Kernel Regression Predictor — Machine Learning/Classical Models

Kernel Regression Predictor

Machine Learning / Classical Models

Evaluates a fitted kernel regression model at inference – what MATLAB's predict returns for a RegressionKernel model (trained with fitrkernel) and one observation. Such a model is a linear model on a random feature expansion of x that approximates a Gaussian kernel:

xs = (x − Mu) ./ Sigma (only for a model trained with 'Standardize', true),   y = Σ_c Beta_c·z_c(xs) + Bias,

where z is MATLAB's Fastfood expansion: for each Hadamard block i, T = H(H(xs·S_i)·G_i permuted by P_i)·B_i·√2/(KernelScale·√o), with H the Walsh–Hadamard transform of order o = 2^{⌈log2 D⌉} (x zero-padded to o entries), and the columns [cos T₁, sin T₁, cos T₂, sin T₂, …] cut to the first n = numel(Beta) and each scaled by 1/√(o·b). This is not the kernel SVM of SVM Predictor: there are no support vectors, only the explicit expansion.

The model is baked in as configuration. MATLAB keeps most of its numbers out of the model's public properties, and publishes them through saveLearnerForCoder(Mdl, 'kmdl'); then s = load('kmdl.mat').compactStruct holds every one below.

Ports

• x – one observation, a column [D,1] with one predictor per row, in the order the model was trained on. D decides the Hadamard order o, which must match the feature maps' width; at most 8 predictors.
• y – the predicted response, a scalar [1,1] whatever D is.

Parameters

• Feature Map S – the Fastfood scaling matrix, [b,o], one row per Hadamard block: s.FeatureMapper.S.
• Feature Map G – the Gaussian scaling matrix, [b,o]: s.FeatureMapper.G.
• Feature Map B – the random signs, [b,o]: s.FeatureMapper.B.
• Feature Map P – the permutations, [b,o], each row a permutation of 1…o (one-based, as MATLAB saves it): double(s.FeatureMapper.P).
• Kernel Scale – the model's KernelScale, a positive number (the resolved value when the model was fitted with 'auto').
• Beta – the linear coefficients, one per expanded feature, [n,1]: s.Impl.Beta. n is the model's NumExpansionDimensions, at most 256, and it must need exactly b = ⌈n/(2o)⌉ Hadamard blocks – the four feature maps and Beta come from the same model.
• Bias – the intercept, a scalar: s.Impl.Bias. Added after the sum.
• Mu – the predictor means, [1,D]: Mdl.Mu. [] (the default) for a model trained without 'Standardize', whose Mu is empty.
• Sigma – the predictor standard deviations, [1,D]: Mdl.Sigma, or [] with Mu. As in MATLAB, a predictor whose Sigma is 0 is centred and not divided.
• Sampling Time (s) – zero or less inherits the solver's rate; a positive value runs the block at that period.

Code export

All ten targets: Python, MATLAB, Java, Rust, C, C++, VHDL, Verilog, SystemVerilog and PLC Structured Text. The whole model is baked into the body at export time; there is no tunable parameter, so a refitted model means a re-export. The feature map is linear in x up to the cosine, so it is folded at export into one dense [D,o·b] matrix and every target writes the sum out term by term – D multiply-adds, one cosine and one sine per column pair. That is why D and n are capped: the limits bound the size of the generated code, not the math.

The three HDL targets are simulation-only real arithmetic: a cosine has no Q16.16 form to call. x is converted from Q16.16 at the port and y is quantized to Q16.16 once, at the output.

Simulink bridge

None. Simulink's RegressionKernel Predict block (Statistics and Machine Learning Toolbox) exists, but its only model parameter, TrainedLearner, is the name of a fitted model object in the MATLAB workspace. That object cannot be built from these numbers – RegressionKernel has no public constructor – and a parameter mapping carries one value to one parameter, so neither direction can cross. The bridge reports the block rather than dropping it silently, and it has no parity testbench, which is the documented consequence of that. The arithmetic is checked against MATLAB's own predict instead, and code export verification covers all ten languages. The Simulink block also has no SampleTime parameter.

Notes

• Algebraic and stateless: the output depends only on the current input. Nonlinear, so it carries no state space.
• Fastfood only. Every model fitrkernel builds uses it – the function has no option to choose another expansion. A model built with the undocumented Kitchen Sinks expansion keeps a matrix W instead of S, G, B and P, and is not carried.
• ResponseTransform: a model whose ResponseTransform is not 'none' (the default) applies that function after the sum; put it downstream of this block.
• Missing values differ. MATLAB replaces the prediction for an observation holding a NaN with its PredictionForMissingValue (by default the median of the training responses); here the NaN propagates to y.
• Agreement with predict is to rounding, not bit for bit: MATLAB applies the butterflies to each observation, this block applies their product, folded once. The two differ by about 10⁻¹⁵.