Why resampling distorts probabilities
By Bayes' rule the model's odds are prior odds x likelihood ratio. Training at positive rate r instead of the
real rate π multiplies the prior odds by (r / (1 − r)) / (π / (1 − π)). Undo it:
odds_true = odds_model x (π / (1 − π)) / (r / (1 − r))
p_true = p·a / (p·a + (1 − p)·b), a = π / r, b = (1 − π) / (1 − r)Exact for pure prior shift (the features' class-conditional distributions are unchanged, which holds for random under/oversampling). For SMOTE (synthetic points) and class weights it is a good first-order correction; check with a calibration curve.
import numpy as np
def prior_correct(p, train_rate, true_rate):
a, b = true_rate / train_rate, (1 - true_rate) / (1 - train_rate)
return p * a / (p * a + (1 - p) * b)For class weights w1 (positives) and w0 (negatives) the effective training rate is
r = w1·π / (w1·π + w0·(1 − π)).
Calibration methods
from sklearn.calibration import CalibratedClassifierCV, calibration_curve
cal = CalibratedClassifierCV(estimator=model, method="isotonic", cv=5) # or method="sigmoid" for small data
cal.fit(X_train, y_train)
frac_pos, mean_pred = calibration_curve(y_test, cal.predict_proba(X_test)[:, 1], n_bins=10, strategy="quantile")sigmoid(Platt) for few positives;isotonicwith plenty of data.- Calibrate on data at the natural prevalence.
FrozenEstimator(scikit-learn >= 1.6) wraps an already-fitted model to calibrate on a holdout (CalibratedClassifierCV(FrozenEstimator(model))); the oldercv="prefit"option was deprecated.
Checking calibration
| Check | Tool |
|---|---|
| Reliability curve | calibration_curve with quantile bins (equal counts) |
| ECE | weighted mean |
| Brier score | proper scoring rule; decreases with better calibration and discrimination |
| Mean prediction vs prevalence | quick sanity check |
Prevalence drift in production
If the real positive rate changes (fraud spike, seasonal churn), calibrated probabilities drift even when ranking is stable. Monitor mean predicted probability vs observed rate (with label delay); apply the same prior-shift formula with the new π, or recalibrate on recent labelled data. Capacity-based thresholds (top K) are robust to prevalence changes; fixed probability thresholds are not.
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.