adelie.glm.binomial#

adelie.glm.binomial(y: ndarray, *, weights: ndarray | None = None, link: str = 'logit', dtype: float32 | float64 | None = None)[source]#

Creates a Binomial GLM family object.

The Binomial GLM family with the logit link function specifies the loss function as:

\begin{array}{r} ℓ (η) = \sum_{i = 1}^{n} w_{i} (- y_{i} η_{i} + \log (1 + e^{η_{i}})) \end{array}

The link function is given by

\begin{aligned} g (μ)_{i} & = \log (\frac{μ_{i}}{1 - μ_{i}}) \end{aligned}

The Binomial GLM family with the probit link function specifies the loss function as:

\begin{array}{r} ℓ (η) = - \sum_{i = 1}^{n} w_{i} (y_{i} \log (Φ (η_{i})) + (1 - y_{i}) \log (1 - Φ (η_{i}))) \end{array}

where $Φ$ is the standard normal CDF. The link function is given by

\begin{aligned} g (μ)_{i} & = Φ^{- 1} (μ_{i}) \end{aligned}

We assume that $y_{i} \in [0, 1]$ .

Parameters:

y(n,) ndarray

Response vector $y$ .

weights(n,) ndarray, optional

Observation weights $W$ . Weights are normalized such that they sum to 1. Default is None, in which case, it is set to np.full(n, 1/n).

linkstr, optional

The link function type. It must be one of the following:

"logit": the logit link function.

"probit": the probit link function.

Default is "logit".

dtypeUnion[float32, float64], optional

The underlying data type. If None, it is inferred from y, in which case y must have an underlying data type of numpy.float32 or numpy.float64. Default is None.

Returns:

glm: Binomial GLM object.