lts_linear_regression

ctapipe.fitting.lts_linear_regression(x, y, samples=20, relative_sample_size=0.85, max_iterations=20, eps=1e-12, rng=Generator(PCG64) at 0x7C0B4AE62500)

Perform a Least Trimmed Squares regression.

This is based on algorithm (2) described in [RVD06]

We start from randomly sampled two points of the dataset and then iteratively choose the relative_sample_size fraction of points with the smallest residuals to redo the fit until it convergtes.

This is done for samples initial samples and the solution with the lowest residual sum of squares is returned along with that error.

Parameters:

x: np.array

x values for the linear regression

y: np.array

y values for the linear regression

samples: int

How many initial samples to generate. For each sample, the C-step optimization is performed and the result with the lowest sum of squares is returned.

relative_sample_size: float

Portion of points to be used for the fit, should be > 0.5

max_iterations: int

maximum number of C-Steps performed for each sample. The fit should converge much faster (normally after < 10 iterations)

eps: float

differences in residual sum of squares at which the iteration will be stopped

rng: numpy.random.Generator

Random generator for drawing fit samples

Returns:

beta: np.array

Parameter vector of the linear regression

error: float

Residual sum of squares of the best fit