Activation functions¶

statinf.ml.activations.elu(x, alpha=1.0)[source]¶

Exponential Linear Unit activation function.

Parameters

x (float or numpy.array) – Input value

Formula

\[\begin{split}\mathrm{elu}(x) = \begin{cases} x, & x > 0\\ \alpha \left(e^{x} - 1\right), & x \le 0 \end{cases}\end{split}\]

Returns

Activated value.

Return type

float

statinf.ml.activations.logit(x, weights, bias=0)[source]¶

Logistic function

Parameters

• x (numpy.array) – Input value

• weights (numpy.array) – Vector of weights \(\beta\)

• bias (numpy.array) – Vector of bias \(\epsilon\), defaults to 0.

Returns

Logistic transformation: \(\mathrm{logit}(x, \beta) = \dfrac{1}{1 + e^{-x \beta}}\)

Return type

float

statinf.ml.activations.relu(x)[source]¶

Rectified Linear Unit activation function.

Parameters

x (float or numpy.array) – Input value

Returns

Activated value: \(\mathrm{relu}(x) = \max(0, x)\)

Return type

float

statinf.ml.activations.sigmoid(x)[source]¶

Sigmoid activation function.

Parameters

x (float or numpy.array) – Input value

Returns

Sigmoid activated value: \(sigmoid(x) = \dfrac{1}{1 + e^{-x}}\)

Return type

float

statinf.ml.activations.softmax(x, axis=- 1)[source]¶

Softmax activation function.

Parameters

x (float or numpy.array) – Input value

Returns

Activated value: \(\mathrm{softmax}(x) = \frac{\exp(x_i)}{\sum_j \exp(x_j)}\)

Return type

float

statinf.ml.activations.softplus(x)[source]¶

Softplus activation function.

Parameters

x (float or numpy.array) – Input value

Returns

Activated value: \(\mathrm{softplus}(x) = \log(1 + e^{-x})\)

Return type

float

statinf.ml.activations.tanh(x)[source]¶

Hyperbolic tangent activation function.

Parameters

x (float or numpy.array) – Input value

Returns

Activated value: \(\tanh(x)\)

Return type

float