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Additions to week2 MLAI.
This commit is contained in:
Neil Lawrence
parent
fb3946aa0a
commit
765e808c2b
3 changed files with 62 additions and 47 deletions
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@ -10,10 +10,11 @@ except:
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pass
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import numpy as np
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import GPy
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import pods
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def olympic_marathon_men(optimize=True, plot=True):
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"""Run a standard Gaussian process regression on the Olympic marathon data."""
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data = GPy.util.datasets.olympic_marathon_men()
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data = pods.datasets.olympic_marathon_men()
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# create simple GP Model
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m = GPy.models.GPRegression(data['X'], data['Y'])
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@ -82,7 +83,7 @@ def epomeo_gpx(max_iters=200, optimize=True, plot=True):
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from the Mount Epomeo runs. Requires gpxpy to be installed on your system
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to load in the data.
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"""
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data = GPy.util.datasets.epomeo_gpx()
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data = pods.datasets.epomeo_gpx()
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num_data_list = []
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for Xpart in data['X']:
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num_data_list.append(Xpart.shape[0])
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@ -107,9 +108,9 @@ def epomeo_gpx(max_iters=200, optimize=True, plot=True):
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k = k1**k2
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m = GPy.models.SparseGPRegression(t, Y, kernel=k, Z=Z, normalize_Y=True)
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m.constrain_fixed('.*rbf_var', 1.)
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m.constrain_fixed('iip')
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m.constrain_bounded('noise_variance', 1e-3, 1e-1)
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m.constrain_fixed('.*variance', 1.)
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m.inducing_inputs.constrain_fixed()
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m.Gaussian_noise.variance.constrain_bounded(1e-3, 1e-1)
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m.optimize(max_iters=max_iters,messages=True)
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return m
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@ -125,7 +126,7 @@ def multiple_optima(gene_number=937, resolution=80, model_restarts=10, seed=1000
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length_scales = np.linspace(0.1, 60., resolution)
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log_SNRs = np.linspace(-3., 4., resolution)
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data = GPy.util.datasets.della_gatta_TRP63_gene_expression(data_set='della_gatta',gene_number=gene_number)
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data = pods.datasets.della_gatta_TRP63_gene_expression(data_set='della_gatta',gene_number=gene_number)
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# data['Y'] = data['Y'][0::2, :]
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# data['X'] = data['X'][0::2, :]
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@ -151,16 +152,16 @@ def multiple_optima(gene_number=937, resolution=80, model_restarts=10, seed=1000
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kern = GPy.kern.RBF(1, variance=np.random.uniform(1e-3, 1), lengthscale=np.random.uniform(5, 50))
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m = GPy.models.GPRegression(data['X'], data['Y'], kernel=kern)
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m['noise_variance'] = np.random.uniform(1e-3, 1)
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optim_point_x[0] = m['rbf_lengthscale']
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optim_point_y[0] = np.log10(m['rbf_variance']) - np.log10(m['noise_variance']);
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m.Gaussian_noise.variance = np.random.uniform(1e-3, 1)
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optim_point_x[0] = m.rbf.lengthscale
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optim_point_y[0] = np.log10(m.rbf.variance) - np.log10(m.Gaussian_noise.variance);
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# optimize
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if optimize:
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m.optimize('scg', xtol=1e-6, ftol=1e-6, max_iters=max_iters)
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optim_point_x[1] = m['rbf_lengthscale']
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optim_point_y[1] = np.log10(m['rbf_variance']) - np.log10(m['noise_variance']);
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optim_point_x[1] = m.rbf.lengthscale
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optim_point_y[1] = np.log10(m.rbf.variance) - np.log10(m.Gaussian_noise.variance);
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if plot:
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pb.arrow(optim_point_x[0], optim_point_y[0], optim_point_x[1] - optim_point_x[0], optim_point_y[1] - optim_point_y[0], label=str(i), head_length=1, head_width=0.5, fc='k', ec='k')
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@ -191,7 +192,7 @@ def _contour_data(data, length_scales, log_SNRs, kernel_call=GPy.kern.RBF):
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noise_var = total_var / (1. + SNR)
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signal_var = total_var - noise_var
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model.kern['.*variance'] = signal_var
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model['noise_variance'] = noise_var
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model.Gaussian_noise.variance = noise_var
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length_scale_lls = []
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for length_scale in length_scales:
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@ -205,13 +206,13 @@ def _contour_data(data, length_scales, log_SNRs, kernel_call=GPy.kern.RBF):
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def olympic_100m_men(optimize=True, plot=True):
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"""Run a standard Gaussian process regression on the Rogers and Girolami olympics data."""
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data = GPy.util.datasets.olympic_100m_men()
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data = pods.datasets.olympic_100m_men()
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# create simple GP Model
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m = GPy.models.GPRegression(data['X'], data['Y'])
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# set the lengthscale to be something sensible (defaults to 1)
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m['rbf_lengthscale'] = 10
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m.rbf.lengthscale = 10
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if optimize:
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m.optimize('bfgs', max_iters=200)
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@ -222,7 +223,7 @@ def olympic_100m_men(optimize=True, plot=True):
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def toy_rbf_1d(optimize=True, plot=True):
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"""Run a simple demonstration of a standard Gaussian process fitting it to data sampled from an RBF covariance."""
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data = GPy.util.datasets.toy_rbf_1d()
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data = pods.datasets.toy_rbf_1d()
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# create simple GP Model
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m = GPy.models.GPRegression(data['X'], data['Y'])
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@ -236,7 +237,7 @@ def toy_rbf_1d(optimize=True, plot=True):
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def toy_rbf_1d_50(optimize=True, plot=True):
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"""Run a simple demonstration of a standard Gaussian process fitting it to data sampled from an RBF covariance."""
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data = GPy.util.datasets.toy_rbf_1d_50()
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data = pods.datasets.toy_rbf_1d_50()
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# create simple GP Model
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m = GPy.models.GPRegression(data['X'], data['Y'])
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@ -303,12 +304,11 @@ def toy_ARD(max_iters=1000, kernel_type='linear', num_samples=300, D=4, optimize
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# m.set_prior('.*lengthscale',len_prior)
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if optimize:
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m.optimize(optimizer='scg', max_iters=max_iters, messages=1)
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m.optimize(optimizer='scg', max_iters=max_iters)
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if plot:
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m.kern.plot_ARD()
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print m
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return m
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def toy_ARD_sparse(max_iters=1000, kernel_type='linear', num_samples=300, D=4, optimize=True, plot=True):
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@ -343,24 +343,23 @@ def toy_ARD_sparse(max_iters=1000, kernel_type='linear', num_samples=300, D=4, o
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# m.set_prior('.*lengthscale',len_prior)
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if optimize:
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m.optimize(optimizer='scg', max_iters=max_iters, messages=1)
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m.optimize(optimizer='scg', max_iters=max_iters)
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if plot:
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m.kern.plot_ARD()
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print m
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return m
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def robot_wireless(max_iters=100, kernel=None, optimize=True, plot=True):
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"""Predict the location of a robot given wirelss signal strength readings."""
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data = GPy.util.datasets.robot_wireless()
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data = pods.datasets.robot_wireless()
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# create simple GP Model
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m = GPy.models.GPRegression(data['Y'], data['X'], kernel=kernel)
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# optimize
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if optimize:
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m.optimize(messages=True, max_iters=max_iters)
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m.optimize(max_iters=max_iters)
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Xpredict = m.predict(data['Ytest'])[0]
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if plot:
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@ -372,13 +371,12 @@ def robot_wireless(max_iters=100, kernel=None, optimize=True, plot=True):
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sse = ((data['Xtest'] - Xpredict)**2).sum()
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print m
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print('Sum of squares error on test data: ' + str(sse))
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return m
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def silhouette(max_iters=100, optimize=True, plot=True):
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"""Predict the pose of a figure given a silhouette. This is a task from Agarwal and Triggs 2004 ICML paper."""
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data = GPy.util.datasets.silhouette()
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data = pods.datasets.silhouette()
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# create simple GP Model
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m = GPy.models.GPRegression(data['X'], data['Y'])
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@ -390,7 +388,7 @@ def silhouette(max_iters=100, optimize=True, plot=True):
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print m
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return m
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def sparse_GP_regression_1D(num_samples=400, num_inducing=5, max_iters=100, optimize=True, plot=True, checkgrad=True):
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def sparse_GP_regression_1D(num_samples=400, num_inducing=5, max_iters=100, optimize=True, plot=True, checkgrad=False):
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"""Run a 1D example of a sparse GP regression."""
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# sample inputs and outputs
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X = np.random.uniform(-3., 3., (num_samples, 1))
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@ -401,10 +399,10 @@ def sparse_GP_regression_1D(num_samples=400, num_inducing=5, max_iters=100, opti
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m = GPy.models.SparseGPRegression(X, Y, kernel=rbf, num_inducing=num_inducing)
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if checkgrad:
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m.checkgrad(verbose=1)
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m.checkgrad()
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if optimize:
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m.optimize('tnc', messages=1, max_iters=max_iters)
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m.optimize('tnc', max_iters=max_iters)
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if plot:
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m.plot()
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