losses

losses

Functions

Name	Description
L1_entropy	Entropy of the basis \(\phi\).
L1_norm	L1 norm of the basis \(\phi\).
mae	Mean absolute error
mse	Mean squared error
rmse	Root mean squared error
total_loss	Total loss function.

L1_entropy

losses.L1_entropy(L1_norm)

Entropy of the basis \(\phi\).

\[ - \sum_{i=1}^{N} \phi_i \log \left( \phi_i \right) \]

Parameters

Name	Type	Description	Default
L1_norm	Array	L1 norm of the basis with shape (\(N\),)	required

Returns

Name	Type	Description
Array	Array	entropy of the basis with shape (\(N\),)

L1_norm

losses.L1_norm(phi)

L1 norm of the basis \(\phi\).

Parameters

Name	Type	Description	Default
phi	Array	basis with shape (\(D\), \(N\))	required

Returns

Name	Type	Description
Array	Array	L1 norm of the basis with shape (\(N\),)

mae

losses.mae(y_train, y_pred)

Mean absolute error

\[ \mathrm{MAE} = \frac{1}{D} \sum_{i=1}^D |y_i - \hat{y}_i| \]

Parameters

Name	Type	Description	Default
y_train	Array	target value with shape (D, 1)	required
y_pred	Array	prediction with shape (D, 1)	required

Returns

Name	Type	Description
Array	Array	mean absolute error with shape (1,)

mse

losses.mse(y_train, y_pred)

Mean squared error

\[ \mathrm{MSE} = \frac{1}{D} \sum_{i=1}^D (y_i - \hat{y}_i)^2 \]

Parameters

Name	Type	Description	Default
y_train	Array	target value with shape (D, 1)	required
y_pred	Array	prediction with shape (D, 1)	required

Returns

Name	Type	Description
Array	Array	mean squared error with shape (1,)

rmse

losses.rmse(y_train, y_pred)

Root mean squared error

\[ \mathrm{RMSE} = \sqrt{\frac{1}{D} \sum_{i=1}^D (y_i - \hat{y}_i)^2} \]

Parameters

Name	Type	Description	Default
y_train	Array	target value with shape (D, 1)	required
y_pred	Array	prediction with shape (D, 1)	required

Returns

Name	Type	Description
Array	Array	root mean squared error with shape (1,)

total_loss

losses.total_loss(y_train, y_pred, basis, lambda1=0.01, mu1=1.0, mu2=1.0)

Total loss function.

\[ \mathrm{total\_loss} = \mathrm{MSE} + \lambda (\mu_1 \mathrm{L1\_entropy} + \mu_2 \mathrm{L1\_entropy}) \]

Parameters

Name	Type	Description	Default
y_train	Array	target value with shape (D, 1)	required
y_pred	Array	prediction with shape (D, 1)	required
basis	list[Array]	basis with shape (D, N)	required

Returns

Name	Type	Description
Array	Array	total loss with shape (1,)