Machine learning: API index

Find an operation by its purpose. Entries link to the complete signature and contract.

HMath.DeepLearning.Core

API	Purpose
Activation	Scalar activation selector.
Sigmoid	Declaration and type contract below.
Tanh	Declaration and type contract below.
ReLU	Declaration and type contract below.
LeakyReLU	Declaration and type contract below.
PReLU	Declaration and type contract below.
ELU	Declaration and type contract below.
SELU	Declaration and type contract below.
GELU	Declaration and type contract below.
SiLU	Declaration and type contract below.
Mish	Declaration and type contract below.
Softplus	Declaration and type contract below.
Softsign	Declaration and type contract below.
HardSigmoid	Declaration and type contract below.
HardSwish	Declaration and type contract below.
activation	Given Activation selector then finite scalar, evaluate the selected activation.
activationDerivative	Evaluate the analytic first derivative with documented kink conventions and stable saturated sigmoid/tanh behavior.
activationExpr	Embed the checked activation and analytic custom reverse rule in an automatic differentiation graph.
softmax	Exponentiate stable log-softmax values; the output sums to one within floating error.
logSoftmax	Normalize a nonempty finite vector in log space after subtracting its maximum.
sparsemax	Project a finite vector onto the probability simplex using sorted active-support thresholds.
gatedLinearUnit	Multiply values by sigmoid(gates), requiring equal vector lengths.
softmaxExpr	First-order softmax reverse rule, including cross-coordinate coupling.
logSoftmaxExpr	First-order stable log-softmax rule; gradient rows sum to zero.
sparsemaxExpr	Sparsemax's piecewise-linear Jacobian.
ctcLossExpr	CTC graph operation on rectangular time-major log probabilities.
Reduction	Loss aggregation: Sum adds elementwise losses and Mean divides by their count; vector-level loss exceptions are documented by loss.
Sum	Declaration and type contract below.
Mean	Declaration and type contract below.
Loss	Checked loss selector,including squared/absolute error,cross entropy,KL,hinge,cosine,and parameterized Hubersmooth losses.
MeanSquaredError	Declaration and type contract below.
MeanAbsoluteError	Declaration and type contract below.
Huber	Declaration and type contract below.
SmoothL1	Declaration and type contract below.
BinaryCrossEntropy	Declaration and type contract below.
CategoricalCrossEntropy	Declaration and type contract below.
NegativeLogLikelihood	Declaration and type contract below.
KLDivergence	Declaration and type contract below.
CosineLoss	Declaration and type contract below.
Hinge	Declaration and type contract below.
loss	Evaluate the selected checked loss.
lossGradient	Analytic derivatives with respect to predictions under the exact loss/reduction convention.
lossExpr	Use a constant target with symbolic prediction inputs and the matching analytic reverse rule.
binaryCrossEntropyLogits	Stable binary cross entropy from logits and [0,1] targets, including extreme finite logits.
categoricalCrossEntropyLogits	Cross entropy from one class-logit vector; nonnegative targets must sum to one.
regularization	Return l1sum(abs(w)) + l2/2sum(w*w); both coefficients must be finite and nonnegative.
contrastiveLoss	Pairwise Euclidean contrastive loss; similar=True penalizes squared distance and dissimilar pairs use the positive margin.
tripletLoss	Return max(0,positiveDistance-negativeDistance+margin) for equal nonempty vector dimensions.
focalLoss	Mean binary focal loss with alpha in [0,1], gamma>=0, and exact zero/one targets.
diceLoss	Soft segmentation overlap losses on [0,1] values; positive smoothing defines the empty-mask case.
iouLoss	Soft segmentation overlap losses on [0,1] values; positive smoothing defines the empty-mask case.
ctcLoss	Single sequence, time-major log-probabilities [time,class].
ctcLossGradient	Given blank class index, target labels, then rectangular time-by-class log probabilities, return CTC negative log likelihood and gradient rows.

HMath.DeepLearning.Layers

API	Purpose
Training	Layer mode: Training updates/uses batch statistics; Inference uses retained running statistics.
Training	Declaration and type contract below.
Inference	Declaration and type contract below.
dropout	Inverted dropout.
spatialDropout	Sample one inverted dropout mask per N,C pair and share it across every spatial position.
BatchNormState	Per-channel running mean/variance and incorporated training-batch count for batch normalization.
BatchNormState	Declaration and type contract below.
runningMean	Per-channel running mean used during inference.
runningVariance	Per-channel running variance used during inference.
batchesSeen	Number of training batches incorporated into running statistics.
batchNorm	Population variance normalizes a training batch; unbiased sample variance updates runningVariance (a one-element batch uses population variance).
layerNorm	Normalize the selected number of trailing axes independently for each remaining prefix index.
instanceNorm	Normalize spatial axes separately per batch/channel in N,C,spatial layout.
groupNorm	Normalize channels/spatial positions per batch and channel group; channel count must be divisible by groups.
rmsNorm	Divide trailing-axis groups by sqrt(mean(x*x)+epsilon), without subtracting a mean.
weightNorm	Normalize each selected-axis slice and multiply it by the matching explicit magnitude; zero directions fail.
Initializer	Weight initializer selector: XavierKaiming uniformnormal,Orthogonal gain,or TruncatedNormal mean sigma cutoff. initializeWeights also takes explicit fan counts and RNG.
XavierUniform	Declaration and type contract below.
XavierNormal	Declaration and type contract below.
KaimingUniform	Declaration and type contract below.
KaimingNormal	Declaration and type contract below.
Orthogonal	Declaration and type contract below.
TruncatedNormal	Declaration and type contract below.
initializeWeights	Generate an immutable tensor and advanced RNG.
embedding	Gather checked row indices from [vocabulary,features] weights in requested order.
dense	Apply x*transpose(weights)+bias to [batch,in] inputs and [out,in] weights.
denseAD	Symbolic dense layer with gradients through inputs, weights, and explicit bias expressions.
ConvOptions	Per-axis stride,padding,dilation,and channel-group settings for checked convolution.
ConvOptions	Declaration and type contract below.
convolutionStride	Positive spatial stride per convolution axis.
convolutionPadding	Nonnegative symmetric padding per spatial axis.
convolutionDilation	Positive spacing between kernel elements per spatial axis.
convolutionGroups	Positive group count dividing input/output channels for grouped convolution.
convolution	Direct checked 1D2D3D cross-correlation with grouped channels and explicit stridepaddingdilation.
transposedConvolution	Direct adjoint-layout convolution; output padding is per-axis and strictly less than stride.
depthwiseConvolution	Set groups to input channels; output channel multipliers remain explicit in the weight shape.
convolutionAD	Construct the same direct convolution from scalar graph arithmetic, with automatic inputkernelbias gradients.
PoolMode	Pooling reduction selector: MaxPool or AveragePool over each checked window.
MaxPool	Declaration and type contract below.
AveragePool	Declaration and type contract below.
pooling	Windowed max/average pooling.
adaptivePooling	Partition spatial axes by floor/ceil output-bin boundaries, then reduce each bin.
globalPooling	Reduce all spatial positions to one value per N,C pair.
scaledDotProductAttention	Return attended values and normalized weights for Q[N,D],K[M,D],V[M,F]; True masks permit keys.
multiheadAttention	Split feature dimension into equal heads, attend independently, concatenate.
causalMask	Build a query-by-key allowed mask, with an explicit cached-prefix offset.
rotaryEmbedding	Rotate adjacent feature pairs at sequence positions offset+i; feature dimension must be even.
sinusoidalEncoding	Return [position,feature] sine/cosine positional encoding with base 10000.
alibiBias	Return nonpositive slope-scaled absolute position offsets; combine with a causal allowed mask if required.
KVCache	Opaque retained attention keys/values for incremental decoding; use checked cache append/attention operations.
emptyCache	Create an owned immutable key/value cache with fixed positive capacity and feature widths.
appendCache	Append equal-length key/value sequences without truncating history; reject capacity or feature mismatches.
cacheValues	Return immutable accumulated key/value tensors, preserving insertion order.
transformerFeedForward	Compose dense, checked elementwise activation, and dense layers with explicit parameters.
layerNormAD	Symbolic trailing-axis layer normalization.
rmsNormAD	Symbolic RMS normalization; its denominator includes all trailing axes.
scaledDotProductAttentionAD	First-order reverse attention graph, including Q/K score and V gradients.

HMath.DeepLearning.Metrics

API	Purpose
ClassificationMetrics	Accuracy and per-class precision,recall,and F1 values ordered by class index.
ClassificationMetrics	Declaration and type contract below.
accuracy	Fraction of correctly predicted samples.
precisionByClass	Per-class true positives divided by predicted positives; ordering follows class indices.
recallByClass	Per-class true positives divided by actual positives.
f1ByClass	Per-class harmonic mean of precision and recall, following the metric function's zero-denominator convention.
confusionMatrix	Count [trueClass,predictedClass] pairs for a positive explicit class count.
classificationMetrics	Return accuracy and per-class precision, recall, and F1 with zero for undefined class denominators.
topKAccuracy	Measure whether truth lies among descending top-k scores; equal scores prefer the smaller class index.
rocAUC	Compute the exact positive/negative rank-pair ROC area; both classes are required and ties count half.
prAUC	Integrate the precision-recall curve by grouped-score trapezoids, requiring at least one positive example.
perplexity	Exponentiate the negative mean true-token log probability; empty or positive log probabilities fail.
cosineSimilarityMatrix	Compare every [M,D] row with every [N,D] row using scale-safe unit vectors; zero vectors fail.
marginRankingLoss	Mean hinge on signed (+/-1) pair ordering with a nonnegative finite margin.

HMath.DeepLearning.Precision

API	Purpose
Quantization	Integer quantization policy: Symmetric around zero or Asymmetric with a learned zero point.
Symmetric	Declaration and type contract below.
Asymmetric	Declaration and type contract below.
QuantizedTensor	Opaque Int8 tensor with shape,optional channel axis,scales,and zero points.
quantize	Calibrate finite nonempty values per tensor or selected axis.
dequantize	Decode owned INT8 values using scale*(q-zeroPoint), rejecting floating arithmetic overflow.
quantizedValues	Return signed INT8 storage in logical row-major order.
quantizationScales	Return one positive scale per calibrated channel, or a single per-tensor scale.
quantizationZeroPoints	Return integer zero offsets under the selected symmetric/asymmetric calibration.
int8Gemm	Multiply two INT8 matrices with exact integer accumulation; supports per-row A/per-column B or per-tensor scales.
Precision	Mixed-precision storage/rounding selector FP16 or BF16; operations report finite/overflow conditions through the checked precision API.
FP16	Declaration and type contract below.
BF16	Declaration and type contract below.
reducedGemm	Round operands to the chosen 16-bit format, accumulate in Float32, and return checked Double values.
LossScaler	Dynamic mixed-precision loss-scale state with finite-step growth tracking.
LossScaler	Declaration and type contract below.
lossScale	Positive scaling factor applied to loss/gradients in mixed-precision training.
scaleGrowthInterval	Number of consecutive finite updates before loss-scale growth.
finiteSteps	Current count of consecutive finite updates since the last reset/growth.
initialLossScaler	Create a positive finite loss scale and positive growth interval; zero accumulated finite steps.
scaleLoss	Multiply a finite loss by the checked current scale; overflow is a structured failure.
unscaleGradients	False means overflow: every caller must skip the entire optimizer update.
updateLossScaler	Halve scale after overflow; double after growthInterval finite updates, with a bounded maximum.
gradientNorm	Compute a checked scaled Euclidean norm; unrepresentable final norms fail explicitly.
clipGradients	Clip norm through the shared overflow-safe automatic-differentiation gradient utility.

HMath.MachineLearning

API	Purpose
Dataset	Finite observations as rows with a fixed, positive feature count.
MLConfig	Positive iteration limittolerancerate and an explicit reproducible seed.
MLConfig	Declaration and type contract below.
mlIterations	Maximum outer iterations per fitted algorithm.
mlTolerance	Absolute algorithm-specific stopping residual.
mlRate	Positive gradient step size, where used.
mlSeed	Seed for initialization, projection, or stochastic updates.
defaultMLConfig	500 iterations, absolute residual tolerance 1e-8, rate 0.05, PCG seed 42.
Fit	A finite budget is a valid stopping point, distinct from convergence.
Fit	Declaration and type contract below.
fitted	Best fitted model retained when fitting stops.
fitIterations	Completed fitting iterations.
fitResidual	Algorithm-specific finite stopping residual at the returned model.
fitConverged	Whether the selected stopping residual met tolerance; a budget stop may return False.

HMath.MachineLearning.Clustering

API	Purpose
ClusterModel	Fitted cluster centroids as cluster-by-feature observations; prediction assigns new queries to the learned centers.
clusterCenters	Cluster centroids as cluster-by-feature rows.
predictClusters	Assign each row to its closest squared-Euclidean center; ties use the first center.
kMeans	Seeded random-center Lloyd iteration; residual is total center displacement.
kMeansPlusPlus	D-squared k-means++ initialization followed by Lloyd center updates.
miniBatchKMeans	Online center updates with per-cluster counts and seeded shuffled batches.
kMedoids	PAM exhaustive medoid swaps.
GaussianMixture	Fitted component probabilities,mean vectors,and covariance matrices in shared component order.
mixtureWeights	Gaussian-mixture component probabilities in component order.
mixtureMeans	Component mean vectors, matching mixtureWeights order.
mixtureCovariances	One feature-by-feature covariance matrix per Gaussian component.
fitGaussianMixture	Full-covariance EM initialized by k-means++; positive ridge is added at each covariance update.
mixtureResponsibilities	Compute normalized posterior component probabilities with log-sum-exp stabilization.
dbscan	Density expansion using a positive Euclidean radius; minimumPoints includes the observation itself.
optics	OPTICS (Ankerst et al., SIGMOD 1999): ordered point index, core distance, reachability distance.
extractOPTICS	Extract DBSCAN-style labels at epsilon from a checked OPTICS ordering; noise is -1.
meanShift	Gaussian-kernel mean shift from every training point; modes within bandwidth/2 are merged.
Linkage	Single, complete, average Euclidean distance or Ward variance-increase linkage.
Single	Declaration and type contract below.
Complete	Declaration and type contract below.
Average	Declaration and type contract below.
Ward	Declaration and type contract below.
Merge	One hierarchical-clustering merge, retaining child IDs,linkage distance,and merged observation count.
Merge	Declaration and type contract below.
leftCluster	Left child cluster ID in a hierarchical merge.
rightCluster	Right child cluster ID in a hierarchical merge.
mergeDistance	Linkage distance at which the two child clusters merge.
mergedSize	Number of original observations in the merged cluster.
hierarchical	Agglomerate the closest active clusters to produce all n-1 linkage rows.
cutHierarchy	Validate the entire hierarchy and return k cluster labels in original observation order.
spectralClustering	Cluster row-normalized leading eigenvectors of the normalized Gaussian affinity matrix.
affinityPropagation	The preference is the common diagonal similarity; damping is in [0.5,1).

HMath.MachineLearning.Decomposition

API	Purpose
PCA	Fitted feature center,principal-component directions,and their explained variances; use transform functions for new observations.
pcaMean	Training feature means subtracted before projection.
pcaComponents	Principal component loading vectors in component order.
pcaVariances	Explained variances associated with the retained principal components.
fitPCA	Fit count principal axes from at least two observations; uses sample covariance (denominator n-1).
transformPCA	Center with the training mean and project onto retained axes; no whitening is applied.
inversePCA	Reconstruct original features from retained scores and restore the training mean.
IncrementalPCA	Exact sufficient statistics, including between-batch mean correction.
incrementalPCA	Create empty running covariance state for a positive feature dimension.
updatePCA	Merge observations by Welford updates.
mergePCA	Combine independent batch statistics with the between-mean scatter correction.
finishPCA	Extract principal axes from accumulated sample covariance; requires at least two observations.
KernelPCA	Centered training kernel state and normalized positive eigenvectors.
fitKernelPCA	Fit kernel principal axes; count must be smaller than n and within positive numerical rank.
transformKernelPCA	Center query kernels with training means before projection, without fitting query statistics.
truncatedSVD	Return reduced (U, singular values, V-transpose) from LAPACK, keeping the largest count values.
ICA	Training center and whitened unmixing directions; component signs/permutations are arbitrary.
fitICA	Symmetric FastICA with tanh nonlinearity (Hyvarinen 1999), whitening by sample covariance.
transformICA	Apply the fitted centering and unmixing directions to new observations.
FactorAnalysis	Fitted feature center,latent factor loadings,and diagonal feature-noise variances.
factorLoadings	Fitted feature-by-factor loading matrix.
factorNoise	Per-feature residual noise variances in the factor model.
fitFactorAnalysis	Gaussian factor-analysis EM with diagonal noise floor.
CCA	Paired training centers, canonical directions, and regularized canonical correlations.
fitCCA	Fit paired canonical directions with a strictly positive diagonal covariance ridge.
transformCCA	Project paired query rows with fitted training centers and canonical directions.
canonicalCorrelations	Singular values of the whitened cross-covariance, in descending order.
PLS	PLS2 regression state with predictor/response centers and a feature-by-response coefficient matrix.
fitPLS	PLS2 NIPALS with regression deflation; count cannot exceed the predictor rank.
predictPLS	Predict response rows using fitted PLS coefficients and training centers.
randomProjection	Seeded Gaussian projection with variance 1/dimension per coefficient.
classicalMDS	Classical metric MDS.
isomap	Build a symmetric k-neighbor graph, compute geodesics, then metric MDS.
tsne	Exact all-pairs t-SNE; perplexity must be strictly between one and n.
umap	Exact full fuzzy-set cross entropy, caller supplies fitted curve a,b.

HMath.MachineLearning.Internal

API	Purpose
Dataset	Finite observations as rows with a fixed, positive feature count.
MLConfig	Positive iteration limittolerancerate and an explicit reproducible seed.
MLConfig	Declaration and type contract below.
mlIterations	Maximum outer iterations per fitted algorithm.
mlTolerance	Absolute algorithm-specific stopping residual.
mlRate	Positive gradient step size, where used.
mlSeed	Seed for initialization, projection, or stochastic updates.
defaultMLConfig	500 iterations, absolute residual tolerance 1e-8, rate 0.05, PCG seed 42.
Fit	A finite budget is a valid stopping point, distinct from convergence.
Fit	Declaration and type contract below.
fitted	Best fitted model retained when fitting stops.
fitIterations	Completed fitting iterations.
fitResidual	Algorithm-specific finite stopping residual at the returned model.
fitConverged	Whether the selected stopping residual met tolerance; a budget stop may return False.
finite	Test whether Double is neither NaN nor infinite.
checked	Validate a list of finite numerical values, returning Right () or Left NonFiniteResult.
require	Given condition then diagnostic, return Right () or Left InvalidArgument prefixed with ML context.
config	Validate positive iteration count and positive finite tolerance/learning rate of MLConfig.
dataset	Validate a nonempty finite rectangular observation-by-feature list with positive feature count and Int-safe size.
responses	Given dataset then finite response list, validate dataset and equal observationresponse count.
queries	Given expected feature dimension then query rows, validate every row width and finite values.
dot	Unchecked list inner product using zipWith; unequal lengths truncate.
add	Unchecked coordinatewise list addition, truncating to shorter length; checked estimator callers validate dimensions.
sub	Unchecked coordinatewise left-minus-right list subtraction, truncating to shorter length.
scale	Given scalar then coordinate list, multiply each coordinate without checked finiteness validation.
norm	Return scaled Euclidean norm of a coordinate list, zero for empty/all-zero input.
dist2	Return squared Euclidean distance using sub and dot.
meanV	Return per-feature means for a nonempty equal-width dataset.
matmul	Unchecked dense row-list matrix multiplication via row/column dot products.
ident	Return n-by-n Double identity rows for a nonnegative dimension; nonpositive n gives [].
replace	Given index,new value,then list, replace by take/drop reconstruction.
matrix	Validate dataset then construct row-major Matrix Double with matching dimensions.
rows	Convert Matrix to dense row lists, preserving explicit zero-column row count.
pinv	Compute a validated dataset pseudoinverse using relative singular-value tolerance 1e-12 and return dense rows.
solveLS	Given dataset then response list, solve least squares through the pseudoinverse.
inverse	Validate a square dataset, compute pseudoinverse and require inverse reconstruction residual below 1e-6*n.
symmetricEigen	Validate finite square approximately symmetric dataset, symmetrize and eigendecompose.
argmin	Return zero-based first index of a minimum in a nonempty list.
argmax	Return zero-based index selected by maximumBy on a nonempty list, with later equal maxima preferred.
iterateFit	Deterministic reference iteration; residual is supplied by each estimator.
foldEither	Monadic left fold: given checked step,initial accumulator,then list, stop at first Left MathError and otherwise return final accumulator.
firstRow	Return the first row of nested lists, or [] for an empty outer list.

HMath.MachineLearning.Neighbors

API	Purpose
IndexKind	Axis-aligned KD partitions or enclosing Euclidean ball partitions.
KDTree	Declaration and type contract below.
BallTree	Declaration and type contract below.
SpatialIndex	Immutable tree retaining original observation IDs and its validated feature dimension.
buildIndex	Build an exact search tree with at most leafSize observations per leaf.
NeighborResult	Neighbor indices/distances plus visited-leaf and exhaustive-search diagnostics.
NeighborResult	Declaration and type contract below.
neighbors	Training-row indices paired with returned Euclidean distances, ordered by distance and then index.
visitedLeaves	Number of leaves visited against the explicit query budget.
exhaustive	True if the neighbor search completed its exact stopping condition; False if unexplored nodes may improve candidates.
nearestNeighbors	maxLeaves is a query work budget.
knnRegress	Average the k exact nearest training responses for each query row.
knnClassify	Majority vote among k exact neighbors; targets follow original training row order.
LSH	Seeded p-stable Euclidean hash tables retaining Gaussian projections and offset buckets.
buildLSH	Build tables with projections scalar hashes each and positive bucket width.
queryLSH	Rank matching-bucket candidates by exact distance; may return fewer than k results, including none.
localOutlierFactor	Training-set LOF with ties included at the kth neighbor distance.
IsolationForest	Owned random isolation trees with fixed training dimension and subsample size.
fitIsolationForest	Seeded independent isolation trees using subsamples of 2..2048 observations.
scoreIsolationForest	Return 2^(-mean corrected path length / expected random-tree path length); larger means more anomalous.
OneClassSVM	Kernel novelty detector with normalized nonnegative dual weights and learned offset.
fitOneClassSVM	nu-SVM dual coordinate descent: sum alpha=1, 0<=alpha<=1/(nu*n).
decisionOneClassSVM	Return signed novelty margins: positive indicates an inlier under the fitted kernel boundary.

HMath.MachineLearning.Preprocessing

API	Purpose
Scaling	Population z-score, unit-range, or median/IQR feature scaling.
Standardize	Declaration and type contract below.
MinMax	Declaration and type contract below.
RobustScale	Declaration and type contract below.
Scaler	Immutable training-feature centers and nonzero scales; constant columns use scale one.
fitScaler	Estimate one center and scale per training feature.
transform	Apply training centers/scales to rows with the original feature count; no state is updated.
inverseTransform	Undo a fitted affine scaler, including its constant-feature convention.
QuantileTransformer	Sorted training samples retained separately for each feature.
fitQuantileTransformer	Fit empirical feature quantiles using training rows only.
quantileTransform	Map values to [0,1].
inverseQuantileTransform	Interpolate training order statistics at probabilities in [0,1].
PowerTransform	Box-Cox or Yeo-Johnson with a caller-selected finite power lambda; lambda is not estimated.
BoxCox	Declaration and type contract below.
YeoJohnson	Declaration and type contract below.
powerTransform	Apply the selected power to features.
inversePowerTransform	Invert the selected power, rejecting values outside the transform range.
Imputation	Training-column mean, median, or a finite constant for NaN-valued observations.
MeanImpute	Declaration and type contract below.
MedianImpute	Declaration and type contract below.
ConstantImpute	Declaration and type contract below.
Imputer	Fitted replacement values; an imputer never learns from rows passed to impute.
fitImputer	Treat NaN as missing and reject infinities.
impute	Replace NaN with fitted training values while preserving observed entries and row order.
Encoder	Sorted distinct training categories with stable zero-based integer codes.
UnknownCategory	Whether a previously unseen category fails or produces an all-zero one-hot row.
RejectUnknown	Declaration and type contract below.
ZeroUnknown	Declaration and type contract below.
fitEncoder	Learn sorted category levels from a nonempty training label vector.
labelEncode	Map known categories to zero-based codes; unseen categories fail.
labelDecode	Recover categories from checked integer codes.
oneHotEncode	Emit one column per sorted training category under the explicit unknown-category policy.
Fold	Disjoint indices into the original dataset.
Fold	Declaration and type contract below.
trainingIndices	Zero-based original row indices assigned to training in this fold.
validationIndices	Zero-based original row indices held out for validation in this fold.
trainTestSplit	Seeded split of n row indices.
kFold	Partition n shuffled indices into k nonempty validation folds; each row is held out exactly once.
stratifiedKFold	Round-robin each shuffled class across k folds.
gridSearch	Minimize a user-supplied validation loss, evaluated independently for every candidate/fold.
randomSearch	Sample count distinct candidates from a finite set, then evaluate the supplied folds.

HMath.MachineLearning.Regression

API	Purpose
Penalty	Minimize mean squared error divided by two plus L1 and/or squared L2 coefficient penalties.
Ordinary	Declaration and type contract below.
Ridge	Declaration and type contract below.
Lasso	Declaration and type contract below.
ElasticNet	Declaration and type contract below.
LinearModel	Affine predictor; coefficient zero is the intercept and remaining coefficients follow feature order.
coefficients	Intercept followed by slopes in input feature order.
fitLinear	Fit affine least squares or coordinate-descent elastic net.
predictLinear	Predict one finite response per query row using the fitted intercept and slopes.
polynomialFeatures	Build univariate columns x, x^2, ..., x^degree; the regression intercept supplies the constant.
fitWeighted	Fit affine least squares with nonnegative observation weights.
fitRobust	Huber IRLS with fixed positive residual threshold, including intercept.
BayesianLinear	Posterior-mean linear model together with coefficient covariance, returned by Bayesian regression fitting.
fitBayesian	Isotropic zero-mean Gaussian prior, observation precision beta.
bayesianMean	Posterior-mean fitted linear model.
bayesianCovariance	Posterior covariance matrix of linear coefficients.
RecursiveLS	Owned online regression coefficients and inverse information, with fixed forgetting factor.
recursiveLS	Initial inverse information delta I; forgetting factor in (0,1].
updateRecursiveLS	Assimilate one feature row/response using the matrix inversion lemma.
recursiveCoefficients	Current intercept and slopes; updating creates a new state.
GLMFamily	Bernoulli mean with logistic link, or nonnegative response mean with log link.
BinomialLogit	Declaration and type contract below.
PoissonLog	Declaration and type contract below.
GLM	Fitted generalized linear model with intercept and family-specific inverse link.
fitGLM	Damped Newton/IRLS with nonnegative slope ridge.
predictGLM	Return conditional means: probabilities for BinomialLogit, positive rates for PoissonLog.
MultinomialModel	Softmax class weights and sorted original integer labels.
fitMultinomial	Fit all class logits by full-batch gradient descent with slope ridge.
predictMultinomial	Return sorted (original label, probability) pairs for each observation.
Kernel	Positive-semidefinite linear, polynomial, or Gaussian radial basis kernel parameters.
LinearKernel	Declaration and type contract below.
PolynomialKernel	Declaration and type contract below.
RBFKernel	Declaration and type contract below.
kernel	Evaluate a checked PSD kernel on equal-length finite feature vectors.
SVM	Binary kernel decision state, retaining original training observations and signed dual weights.
fitSVM	Deterministic two-coordinate SMO for binary labels -1/+1.
decisionSVM	Return signed kernel margins; zero is the fitted decision boundary.
predictSVM	Classify margins as -1 or +1, with zero assigned +1.
GaussianProcess	Zero-mean Gaussian-process regression posterior with retained training covariance solve.
fitGaussianProcess	Fit a GP with strictly positive observation-noise variance and a checked PSD kernel.
predictGaussianProcess	Return posterior latent-function (mean, variance), excluding observation noise.
GPClassifier	Logistic Gaussian-process classifier fitted with a Laplace Gaussian posterior approximation.
fitGPClassifier	Newton mode fitting for 0/1 labels.
predictGPClassifier	Approximate class-one probabilities using the logistic Gaussian variance correction.
BayesFamily	Gaussian features, nonnegative multinomial counts, or binary Bernoulli features.
GaussianBayes	Declaration and type contract below.
MultinomialBayes	Declaration and type contract below.
BernoulliBayes	Declaration and type contract below.
NaiveBayes	Fitted class priors and family-specific independent feature likelihoods.
fitNaiveBayes	Fit class likelihoods.
predictNaiveBayes	Select the class with greatest log posterior; preserve the original integer labels.
Discriminant	Class priors, means, and regularized inverse covariance/log-determinant state.
fitDiscriminant	False = pooled covariance LDA; True = class covariance QDA.
predictDiscriminant	Classify with Gaussian discriminant log likelihoods using training covariance state.