def callback(params):
        print("Log likelihood {}".format(-objective(params)))
        plt.cla()

        # Show posterior marginals.
        plot_xs = np.reshape(np.linspace(-7, 7, 300), (300,1))
        pred_mean, pred_cov = predict(params, X, y, plot_xs)
        marg_std = np.sqrt(np.diag(pred_cov))
        ax.plot(plot_xs, pred_mean, 'b')
        ax.fill(np.concatenate([plot_xs, plot_xs[::-1]]),
                np.concatenate([pred_mean - 1.96 * marg_std,
                               (pred_mean + 1.96 * marg_std)[::-1]]),
                alpha=.15, fc='Blue', ec='None')

        # Show samples from posterior.
        rs = npr.RandomState(0)
        sampled_funcs = rs.multivariate_normal(pred_mean, pred_cov, size=10)
        ax.plot(plot_xs, sampled_funcs.T)

        ax.plot(X, y, 'kx')
        ax.set_ylim([-1.5, 1.5])
        ax.set_xticks([])
        ax.set_yticks([])
        plt.draw()
        plt.pause(1.0/60.0)
    def callback(params, t, g):
        print("Iteration {} lower bound {}".format(t, -objective(params, t)))

        plt.cla()
        target_distribution = lambda x: np.exp(log_posterior(x, t))
        plot_isocontours(ax, target_distribution)

        mean, log_std = unpack_params(params)
        variational_contour = lambda x: mvn.pdf(x, mean, np.diag(np.exp(2 * log_std)))
        plot_isocontours(ax, variational_contour)
        plt.draw()
        plt.pause(1.0 / 30.0)
示例#3
0
 def unpack_params(params):
     """Unpacks parameter vector into the proportions, means and covariances
     of each mixture component.  The covariance matrices are parametrized by
     their Cholesky decompositions."""
     log_proportions    = parser.get(params, 'log proportions')
     normalized_log_proportions = log_proportions - logsumexp(log_proportions)
     means              = parser.get(params, 'means')
     lower_tris = np.tril(parser.get(params, 'lower triangles'), k=-1)
     diag_chols = np.exp( parser.get(params, 'log diagonals'))
     chols = []
     for lower_tri, diag in zip(lower_tris, diag_chols):
         chols.append(np.expand_dims(lower_tri + np.diag(diag), 0))
     chols = np.concatenate(chols, axis=0)
     return normalized_log_proportions, means, chols