# theanets.losses.MeanSquaredError¶

class theanets.losses.MeanSquaredError(target, weight=1.0, weighted=False, output_name='out')

Mean-squared-error (MSE) loss function.

Notes

The mean squared error (MSE) loss computes the mean of the squared difference between the output of a computation graph $$x = (x_1, \dots, x_d)$$ and its expected target value $$t = (t_1, \dots, t_d)$$. Mathematically,

$\begin{split}\begin{eqnarray*} \mathcal{L}(x, t) &=& \frac{1}{d} \|x - t\|_2^2 \\ &=& \frac{1}{d} \sum_{i=1}^d (x_i - t_i)^2 \end{eqnarray*}\end{split}$

Whereas some MSE computations return the sum over dimensions, the MSE here is computed as an average over the dimensionality of the data.

For cases where $$x$$ and $$t$$ are matrices, the MSE computes the average over corresponding rows in $$x$$ and $$t$$:

$\mathcal{L}(X, T) = \frac{1}{dm} \sum_{j=1}^m \sum_{i=1}^d (x_{ji} - t_{ji})^2$
__init__(target, weight=1.0, weighted=False, output_name='out')

Methods

 __init__(target[, weight, weighted, output_name]) log() Log some diagnostic info about this loss.

Attributes

 variables A list of Theano variables used in this loss.