sgpr.py 文件源码

def compute_upper_bound(self):
        num_data = tf.cast(tf.shape(self.Y)[0], settings.float_type)

        Kdiag = self.kern.Kdiag(self.X)
        Kuu = self.feature.Kuu(self.kern, jitter=settings.numerics.jitter_level)
        Kuf = self.feature.Kuf(self.kern, self.X)

        L = tf.cholesky(Kuu)
        LB = tf.cholesky(Kuu + self.likelihood.variance ** -1.0 * tf.matmul(Kuf, Kuf, transpose_b=True))

        LinvKuf = tf.matrix_triangular_solve(L, Kuf, lower=True)
        # Using the Trace bound, from Titsias' presentation
        c = tf.reduce_sum(Kdiag) - tf.reduce_sum(LinvKuf ** 2.0)
        # Kff = self.kern.K(self.X)
        # Qff = tf.matmul(Kuf, LinvKuf, transpose_a=True)

        # Alternative bound on max eigenval:
        # c = tf.reduce_max(tf.reduce_sum(tf.abs(Kff - Qff), 0))
        corrected_noise = self.likelihood.variance + c

        const = -0.5 * num_data * tf.log(2 * np.pi * self.likelihood.variance)
        logdet = tf.reduce_sum(tf.log(tf.diag_part(L))) - tf.reduce_sum(tf.log(tf.diag_part(LB)))

        LC = tf.cholesky(Kuu + corrected_noise ** -1.0 * tf.matmul(Kuf, Kuf, transpose_b=True))
        v = tf.matrix_triangular_solve(LC, corrected_noise ** -1.0 * tf.matmul(Kuf, self.Y), lower=True)
        quad = -0.5 * corrected_noise ** -1.0 * tf.reduce_sum(self.Y ** 2.0) + 0.5 * tf.reduce_sum(v ** 2.0)

        return const + logdet + quad