mushi.loss_functions

Loss functions for measuring goodness of fit.

Each loss function takes an expected data matrix \(\mathbb{E}[\mathbf X]\) and an observed data matrix \(\mathbf X\), and returns a loss value. Higher loss means worse fit between \(\mathbf X\) and \(\mathbb{E}[\mathbf X]\).

Examples

>>> import mushi.loss_functions as lf
>>> import numpy as np

Define expected data matrix \(\mathbb{E}[\mathbf X]\) and an observed data matrix \(\mathbf X\) as \(10\times 10\) arrays of ones (for this trivial example):

>>> E = np.ones((10, 10))
>>> X = np.ones((10, 10))

Compute various losses:

• Poisson random field

  >>> lf.prf(E, X)
  DeviceArray(100., dtype=float64)
  

• Generalized Kullback-Leibler divergence

  >>> lf.dkl(E, X)
  DeviceArray(0., dtype=float64)
  

• Least squares

  >>> lf.lsq(E, X)
  0.0
  

Functions

dkl	Generalized Kullback-Liebler divergence, a Bregman divergence (ignores constant term)
lsq	Least-squares loss
prf	Poisson random field loss