Пример #1
0
def experiment_kiss(dataset=PUMADYN32NM, m=100, proj_d=2, cov='covSEard', standardize=True, proj=None):
    assert proj in {None, 'norm', 'orth'}
    train_x, train_y, test_x, test_y = load_dataset(dataset)
    if standardize:
        scaler = StandardScaler()
        train_x = scaler.fit_transform(train_x)
        test_x = scaler.transform(test_x)

    n, d = train_x.shape
    print 'Train KISS with {} data points and {} dimension'.format(n, d)
    # get GP functionality
    gp = GaussianProcess()
    # subtract mean
    train_y -= np.mean(train_y)
    test_y -= np.mean(train_y)
    # projection matrix
    P = np.random.normal(size=(proj_d, d))
    # initialization
    hyp_lik = float(0.5 * np.log(np.var(train_y) / 4))
    if cov == 'covSEard':
        init_x = np.dot(train_x, P.T)
        init_ell = np.log((np.max(init_x, axis=0) - np.min(init_x, axis=0)) / 2)
        hyp_cov = np.append(init_ell, [0.5 * np.log(np.var(train_y))])
    else:
        hyp_cov = np.asarray([np.log(5), 0.5 * np.log(np.var(train_y))])

    hyp_old = {'mean': [], 'lik': hyp_lik, 'cov': hyp_cov, 'proj': P}
    opt = {'cg_maxit': 500, 'cg_tol': 1e-5}
    if proj is not None:
        opt['proj'] = proj
    hyp = gp.train_kiss(train_x, train_y.reshape(-1, 1), k=m, hyp=hyp_old, opt=opt, n_iter=100)
    test_mean, test_var = gp.predict_kiss(train_x, train_y.reshape(-1, 1), k=m, xstar=test_x, opt=opt, hyp=hyp, cov=cov)

    print 'KISS error:'
    print_error(test_y, test_mean)
Пример #2
0
def experiment1D():
    gp = GaussianProcess()
    # setup data
    n = 500
    m = 50
    f = lambda x: np.sin(x) * np.exp(-x**2 / 50)
    X = np.random.uniform(-10, 10, size=n)
    X = np.sort(X)
    y = f(X) + np.random.normal(0, 1, size=n)
    y -= np.mean(y)

    x_min, x_max = np.min(X), np.max(X)
    U = np.linspace(x_min, x_max, m).reshape(-1, 1)

    X = X.reshape(-1, 1)
    hyp_cov = np.asarray([np.log(1), np.log(2)])
    hyp_lik = float(np.log(1))
    hyp_old = {'mean': [], 'lik': hyp_lik, 'cov': hyp_cov}
    hyp = gp.train_exact(X, y.reshape(-1, 1), hyp_old)
    hyp_cov = hyp['cov'][0]
    sigmasq = np.exp(2 * hyp['lik'])
    kernel = SEiso()
    distill = Distillation(X=X,
                           y=y,
                           U=U,
                           kernel=kernel,
                           hyp=hyp_cov,
                           num_iters=10,
                           eta=5e-4,
                           sigmasq=sigmasq,
                           width=3,
                           use_kmeans=True,
                           optimizer='sgd')
    distill.grad_descent()
    distill.precompute(use_true_K=False)

    xx = np.linspace(x_min, x_max, 2 * n)
    mm_true, vv_true = gp.predict_exact(X,
                                        y.reshape(-1, 1),
                                        xx.reshape(-1, 1),
                                        hyp=hyp)

    mm = []
    vv = []

    opt = {'cg_maxit': 500, 'cg_tol': 1e-5}
    k = n / 2
    hyp = gp.train_kiss(X, y.reshape(-1, 1), k, hyp=hyp_old, opt=opt)
    mm_kiss, vv_kiss = gp.predict_kiss(X,
                                       y.reshape(-1, 1),
                                       xx.reshape(-1, 1),
                                       k,
                                       hyp=hyp,
                                       opt=opt)

    for xstar in xx:
        xstar = np.asarray([xstar])
        mstar, vstar = distill.predict(xstar, width=3)
        vv.append(vstar)
        mm.append(mstar)

    mm = np.asarray(mm).flatten()
    vv = np.asarray(vv).flatten()
    mm_kiss = np.asarray(mm_kiss).flatten()
    vv_kiss = np.asarray(vv_kiss).flatten()

    plt.fill_between(xx,
                     mm - np.sqrt(vv) * 2,
                     mm + np.sqrt(vv) * 2,
                     color='gray',
                     alpha=.5)
    plt.plot(xx, mm_true, color='y', lw=3, label='exact mean')
    plt.plot(xx, mm, color='r', lw=3, label='distill mean', ls='dotted')
    plt.plot(xx, mm_kiss, color='g', lw=3, label='kiss mean', ls=':')
    plt.plot(xx, f(xx), lw=3, label='true value', ls='dashed')
    plt.scatter(X, y, color='m', label='train data', marker='+')
    plt.xlim([x_min, x_max])
    plt.legend()
    plt.show()

    plt.plot(xx, vv_kiss, color='g', lw=3, label='kiss var', ls=':')
    plt.plot(xx, vv_true, color='y', lw=3, label='exact var')
    plt.plot(xx, vv, color='r', lw=3, label='distill var', ls='dotted')
    plt.xlim([x_min, x_max])
    plt.legend()
    plt.show()