def main(): # Load data X = pickle.load(open(data_fn, "rb")) N, D = X.shape # Model parameters alpha = 1. K = 4 # number of components mu_scale = 3.0 covar_scale = 1.0 # Sampling parameters n_runs = 2 n_iter = 12 # Intialize prior m_0 = np.zeros(D) k_0 = covar_scale**2 / mu_scale**2 v_0 = D + 3 S_0 = covar_scale**2 * v_0 * np.eye(D) prior = NIW(m_0, k_0, v_0, S_0) # Initialize component assignment: this is not random for testing purposes z = np.array([i * np.ones(N / K) for i in range(K)], dtype=np.int).flatten() # Setup FBGMM fbgmm = FBGMM(X, prior, alpha, K, assignments=z) print("Initial log marginal prob:", fbgmm.log_marg()) # Perform several Gibbs sampling runs and average the log marginals log_margs = np.zeros(n_iter) for j in range(n_runs): # Perform Gibbs sampling record = fbgmm.gibbs_sample(n_iter) log_margs += record["log_marg"] log_margs /= n_runs # Plot results fig = plt.figure() ax = fig.add_subplot(111) plot_mixture_model(ax, fbgmm) for k in range(fbgmm.components.K): mu, sigma = fbgmm.components.rand_k(k) plot_ellipse(ax, mu, sigma) # Plot log probability plt.figure() plt.plot(list(range(n_iter)), log_margs) plt.xlabel("Iterations") plt.ylabel("Log prob") plt.show()
def gmm(X, K=4, n_iter=100, alpha=1.0, mu_scale=4.0, var_scale=0.5, covar_scale=0.7, posterior_predictive_check=False): N, D = X.shape # Initialize prior m_0 = np.zeros(D) k_0 = covar_scale**2 / mu_scale**2 v_0 = D + 3 S_0 = covar_scale**2 * v_0 * np.ones(D) prior = NIW(m_0, k_0, v_0, S_0) # Setup FBGMM fbgmm = FBGMM(X, prior, alpha, K, "rand") # Perform Gibbs sampling record = fbgmm.gibbs_sample(n_iter) K = fbgmm.components.K mus = np.zeros(shape=(K, D)) covars = [np.zeros((D, D)) for i in range(0, K)] for k in range(fbgmm.components.K): mu, var = fbgmm.components.rand_k(k) mus[k, :] = mu covars[k] = np.diag(var) # Generate new points for posterior predictive check # Generate the same number of points as N if posterior_predictive_check: np.random.seed(1) rstate = 1 alphas = (alpha / K) + fbgmm.components.counts pis = dirichlet.rvs(alphas, random_state=rstate)[0] Z = np.zeros(N, dtype=np.uint32) X = np.zeros((N, D)) for n in range(N): Z[n] = np.floor(np.argmax(multinomial(1, pis))) X[n] = multivariate_normal.rvs(mean=mus[Z[n]], cov=covars[Z[n]]) return fbgmm.components.assignments, mus, (X, Z) return fbgmm.components.assignments, mus
def test_sampling_2d_assignments(): random.seed(1) np.random.seed(1) # Data parameters D = 2 # dimensions N = 100 # number of points to generate K_true = 4 # the true number of components # Model parameters alpha = 1. K = 3 # number of components n_iter = 10 # Generate data mu_scale = 4.0 covar_scale = 0.7 z_true = np.random.randint(0, K_true, N) mu = np.random.randn(D, K_true)*mu_scale X = mu[:, z_true] + np.random.randn(D, N)*covar_scale X = X.T # Intialize prior m_0 = np.zeros(D) k_0 = covar_scale**2/mu_scale**2 v_0 = D + 3 S_0 = covar_scale**2*v_0*np.eye(D) prior = NIW(m_0, k_0, v_0, S_0) # Setup FBGMM fbgmm = FBGMM(X, prior, alpha, K, "rand") # Perform Gibbs sampling record = fbgmm.gibbs_sample(n_iter) assignments_expected = np.array([ 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 2, 1, 1, 0, 2, 2, 0, 0, 2, 1, 0, 1, 0, 0, 0, 2, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 2, 1, 2, 0, 0, 0, 2, 1, 2, 2, 1, 0, 0, 1, 0, 2, 2, 1, 2, 0, 0, 2 ]) assignments = fbgmm.components.assignments npt.assert_array_equal(assignments, assignments_expected)
def main(): # Data parameters D = 2 # dimensions N = 100 # number of points to generate K_true = 4 # the true number of components # Model parameters alpha = 1. K = 4 # number of components n_iter = 20 # Generate data mu_scale = 4.0 covar_scale = 0.7 z_true = np.random.randint(0, K_true, N) mu = np.random.randn(D, K_true) * mu_scale X = mu[:, z_true] + np.random.randn(D, N) * covar_scale X = X.T # Intialize prior var_scale = 0.5 # if you make this really small, you basically get k-means mu_0 = np.zeros(D) k_0 = covar_scale**2 / mu_scale**2 var = covar_scale**2 * np.ones(D) * var_scale var_0 = var / k_0 prior = FixedVarPrior(var, mu_0, var_0) # Setup FBGMM fbgmm = FBGMM(X, prior, alpha, K, "rand", covariance_type="fixed") # Perform Gibbs sampling record = fbgmm.gibbs_sample(n_iter) # Plot results fig = plt.figure() ax = fig.add_subplot(111) plot_mixture_model(ax, fbgmm) for k in range(fbgmm.components.K): mu = fbgmm.components.rand_k(k) sigma = np.diag(var) plot_ellipse(ax, mu, sigma) plt.show()
def test_sampling_2d_log_marg_deleted_components(): random.seed(1) np.random.seed(1) # Data parameters D = 2 # dimensions N = 10 # number of points to generate K_true = 4 # the true number of components # Model parameters alpha = 1. K = 6 # number of components n_iter = 1 # Generate data mu_scale = 4.0 covar_scale = 0.7 z_true = np.random.randint(0, K_true, N) mu = np.random.randn(D, K_true)*mu_scale X = mu[:, z_true] + np.random.randn(D, N)*covar_scale X = X.T # Intialize prior m_0 = np.zeros(D) k_0 = covar_scale**2/mu_scale**2 v_0 = D + 3 S_0 = covar_scale**2*v_0*np.eye(D) prior = NIW(m_0, k_0, v_0, S_0) # Setup FBGMM fbgmm = FBGMM(X, prior, alpha, K, "rand") # Perform Gibbs sampling record = fbgmm.gibbs_sample(n_iter) expected_log_marg = -60.1448630929 log_marg = fbgmm.log_marg() print(fbgmm.components.assignments) npt.assert_almost_equal(log_marg, expected_log_marg)
def main(): # Data parameters D = 2 # dimensions N = 100 # number of points to generate K_true = 4 # the true number of components # Model parameters alpha = 1. K = 4 # number of components n_iter = 20 # Generate data mu_scale = 4.0 covar_scale = 0.7 z_true = np.random.randint(0, K_true, N) mu = np.random.randn(D, K_true) * mu_scale X = mu[:, z_true] + np.random.randn(D, N) * covar_scale X = X.T # Intialize prior m_0 = np.zeros(D) k_0 = covar_scale**2 / mu_scale**2 v_0 = D + 3 S_0 = covar_scale**2 * v_0 * np.eye(D) prior = NIW(m_0, k_0, v_0, S_0) # Setup FBGMM fbgmm = FBGMM(X, prior, alpha, K, "rand") # Perform Gibbs sampling record = fbgmm.gibbs_sample(n_iter) # Plot results fig = plt.figure() ax = fig.add_subplot(111) plot_mixture_model(ax, fbgmm) for k in range(fbgmm.components.K): # mu, sigma = fbgmm.components.map(k) mu, sigma = fbgmm.components.rand_k(k) plot_ellipse(ax, mu, sigma) plt.show()