Incremental Regression Linear Fit — Machine Learning/Incremental Learning

Incremental Regression Linear Fit

Machine Learning / Incremental Learning

Fits a linear regression model online, one observation per step, and puts the model on a bus every step: y ≈ x·β + b. This is MATLAB's incrementalRegressionLinear learner with its default scale-invariant solver (Statistics and Machine Learning Toolbox), as Simulink's IncrementalRegressionLinear Fit block runs it. The first Estimation Period observations are used only to estimate what the learner estimates (the predictors' means and standard deviations under Standardize, and Epsilon); every later one updates β and b. Feed the bus to an IncrementalRegressionLinear Predict block.

Ports

• x – one observation of the P predictors, a row [1,P]. P is read off this width.
• y – the response of that observation, [1,1]. A NaN in x or y skips the observation, where Simulink's block lets it in: a NaN predictor turns its Beta NaN for the rest of the run, and a NaN response still moves it.
• mdl (bus) – the learner after this observation, a bus of seven elements: Beta [P,1], Bias [1,1], IsWarm (bool, true once Metrics Warmup Period observations have been trained on), CanPredict (bool, false only while standardization is still being estimated), Mu [P,1] and Sigma [P,1] (the standardization, 0 and 1 when there is none) and Epsilon [1,1] (0 for the leastsquares learner).

Parameters

• Learner – the loss the solver minimizes:
  • svm (the default) – the epsilon-insensitive loss of a support vector machine regression;
  • leastsquares – the squared error.
• Epsilon – half the width of the svm loss's insensitive band, 0.1 by default; not used by leastsquares.
• Estimate Epsilon – on (the default, MATLAB's 'auto'): Epsilon is re-estimated from the responses of the estimation period, as their interquartile range divided by 13.49 (0.1 when that is zero); off: Epsilon stays as set.
• Standardize – off (the default) or on: center and scale each predictor by its mean and standard deviation over the estimation period.
• Estimation Period – how many observations the estimation uses, 1000 by default as in MATLAB. It applies only when something is estimated (Standardize on, or the svm learner with Estimate Epsilon on); otherwise every observation trains.
• Metrics Warmup Period – how many trained observations make the model warm (IsWarm), 1000 by default.
• Sampling Time (s) – zero or less inherits the solver's rate; a positive value runs the block at that period.

When a run is refused

An x that is not a row, a y that is not [1,1], a negative or fractional period, a negative Epsilon, or Standardize on with an Estimation Period of 0.

Code export

Six targets: Python, MATLAB, Java, Rust, C and C++, each carrying the learner's whole state and running the same step as the live block, in the same arithmetic order. The hardware targets (VHDL, Verilog, SystemVerilog) and PLC Structured Text carry no bus, so an export to one stops and names the block.

Simulink bridge

None. Simulink's block takes its learner as InitialLearner, the name of an incrementalRegressionLinear object in the MATLAB workspace, rather than as dialog parameters, so there is nothing in its dialog to map these configs onto or read them back from.

Notes

• Stateful: the state is the solver's (four running sums per coefficient and the largest response seen), the estimation sums, and the counts.
• The bus at a step has already learnt that step's observation, as in Simulink: a Predict block fed the same x sees a model trained on it.
• Timing follows Simulink's block, not MATLAB's fit(): the estimated Mu, Sigma and Epsilon appear one step after the estimation period ends, and IsWarm turns true one step after fit() would set it.
• A predictor that does not vary over the estimation period gets Sigma 0 and is left unscaled, as MATLAB's learner leaves it; Simulink's block divides by that zero and its Beta turns NaN.
• One observation per step; Simulink's block also takes several rows at a time, and its optional weights and reset inputs are not offered.
• Verified against R2026a: over 120 steps in four configurations (svm with Epsilon estimated, leastsquares standardized, svm with a fixed Epsilon, svm standardized), Beta and Bias agree with Simulink's block within 10⁻¹⁴, and IsWarm, CanPredict, Mu, Sigma and Epsilon at every step.