What each loss estimates
| Loss | Minimiser of E[L(y, ŷ)] | Consequence |
|---|---|---|
| Squared error | conditional mean | sensitive to outliers; right for sums/totals |
| Absolute error | conditional median | robust; biased low for skewed targets when sums matter |
| Huber (δ) | between mean and median | quadratic near 0, linear beyond δ; tune δ (~1.35 x residual SD) |
| Pinball at q | conditional q-quantile | intervals, service levels |
| Poisson deviance | mean, variance ∝ mean | counts, rates with exposure |
| Gamma deviance | mean, variance ∝ mean² | positive amounts with multiplicative noise |
| Tweedie deviance, power p | mean, variance ∝ mean^p | p in (1,2): compound Poisson-Gamma, exact zeros + positive tail |
Train with the loss whose minimiser is the quantity the business reports. If you report MAE but train with squared error on a skewed target, you optimise something else.
Log targets and retransformation bias
Fitting log1p(y) with squared error estimates E[log(1 + y) | x]. Back-transforming gives roughly the
conditional median (exactly, for log-normal errors), which is below the mean:
E[y | x] = exp(μ + σ²/2) while exp(E[log y | x]) = exp(μ)Corrections:
- Smearing (Duan 1983):
ŷ_mean = exp(prediction) * mean(exp(residuals_log))with residuals on the log scale from validation data. Non-parametric and simple. - Normal theory: multiply by
exp(σ̂²/2)(assumes log-normal residuals). - Use a deviance loss instead (Gamma, Tweedie) with a log link: estimates the mean directly.
When the decision uses typical values (median house price), the log model without correction is fine.
Tweedie power
- p = 1: Poisson; p = 2: Gamma; 1 < p < 2: point mass at zero plus continuous positive part.
- Typical insurance pure premium: p ≈ 1.5-1.7.
- Choose by CV: fit p in {1.2, 1.4, 1.5, 1.6, 1.8} and compare out-of-fold deviance at a fixed p (or a business metric such as Gini/Lorenz for ranking); deviances at different p are not comparable to each other.
tweediepackages andstatsmodelscan estimate p by profile likelihood.
Two-part (hurdle) models
E[y | x] = P(y > 0 | x) * E[y | y > 0, x]Fit a classifier on all rows and a positive regressor (Gamma / log target) on positive rows. Use when zeros are generated by a different mechanism (no claim vs claim severity; no purchase vs basket size), and when you need the two parts separately for decisions or explanations.
Proportions
Targets in [0, 1] (utilisation, conversion rate per segment):
- logit transform:
y' = log((y + ε) / (1 − y + ε)), fit, invert withexpit; - cross-entropy on soft labels (LightGBM
cross_entropy, XGBoostreg:logistic) keeps predictions in (0, 1); - beta regression (statsmodels) for a GLM view;
- for ratios of counts (clicks / impressions), model the counts with Poisson/binomial and the denominator as exposure or weight.
Counts with exposure
Rate = count / exposure. Two equivalent fits:
- target = count, offset = log(exposure) (GLMs, LightGBM
init_score, XGBoostbase_margin); - target = count / exposure, sample_weight = exposure (scikit-learn GLMs and HGB).
Forgetting exposure makes long-exposure entities look risky.
Censored and truncated targets
Durations still running (censored) need survival models (survival-analysis-model-builder). Targets truncated by a cap (sales capped by stock) underestimate demand: flag censored rows and model demand accordingly.
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.