Method fit

numpy_ml/linear_models/linear_regression.py:172–216

r""" Fit regression coefficients via maximum likelihood. Parameters ---------- X : :py:class:`ndarray ` of shape `(N, M)` A dataset consisting of `N` examples, each of dimension `M`. y : :py:class:`ndarray ` of shape

(self, X, y, weights=None)

        beta += S_inv @ X.T @ (y - X @ beta)

    def fit(self, X, y, weights=None):
        r"""
        Fit regression coefficients via maximum likelihood.

        Parameters
        ----------
        X : :py:class:`ndarray <numpy.ndarray>` of shape `(N, M)`
            A dataset consisting of `N` examples, each of dimension `M`.
        y : :py:class:`ndarray <numpy.ndarray>` of shape `(N, K)`
            The targets for each of the `N` examples in `X`, where each target
            has dimension `K`.
        weights : :py:class:`ndarray <numpy.ndarray>` of shape `(N,)` or None
            Weights associated with the examples in `X`. Examples
            with larger weights exert greater influence on model fit.  When
            `y` is a vector (i.e., `K = 1`), weights should be set to the
            reciporical of the variance for each measurement (i.e., :math:`w_i
            = 1/\sigma^2_i`). When `K > 1`, it is assumed that all columns of
            `y` share the same weight :math:`w_i`. If None, examples are
            weighted equally, resulting in the standard linear least squares
            update.  Default is None.

        Returns
        -------
        self : :class:`LinearRegression <numpy_ml.linear_models.LinearRegression>` instance
        """  # noqa: E501
        N = X.shape[0]

        weights = np.ones(N) if weights is None else np.atleast_1d(weights)
        weights = np.squeeze(weights) if weights.size > 1 else weights
        err_str = f"weights must have shape ({N},) but got {weights.shape}"
        assert weights.shape == (N,), err_str

        # scale X and y by the weight associated with each example
        W = np.diag(np.sqrt(weights))
        X, y = W @ X, W @ y

        # convert X to a design matrix if we're fitting an intercept
        if self.fit_intercept:
            X = np.c_[np.sqrt(weights), X]

        self.sigma_inv = np.linalg.pinv(X.T @ X)
        self.beta = np.atleast_2d(self.sigma_inv @ X.T @ y)

        self._is_fit = True
        return self

    def predict(self, X):
        """