> For the complete documentation index, see [llms.txt](https://docs.algenta.ai/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.algenta.ai/machine-learning.md).

# Machine learning

- [Time-series model selection](https://docs.algenta.ai/machine-learning/ml-model-selection.md): Walk-forward, purged, k-fold and temporal splits for leakage-free time-series model selection.
- [Statistical model comparison](https://docs.algenta.ai/machine-learning/ml-model-comparison.md): Paired bootstrap CIs, exact McNemar and Diebold-Mariano tests that decide whether a candidate model is genuinely better than the champion.
- [Probability calibration](https://docs.algenta.ai/machine-learning/ml-calibration.md): Isotonic (PAV) and z-score affine calibration with reliability diagnostics for turning raw model scores into trustworthy probabilities.
- [Bayesian methods, calibration, and clustering metrics](https://docs.algenta.ai/machine-learning/bayesian-methods-and-calibration-kernels.md): Conjugate Bayesian updates and Monte Carlo A/B testing, general-purpose variational/Laplace inference primitives, probability calibration, and cluster-quality metrics across four independent kernel mo
- [Dense 2D matrices (Matrix2D)](https://docs.algenta.ai/machine-learning/ml-tensor2d.md): Dense 2-D matrix type with matmul, matvec and outer products backing the trainable-model kernels.
- [LSTM and GRU cells](https://docs.algenta.ai/machine-learning/ml-sequence-cells.md): LSTM and GRU cell forward passes with exact gate math for sequence models.
- [LSTM sequence training (BPTT)](https://docs.algenta.ai/machine-learning/ml-sequence-training.md): Full BPTT training loop for LSTM regressors, gradient-checked against finite differences.
- [Bit-exact weight serialization](https://docs.algenta.ai/machine-learning/ml-serialization.md): Bit-exact float64 weight serialization for saving and restoring trained kernels.
- [Gradient-boosted regression trees](https://docs.algenta.ai/machine-learning/ml-gradient-boosting.md): Gradient-boosted regression trees with exact SSE-gain splits, subsampling and shrinkage.
- [Gaussian mixture models](https://docs.algenta.ai/machine-learning/ml-mixture-models.md): Gaussian mixture models fit by log-space EM with BIC/AIC model selection.
- [Hidden Markov models](https://docs.algenta.ai/machine-learning/ml-hmm.md): Hidden Markov models — forward/backward likelihood, Viterbi decoding and Baum-Welch training.
- [Imbalanced-data resampling](https://docs.algenta.ai/machine-learning/ml-imbalance.md): SMOTE, random over/under-sampling and balanced class weights for skewed datasets.
- [Model ensembling](https://docs.algenta.ai/machine-learning/ml-ensembles.md): Stacking and weighted voting ensembles over arbitrary base-model predictions.
- [Conformal prediction intervals](https://docs.algenta.ai/machine-learning/ml-conformal.md): Split-conformal prediction intervals with finite-sample coverage guarantees.
- [Model explainability](https://docs.algenta.ai/machine-learning/ml-explainability.md): KernelSHAP and permutation importance for explaining any model's predictions.
- [Gaussian process regression](https://docs.algenta.ai/machine-learning/ml-gaussian-processes.md): Gaussian process regression with RBF and Matern kernels, exact posterior mean and variance.
- [Hyperparameter search schedules](https://docs.algenta.ai/machine-learning/ml-automl.md): Hyperband successive-halving schedules and Latin-hypercube search plans for hyperparameter optimization.
- [Fit/transform pipelines](https://docs.algenta.ai/machine-learning/ml-pipelines.md): Composable fit/transform preprocessing pipelines (standardize, min-max, chained) with exact inverses.
- [Trainable linear models](https://docs.algenta.ai/machine-learning/ml-linear-models.md): Trainable logistic regression and elastic-net linear models with exact coordinate-descent math.
- [Symmetric eigendecomposition and thin SVD](https://docs.algenta.ai/machine-learning/ml-eigendecomposition.md): Jacobi symmetric eigendecomposition and thin SVD for full-rank spectral computation.
- [AR/MA estimation (ARIMA building blocks)](https://docs.algenta.ai/machine-learning/ml-arima.md): Durbin-Levinson AR estimation, innovations MA fitting and ARIMA forecasting building blocks.
- [Feature hashing (the hashing trick)](https://docs.algenta.ai/machine-learning/ml-feature-hashing.md): Seeded FNV-1a feature hashing for fixed-width vectorization of unbounded feature names.
- [Partial least squares regression (PLS1)](https://docs.algenta.ai/machine-learning/ml-pls.md): NIPALS PLS1 regression for collinear and wide (p > n) feature matrices, sklearn-matched.
- [Trainable SVM classifier (simplified SMO)](https://docs.algenta.ai/machine-learning/ml-svm.md): Trainable soft-margin SVM classifier via simplified SMO with linear and RBF kernels.
- [Batched chain greeks](https://docs.algenta.ai/machine-learning/ml-chain-greeks.md): SIMD-batched Black-Scholes price and greeks across a whole option chain in one call, matching the scalar pricing functions to 1e-9.
- [Classical ML algorithms](https://docs.algenta.ai/machine-learning/ml-classical-algorithms.md): Distance functions, k-means and k-NN, Gaussian Naive Bayes, preprocessing transforms, evaluation metrics, and a bagged decision-stump random forest across seven independent kernel modules.
- [Regression and classification kernels](https://docs.algenta.ai/machine-learning/regression-and-classification-kernels.md): Closed-form OLS/ridge regression, a recursive CART regression tree, four SVM kernel functions with Gram-matrix diagnostics, and ten scalar loss functions for classical supervised learning.
- [Autograd and training stability](https://docs.algenta.ai/machine-learning/autograd-and-training-stability-kernels.md): Reverse-mode autodiff graph bookkeeping, per-operation gradient formulas, ten optimizer update rules, and the loss-scaling/NaN-guard/numerically-safe primitives that keep a training loop from divergin
- [LoRA adapters, checkpoint loading & distillation](https://docs.algenta.ai/machine-learning/lora-distillation-and-weight-loading-kernels.md): Per-element LoRA/DoRA/prefix/prompt adapter math, sharded and quantized checkpoint-loading arithmetic, and classical distillation-column design equations (not neural-network knowledge distillation).
- [Mixture-of-experts and routing](https://docs.algenta.ai/machine-learning/mixture-of-experts-and-routing-kernels.md): Sparse mixture-of-experts math (gating, capacity, load-balance and z-loss) plus the separate, higher-level layer that routes a whole request to a model, precision, or backend by cost and latency.
- [Model lifecycle and interop](https://docs.algenta.ai/machine-learning/model-lifecycle-and-interop-kernels.md): ABI version and layout arithmetic, safetensors/GGUF/ONNX/HuggingFace interop math, data/tensor/pipeline parallelism formulas, and checkpoint/quantization sizing, across four independent Float64 kernel
- [Sequence and state-space models](https://docs.algenta.ai/machine-learning/sequence-and-state-space-model-kernels.md): A 2-layer LSTM training loop with full BPTT and Adam, the per-element linear recurrence math behind Mamba/S4/RetNet-style state-space models, and the scalar heuristics a stateful agent runtime scores
- [RLHF and generative training](https://docs.algenta.ai/machine-learning/rlhf-and-generative-training-kernels.md): Preference-optimization losses for RLHF/DPO alignment, diffusion noise schedules and denoising steps, InfoNCE-style contrastive losses, one-sample-at-a-time online learning updates, and Pareto/TOPSIS
- [Feedback loops and feature engineering](https://docs.algenta.ai/machine-learning/feedback-loops-and-feature-engineering-kernels.md): Scalar scoring functions for the data flywheel (drift, retraining triggers, RLHF reward, calibration) and the scaling/encoding/selection utilities that build model inputs from raw columns.


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