ekernels.py 文件源码

def exKxz(self, Z, Xmu, Xcov):
        """
        It computes the expectation:
        <x_t K_{x_t, Z}>_q_{x_t}
        :param Z: MxD inducing inputs
        :param Xmu: X mean (NxD)
        :param Xcov: NxDxD
        :return: NxMxD
        """

        msg_input_shape = "Currently cannot handle slicing in exKxz."
        assert_input_shape = tf.assert_equal(tf.shape(Xmu)[1], self.input_dim, message=msg_input_shape)
        assert_cov_shape = tf.assert_equal(tf.shape(Xmu), tf.shape(Xcov)[:2], name="assert_Xmu_Xcov_shape")
        with tf.control_dependencies([assert_input_shape, assert_cov_shape]):
            Xmu = tf.identity(Xmu)

        N = tf.shape(Xmu)[0]
        D = tf.shape(Xmu)[1]

        lengthscales = self.lengthscales if self.ARD else tf.zeros((D,), dtype=settings.float_type) + self.lengthscales
        scalemat = tf.expand_dims(tf.matrix_diag(lengthscales ** 2.0), 0) + Xcov  # NxDxD

        det = tf.matrix_determinant(
            tf.expand_dims(tf.eye(tf.shape(Xmu)[1], dtype=settings.float_type), 0) +
            tf.reshape(lengthscales ** -2.0, (1, 1, -1)) * Xcov)  # N

        vec = tf.expand_dims(tf.transpose(Z), 0) - tf.expand_dims(Xmu, 2)  # NxDxM
        smIvec = tf.matrix_solve(scalemat, vec)  # NxDxM
        q = tf.reduce_sum(smIvec * vec, [1])  # NxM

        addvec = tf.matmul(smIvec, Xcov, transpose_a=True) + tf.expand_dims(Xmu, 1)  # NxMxD

        return self.variance * addvec * tf.reshape(det ** -0.5, (N, 1, 1)) * tf.expand_dims(tf.exp(-0.5 * q), 2)