<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def fit(self, X, y=None):
 """ Fit the inlier model given training data. This function attempts to choose reasonable defaults for parameters sigma and rho if none are specified, which could then be adjusted to improve performance. Parameters X : array Examples of inlier data, of dimension N times d (rows are examples, columns are data dimensions) y : array, optional If the inliers have multiple classes, then y contains the class assignments as a vector of length N. If this is specified then the model will attempt to assign test data to one of the inlier classes or to the outlier class. """

        N = X.shape[0]

        if y is None:
            y = np.zeros(N)

        self.classes = list(set(y))
        self.classes.sort()
        self.n_classes = len(self.classes)

        # If no kernel parameters specified, try to choose some defaults
        if not self.sigma:
            self.sigma = median_kneighbour_distance(X)
            self.gamma = self.sigma**-2

        if not self.gamma:
            self.gamma = self.sigma**-2

        if not self.rho:
            self.rho = 0.1

        # choose kernel basis centres
        if self.kernel_pos is None:
            B = min(self.n_kernels_max, N)
            kernel_idx = np.random.permutation(N)
            self.kernel_pos = X[kernel_idx[:B]]
        else:
            B = self.kernel_pos.shape[0]

        # fit coefficients
        Phi = metrics.pairwise.rbf_kernel(X, self.kernel_pos, self.gamma)
        theta = {}
        Phi_PhiT = np.dot(Phi.T, Phi)
        inverse_term = np.linalg.inv(Phi_PhiT + self.rho*np.eye(B))
        for c in self.classes:
            m = (y == c).astype(int)
            theta[c] = np.dot(inverse_term, np.dot(Phi.T, m))

        self.theta = theta