tick.linear_model.ModelPoisReg¶

class tick.linear_model.ModelPoisReg(fit_intercept: bool = True, link: str = 'exponential', n_threads: int = 1)[source]¶

Poisson regression model with identity or exponential link for data with a count label. This class gives first order and second order information for this model (gradient, loss and hessian norm) and can be passed to any solver through the solver’s set_model method. Can lead to overflows with some solvers (see the note below).

Given training data \((x_i, y_i) \in \mathbb R^d \times \mathbb N\) for \(i=1, \ldots, n\), this model considers a goodness-of-fit

\[f(w, b) = \frac 1n \sum_{i=1}^n \ell(y_i, b + x_i^\top w),\]

where \(w \in \mathbb R^d\) is a vector containing the model-weights, \(b \in \mathbb R\) is the intercept (used only whenever fit_intercept=True) and \(\ell : \mathbb R^2 \rightarrow \mathbb R\) is the loss given by

\[\ell(y, y') = e^{y'} - y y'\]

whenever link='exponential' and

\[\ell(y, y') = y' - y \log(y')\]

whenever link='identity', for \(y \in \mathbb N\) and \(y' \in \mathbb R\). Data is passed to this model through the fit(X, y) method where X is the features matrix (dense or sparse) and y is the vector of labels.

Parameters:

fit_intercept : bool

If True, the model uses an intercept

link : str, default=”exponential”

Type of link function

• if "identity": the intensity is the inner product of the model’s coeffs with the features. In this case, one must ensure that the intensity is non-negative

• if "exponential": the intensity is the exponential of the inner product of the model’s coeffs with the features.

Note that link cannot be changed after creation of ModelPoisReg

Attributes:

features : {numpy.ndarray, scipy.sparse.csr_matrix}, shape=(n_samples, n_features)

The features matrix, either dense or sparse

labels : numpy.ndarray, shape=(n_samples,) (read-only)

The labels vector

n_samples : int (read-only)

Number of samples

n_features : int (read-only)

Number of features

n_coeffs : int (read-only)

Total number of coefficients of the model

n_threads : int, default=1 (read-only)

Number of threads used for parallel computation.

• if int <= 0: the number of threads available on the CPU

• otherwise the desired number of threads

dtype : {'float64', 'float32'}, default=’float64’

Type of the data arrays used.

Notes

The gradient and loss for the exponential link case cannot be overflow proof. In this case, only a solver working in the dual (such as SDCA) should be used.

In summary, use grad and call at your own risk when link="exponential"

Examples using tick.linear_model.ModelPoisReg¶