (point, contextual, collective), choose detectors (robust z-score/MAD and IQR rules, Mahalanobis with robust covariance, k-NN distance, LOF, Isolation Forest, one-class SVM, PCA reconstruction / autoencoders, forecasting residuals for time series), combine them by rank, explain each alert by its deviating features, set thresholds from an alert budget or the score distribution, and evaluate with precision@k, PR-AUC and recall on known incidents, or detector agreement when no labels exist. Includes pure-Python detectors (robust z, Mahalanobis, kNN, Isolation Forest, ensemble) and an evaluation script.
catboost-model-builder
Build CatBoost models that use its strengths correctly: raw categorical columns as cat_features (ordered target statistics, no manual encoding), text_features, Pool construction with NaN-safe categories, ordered boosting and has_time for temporal data, symmetric (oblivious) trees, overfitting detector with eval_set and use_best_model, losses for classification, regression (Quantile, Poisson, Tweedie) and ranking (YetiRank), class weights, monotone constraints, feature importance (PredictionValuesChange, LossFunctionChange) and SHAP values, GPU training and model export. Plans cat/text/numeric columns from a CSV and generates a runnable training script, and checks parameter sets for the conflicts CatBoost rejects (iterations vs n_estimators, Bayesian bootstrap with subsample, multiple class-weight options, depth > 16, use_best_model without eval_set).
categorical-encoding-selector
Choose and implement the right encoding for every categorical column given the model family and the data: one-hot (with infrequent-level grouping and handle_unknown), ordinal with an explicit order, cross-fitted target encoding (scikit-learn TargetEncoder, CatBoost ordered statistics, category_encoders inside CV), frequency/count encoding, feature hashing, native categorical support in LightGBM, HistGradientBoosting, XGBoost and CatBoost, prefix levels for codes (zip3, NAICS-2), and embeddings. Measures cardinality, rare-level share, unseen-level rate on a time-ordered holdout and target signal per column, emits the ColumnTransformer, and quantifies target-encoding leakage (in-sample vs out-of-fold vs holdout AUC).
classification-model-selector
Choose the right classification algorithm for tabular, text or mixed data and prove the choice with a fair bake-off: logistic regression (L2, L1, elastic net), linear SVM, naive Bayes, k-NN, RBF SVM, decision trees, random forest, extra trees, HistGradientBoosting, LightGBM, XGBoost, CatBoost, explainable boosting machines (EBM/GAM), points scorecards and MLPs, matched to data size, width, categorical and high-cardinality share, missingness, class imbalance, text, and constraints such as interpretability, monotonic constraints, calibrated probabilities, latency budgets and tiny deployable models. Ranks candidates with starting hyperparameters and cautions, then generates a bake-off script running every candidate on identical CV folds with per-fold metrics, fit time and prediction latency.
clustering-algorithm-selector
Choose the right clustering algorithm and check that clustering makes sense at all: cluster tendency (Hopkins statistic with a correlated-features caveat, nearest-neighbour isolation), then k-means / MiniBatchKMeans, Gaussian mixtures with BIC, agglomerative (Ward, average, complete, single) with dendrograms, DBSCAN, HDBSCAN, OPTICS, spectral clustering, BIRCH, mean shift, k-prototypes and k-modes for mixed or categorical data, and Gower distance, matched to data size, expected shapes, noise, varying density, known k, soft memberships, hierarchy and streaming. Covers preprocessing (scaling, encoding, dimensionality, distance metrics), validation (internal indices, bootstrap stability, external labels, business profiling) and assigning new points.
collaborative-filtering-implementer
Implement collaborative filtering recommenders that beat popularity: item-based kNN with cosine, Jaccard or asymmetric similarity, shrinkage, neighbourhood size, positive-only or mean-centred rating signals and 'because you liked X' explanations; implicit ALS with confidence weighting, BPR pairwise ranking and the closed-form EASE model in plain NumPy, tuned on a temporal validation split by recall@k and NDCG@k and refit on all data; plus user-kNN, explicit matrix factorisation, the implicit/LightFM libraries, hyperparameter ranges, cold-start fallbacks, scaling with sparse matrices and approximate nearest neighbours. Produces top-k lists in the format of the recommendation evaluator.