tick.robust.ModelEpsilonInsensitive

class tick.robust.ModelEpsilonInsensitive(fit_intercept: bool = True, threshold: float = 1, n_threads: int = 1)[source]

Epsilon-Insensitive loss for robust regression. This class gives first order information (gradient and loss) for this model and can be passed to any solver through the solver’s set_model method.

Given training data \((x_i, y_i) \in \mathbb R^d \times \mathbb R\) 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

\[\begin{split}\ell(y, y') = \begin{cases} |y' - y| - \epsilon &\text{ if } |y' - y| > \epsilon \\ 0 &\text{ if } |y' - y| \leq \epsilon \end{cases}\end{split}\]

for \(y, y' \in \mathbb R\), where \(\epsilon > 0\) can be tuned using the threshold argument. 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

threshold : double, default=1.

Positive threshold to be used in the loss function.

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

__init__(fit_intercept: bool = True, threshold: float = 1, n_threads: int = 1)[source]

Initialize self. See help(type(self)) for accurate signature.

fit(features, labels)[source]

Set the data into the model object

Parameters

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,)

The labels vector

Returns

output : ModelEpsilonInsensitive

The current instance with given data

grad(coeffs: numpy.ndarray, out: numpy.ndarray = None) → numpy.ndarray

Computes the gradient of the model at coeffs

Parameters

coeffs : numpy.ndarray

Vector where gradient is computed

out : numpy.ndarray or None

If None a new vector containing the gradient is returned, otherwise, the result is saved in out and returned

Returns

output : numpy.ndarray

The gradient of the model at coeffs

Notes

The fit method must be called to give data to the model, before using grad. An error is raised otherwise.

loss(coeffs: numpy.ndarray) → float

Computes the value of the goodness-of-fit at coeffs

Parameters

coeffs : numpy.ndarray

The loss is computed at this point

Returns

output : float

The value of the loss

Notes

The fit method must be called to give data to the model, before using loss. An error is raised otherwise.

loss_and_grad(coeffs: numpy.ndarray, out: numpy.ndarray = None) → tuple

Computes the value and the gradient of the function at coeffs

Parameters

coeffs : numpy.ndarray

Vector where the loss and gradient are computed

out : numpy.ndarray or None

If None a new vector containing the gradient is returned, otherwise, the result is saved in out and returned

Returns

loss : float

The value of the loss

grad : numpy.ndarray

The gradient of the model at coeffs

Notes

The fit method must be called to give data to the model, before using loss_and_grad. An error is raised otherwise.

Examples using tick.robust.ModelEpsilonInsensitive