Method __init__

numpy_ml/nonparametric/gp.py:19–42

A Gaussian Process (GP) regression model. .. math:: y \mid X, f &\sim \mathcal{N}( [f(x_1), \ldots, f(x_n)], \\alpha I ) \\\\ f \mid X &\sim \\text{GP}(0, K) for data :math:`D = \{(x_1, y_1), \ldots, (x_n, y_n) \}` and a covariance matrix :m

(self, kernel="RBFKernel", alpha=1e-10)

class GPRegression:
    def __init__(self, kernel="RBFKernel", alpha=1e-10):
        """
        A Gaussian Process (GP) regression model.

        .. math::

            y \mid X, f  &\sim  \mathcal{N}( [f(x_1), \ldots, f(x_n)], \\alpha I ) \\\\
            f \mid X     &\sim  \\text{GP}(0, K)

        for data :math:`D = \{(x_1, y_1), \ldots, (x_n, y_n) \}` and a covariance matrix :math:`K_{ij}
        = \\text{kernel}(x_i, x_j)` for all :math:`i, j \in \{1, \ldots, n \}`.

        Parameters
        ----------
        kernel : str
            The kernel to use in fitting the GP prior. Default is 'RBFKernel'.
        alpha : float
            An isotropic noise term for the diagonal in the GP covariance, `K`.
            Larger values correspond to the expectation of greater noise in the
            observed data points. Default is 1e-10.
        """
        self.kernel = KernelInitializer(kernel)()
        self.parameters = {"GP_mean": None, "GP_cov": None, "X": None}
        self.hyperparameters = {"kernel": str(self.kernel), "alpha": alpha}

    def fit(self, X, y):
        """