k-LinReg demo

This demo shows how the k-LinReg algorithm [Lauer, 2013] solves switched linear regression problems by minimizing the global Mean Squared Error over $ N $ data points and $ n $ models, defined as $$ MSE = \frac{1}{N} \sum_{i=1}^N \min_{j=1,\dots, n} (y_i - \theta_j^T x_i )^2 $$

(x = , y = )

Simulation data:
Number of data:
Number of models:
Models:

Gaussian noise (v) std:

Algorithm:
Number of models:
Number of restarts:
or see how it works

Estimated models:

Computing time =
Root Mean Squared Error =

Plot of MSE versus restart index:

green bars indicate possible successes (when MSE equals the best MSE over all restarts)
red bars indicate failures (when a mode gets no data points)