chainer.functions.gaussian_nll¶

chainer.functions.gaussian_nll(x, mean, ln_var, reduce='sum')[source]¶

Computes the negative log-likelihood of a Gaussian distribution.

Given two variable mean representing \(\mu\) and ln_var representing \(\log(\sigma^2)\), this function computes in elementwise manner the negative log-likelihood of \(x\) on a Gaussian distribution \(N(\mu, S)\),

\[-\log N(x; \mu, \sigma^2) = \log\left(\sqrt{(2\pi)^D |S|}\right) + \frac{1}{2}(x - \mu)^\top S^{-1}(x - \mu),\]

where \(D\) is a dimension of \(x\) and \(S\) is a diagonal matrix where \(S_{ii} = \sigma_i^2\).

The output is a variable whose value depends on the value of the option reduce. If it is 'no', it holds the elementwise loss values. If it is 'sum', loss values are summed up.

Parameters:	x (`Variable` or N-dimensional array) – Input variable. mean (`Variable` or N-dimensional array) – A variable representing mean of a Gaussian distribution, \(\mu\). ln_var (`Variable` or N-dimensional array) – A variable representing logarithm of variance of a Gaussian distribution, \(\log(\sigma^2)\). reduce (str) – Reduction option. Its value must be either `'sum'` or `'no'`. Otherwise, `ValueError` is raised.
Returns:	A variable representing the negative log-likelihood. If `reduce` is `'no'`, the output variable holds array whose shape is same as one of (hence both of) input variables. If it is `'sum'`, the output variable holds a scalar value.
Return type:	Variable