SVM Regression Predictor — Machine Learning/Classical Models

SVM Regression Predictor

Machine Learning / Classical Models

Evaluates a fitted support vector regression model at inference – what MATLAB's yfit = predict(Mdl, x) returns for a RegressionSVM (ε-SVR, trained with fitrsvm) and one observation:

z = (x − Mu) ./ Sigma,   f = Σ_i Alpha_i·K(z/s, SV_i/s) + Bias,   y = T(f) – where s is the kernel scale, K the kernel and T the response transform. For the linear kernel the sum is the model's Beta: f = (z/s)·Beta + Bias.

The model is baked in as configuration, pasted from the fitted object; nothing is fitted here and no model file is read.

Ports

• x – one observation, a column [D,1] with one predictor per row, in the order the model was trained on.
• y – the predicted response, a scalar [1,1].

Parameters

• Kernel Function – Mdl.KernelParameters.Function:
  • linear – K = a·b. The default, as in fitrsvm. The model is then given by Beta, and the support vectors are not used.
  • gaussian – K = exp(−‖a − b‖²). MATLAB's 'rbf' is the same kernel and is reported back as gaussian.
  • polynomial – K = (a·b + 1)^Order. The 1 is added after both sides are divided by the kernel scale.
• Beta – Mdl.Beta, [D,1] (a row is accepted): the linear model's coefficients on the standardised, scaled predictors. Used by linear only.
• Support Vectors – Mdl.SupportVectors, [N,D], one per row. MATLAB stores them standardised when the model was trained with 'Standardize',true, and they are pasted as they are. Used by gaussian and polynomial.
• Alpha – Mdl.Alpha, N values, one per support vector, already signed (α − α*). Used by gaussian and polynomial.
• Bias – Mdl.Bias, a scalar. A kernel offset used in training is already folded into it.
• Kernel Scale – Mdl.KernelParameters.Scale, strictly positive. It divides both the predictors and the support vectors.
• Polynomial Order – Mdl.KernelParameters.Order, a whole number from 1 to 32. Used by polynomial only.
• Mu – Mdl.Mu, [1,D], the predictor means of a standardised model. An unstandardised model has none (MATLAB shows []): leave 0. A single value is applied to every predictor.
• Sigma – Mdl.Sigma, [1,D], the predictor standard deviations. An unstandardised model: leave 1. As in MATLAB, a predictor whose Sigma is 0 is centred but not divided.
• Response Transform – T, Mdl.ResponseTransform, spelled as MATLAB spells it:
  • none – y = f. The default, and what fitrsvm sets.
  • logit – 1/(1 + e^−f).
  • doublelogit – 1/(1 + e^−2f).
  • symmetric – 2f − 1.
  • symmetriclogit – 2/(1 + e^−f) − 1.
  • sign – −1, 0 or +1 by the sign of f.
  • ismax and symmetricismax – the constant 1: on a single response the only column is always the maximum. That is what MATLAB returns too.
  invlogit is not offered: it takes log(f/(1−f)), complex for any f outside [0,1]. A function handle cannot be pasted as a number either.
• 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 software targets evaluate exactly the arithmetic above, in the same order.

The HDL story depends on the kernel. A linear model folds – standardisation and scale included – to one affine form w·x + b, and the three HDL targets compute it in genuine Q16.16 fixed point; with none, symmetric, sign, ismax and symmetricismax the whole block stays in fixed point, while logit, doublelogit and symmetriclogit are simulation-only real after f. The gaussian kernel has an exponential and the polynomial kernel raises a standardised, scaled dot product to a power, multiplying its dynamic range with every factor, so for those two the three HDL bodies are simulation-only real arithmetic, quantized at the ports only.

Simulink bridge

None. Simulink's RegressionSVM 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 support vectors, coefficients and a kernel – RegressionSVM 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 in every kernel and transform. The Simulink block also has no SampleTime parameter.

Notes

• Algebraic and stateless: the output depends only on the current input.
• Carries no state space. Every kernel but linear is nonlinear, and even a linear model with no transform is affine rather than linear – the Bias is a constant term, which a feed-through state space y = D·x cannot hold.
• A NaN in x makes MATLAB answer the model's default response; here the NaN propagates to y.
• Not SVM Predictor. That block is a binary classifier whose output is a label, with scikit-learn's kernel conventions (gamma inside the kernel, no standardisation); this one is MATLAB's regression model and publishes a number.