Beispiel #1
0
    def test_riemannian_gradient(self):
        """Test Riemannian gradient of a Gamma node."""

        #
        # Without observations
        #

        # Construct model
        a = np.random.rand()
        b = np.random.rand()
        tau = Gamma(a, b)
        # Random initialization
        tau.initialize_from_parameters(np.random.rand(),
                                       np.random.rand())
        # Initial parameters
        phi0 = tau.phi
        # Gradient
        g = tau.get_riemannian_gradient()
        # Parameters after VB-EM update
        tau.update()
        phi1 = tau.phi
        # Check
        self.assertAllClose(g[0],
                            phi1[0] - phi0[0])
        self.assertAllClose(g[1],
                            phi1[1] - phi0[1])

        #
        # With observations
        #

        # Construct model
        a = np.random.rand()
        b = np.random.rand()
        tau = Gamma(a, b)
        mu = np.random.randn()
        Y = GaussianARD(mu, tau)
        Y.observe(np.random.randn())
        # Random initialization
        tau.initialize_from_parameters(np.random.rand(),
                                       np.random.rand())
        # Initial parameters
        phi0 = tau.phi
        # Gradient
        g = tau.get_riemannian_gradient()
        # Parameters after VB-EM update
        tau.update()
        phi1 = tau.phi
        # Check
        self.assertAllClose(g[0],
                            phi1[0] - phi0[0])
        self.assertAllClose(g[1],
                            phi1[1] - phi0[1])

        pass
Beispiel #2
0
    def test_gradient(self):
        """Test standard gradient of a Gamma node."""
        D = 3

        np.random.seed(42)

        #
        # Without observations
        #

        # Construct model
        a = np.random.rand(D)
        b = np.random.rand(D)
        tau = Gamma(a, b)
        Q = VB(tau)
        # Random initialization
        tau.initialize_from_parameters(np.random.rand(D),
                                       np.random.rand(D))
        # Initial parameters
        phi0 = tau.phi
        # Gradient
        rg = tau.get_riemannian_gradient()
        g = tau.get_gradient(rg)
        # Numerical gradient
        eps = 1e-8
        p0 = tau.get_parameters()
        l0 = Q.compute_lowerbound(ignore_masked=False)
        g_num = [np.zeros(D), np.zeros(D)]
        for i in range(D):
            e = np.zeros(D)
            e[i] = eps
            p1 = p0[0] + e
            tau.set_parameters([p1, p0[1]])
            l1 = Q.compute_lowerbound(ignore_masked=False)
            g_num[0][i] = (l1 - l0) / eps
        for i in range(D):
            e = np.zeros(D)
            e[i] = eps
            p1 = p0[1] + e
            tau.set_parameters([p0[0], p1])
            l1 = Q.compute_lowerbound(ignore_masked=False)
            g_num[1][i] = (l1 - l0) / eps

        # Check
        self.assertAllClose(g[0],
                            g_num[0])
        self.assertAllClose(g[1],
                            g_num[1])

        #
        # With observations
        #

        # Construct model
        a = np.random.rand(D)
        b = np.random.rand(D)
        tau = Gamma(a, b)
        mu = np.random.randn(D)
        Y = GaussianARD(mu, tau)
        Y.observe(np.random.randn(D))
        Q = VB(Y, tau)
        # Random initialization
        tau.initialize_from_parameters(np.random.rand(D),
                                       np.random.rand(D))
        # Initial parameters
        phi0 = tau.phi
        # Gradient
        rg = tau.get_riemannian_gradient()
        g = tau.get_gradient(rg)
        # Numerical gradient
        eps = 1e-8
        p0 = tau.get_parameters()
        l0 = Q.compute_lowerbound(ignore_masked=False)
        g_num = [np.zeros(D), np.zeros(D)]
        for i in range(D):
            e = np.zeros(D)
            e[i] = eps
            p1 = p0[0] + e
            tau.set_parameters([p1, p0[1]])
            l1 = Q.compute_lowerbound(ignore_masked=False)
            g_num[0][i] = (l1 - l0) / eps
        for i in range(D):
            e = np.zeros(D)
            e[i] = eps
            p1 = p0[1] + e
            tau.set_parameters([p0[0], p1])
            l1 = Q.compute_lowerbound(ignore_masked=False)
            g_num[1][i] = (l1 - l0) / eps

        # Check
        self.assertAllClose(g[0],
                            g_num[0])
        self.assertAllClose(g[1],
                            g_num[1])

        pass