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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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@ -6,6 +6,7 @@
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Gaussian Processes classification
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"""
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import GPy
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import pods
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try:
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import pylab as pb
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@ -19,7 +20,7 @@ def oil(num_inducing=50, max_iters=100, kernel=None, optimize=True, plot=True):
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Run a Gaussian process classification on the three phase oil data. The demonstration calls the basic GP classification model and uses EP to approximate the likelihood.
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"""
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data = GPy.util.datasets.oil()
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data = pods.datasets.oil()
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X = data['X']
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Xtest = data['Xtest']
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Y = data['Y'][:, 0:1]
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@ -54,7 +55,7 @@ def toy_linear_1d_classification(seed=default_seed, optimize=True, plot=True):
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"""
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data = GPy.util.datasets.toy_linear_1d_classification(seed=seed)
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data = pods.datasets.toy_linear_1d_classification(seed=seed)
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Y = data['Y'][:, 0:1]
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Y[Y.flatten() == -1] = 0
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@ -87,7 +88,7 @@ def toy_linear_1d_classification_laplace(seed=default_seed, optimize=True, plot=
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"""
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data = GPy.util.datasets.toy_linear_1d_classification(seed=seed)
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data = pods.datasets.toy_linear_1d_classification(seed=seed)
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Y = data['Y'][:, 0:1]
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Y[Y.flatten() == -1] = 0
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@ -123,7 +124,7 @@ def sparse_toy_linear_1d_classification(num_inducing=10, seed=default_seed, opti
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"""
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data = GPy.util.datasets.toy_linear_1d_classification(seed=seed)
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data = pods.datasets.toy_linear_1d_classification(seed=seed)
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Y = data['Y'][:, 0:1]
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Y[Y.flatten() == -1] = 0
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@ -153,7 +154,7 @@ def toy_heaviside(seed=default_seed, optimize=True, plot=True):
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"""
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data = GPy.util.datasets.toy_linear_1d_classification(seed=seed)
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data = pods.datasets.toy_linear_1d_classification(seed=seed)
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Y = data['Y'][:, 0:1]
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Y[Y.flatten() == -1] = 0
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@ -190,7 +191,7 @@ def crescent_data(model_type='Full', num_inducing=10, seed=default_seed, kernel=
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:param kernel: kernel to use in the model
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:type kernel: a GPy kernel
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"""
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data = GPy.util.datasets.crescent_data(seed=seed)
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data = pods.datasets.crescent_data(seed=seed)
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Y = data['Y']
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Y[Y.flatten()==-1] = 0
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@ -1,6 +1,7 @@
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# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
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# Licensed under the BSD 3-clause license (see LICENSE.txt)
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import numpy as _np
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#default_seed = _np.random.seed(123344)
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def bgplvm_test_model(optimize=False, verbose=1, plot=False, output_dim=200, nan=False):
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@ -68,7 +69,8 @@ def bgplvm_test_model(optimize=False, verbose=1, plot=False, output_dim=200, nan
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def gplvm_oil_100(optimize=True, verbose=1, plot=True):
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import GPy
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data = GPy.util.datasets.oil_100()
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import pods
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data = pods.datasets.oil_100()
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Y = data['X']
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# create simple GP model
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kernel = GPy.kern.RBF(6, ARD=True) + GPy.kern.Bias(6)
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@ -80,8 +82,10 @@ def gplvm_oil_100(optimize=True, verbose=1, plot=True):
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def sparse_gplvm_oil(optimize=True, verbose=0, plot=True, N=100, Q=6, num_inducing=15, max_iters=50):
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import GPy
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import pods
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_np.random.seed(0)
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data = GPy.util.datasets.oil()
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data = pods.datasets.oil()
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Y = data['X'][:N]
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Y = Y - Y.mean(0)
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Y /= Y.std(0)
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@ -98,7 +102,7 @@ def sparse_gplvm_oil(optimize=True, verbose=0, plot=True, N=100, Q=6, num_induci
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def swiss_roll(optimize=True, verbose=1, plot=True, N=1000, num_inducing=25, Q=4, sigma=.2):
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import GPy
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from GPy.util.datasets import swiss_roll_generated
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from pods.datasets import swiss_roll_generated
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from GPy.models import BayesianGPLVM
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data = swiss_roll_generated(num_samples=N, sigma=sigma)
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@ -157,9 +161,10 @@ def bgplvm_oil(optimize=True, verbose=1, plot=True, N=200, Q=7, num_inducing=40,
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import GPy
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from matplotlib import pyplot as plt
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import numpy as np
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import pods
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_np.random.seed(0)
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data = GPy.util.datasets.oil()
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data = pods.datasets.oil()
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kernel = GPy.kern.RBF(Q, 1., 1./_np.random.uniform(0,1,(Q,)), ARD=True)# + GPy.kern.Bias(Q, _np.exp(-2))
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Y = data['X'][:N]
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@ -182,9 +187,10 @@ def bgplvm_oil(optimize=True, verbose=1, plot=True, N=200, Q=7, num_inducing=40,
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def ssgplvm_oil(optimize=True, verbose=1, plot=True, N=200, Q=7, num_inducing=40, max_iters=1000, **k):
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import GPy
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from matplotlib import pyplot as plt
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import pods
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_np.random.seed(0)
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data = GPy.util.datasets.oil()
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data = pods.datasets.oil()
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kernel = GPy.kern.RBF(Q, 1., 1./_np.random.uniform(0,1,(Q,)), ARD=True)# + GPy.kern.Bias(Q, _np.exp(-2))
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Y = data['X'][:N]
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@ -441,8 +447,9 @@ def mrd_simulation_missing_data(optimize=True, verbose=True, plot=True, plot_sim
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def brendan_faces(optimize=True, verbose=True, plot=True):
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import GPy
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import pods
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data = GPy.util.datasets.brendan_faces()
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data = pods.datasets.brendan_faces()
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Q = 2
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Y = data['Y']
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Yn = Y - Y.mean()
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@ -465,8 +472,9 @@ def brendan_faces(optimize=True, verbose=True, plot=True):
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def olivetti_faces(optimize=True, verbose=True, plot=True):
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import GPy
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import pods
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data = GPy.util.datasets.olivetti_faces()
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data = pods.datasets.olivetti_faces()
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Q = 2
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Y = data['Y']
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Yn = Y - Y.mean()
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@ -486,7 +494,9 @@ def olivetti_faces(optimize=True, verbose=True, plot=True):
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def stick_play(range=None, frame_rate=15, optimize=False, verbose=True, plot=True):
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import GPy
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data = GPy.util.datasets.osu_run1()
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import pods
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data = pods.datasets.osu_run1()
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# optimize
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if range == None:
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Y = data['Y'].copy()
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@ -501,8 +511,9 @@ def stick_play(range=None, frame_rate=15, optimize=False, verbose=True, plot=Tru
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def stick(kernel=None, optimize=True, verbose=True, plot=True):
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from matplotlib import pyplot as plt
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import GPy
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import pods
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data = GPy.util.datasets.osu_run1()
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data = pods.datasets.osu_run1()
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# optimize
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m = GPy.models.GPLVM(data['Y'], 2, kernel=kernel)
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if optimize: m.optimize('bfgs', messages=verbose, max_f_eval=10000)
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@ -520,8 +531,9 @@ def stick(kernel=None, optimize=True, verbose=True, plot=True):
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def bcgplvm_linear_stick(kernel=None, optimize=True, verbose=True, plot=True):
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from matplotlib import pyplot as plt
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import GPy
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import pods
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data = GPy.util.datasets.osu_run1()
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data = pods.datasets.osu_run1()
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# optimize
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mapping = GPy.mappings.Linear(data['Y'].shape[1], 2)
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m = GPy.models.BCGPLVM(data['Y'], 2, kernel=kernel, mapping=mapping)
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@ -539,8 +551,9 @@ def bcgplvm_linear_stick(kernel=None, optimize=True, verbose=True, plot=True):
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def bcgplvm_stick(kernel=None, optimize=True, verbose=True, plot=True):
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from matplotlib import pyplot as plt
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import GPy
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import pods
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data = GPy.util.datasets.osu_run1()
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data = pods.datasets.osu_run1()
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# optimize
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back_kernel=GPy.kern.RBF(data['Y'].shape[1], lengthscale=5.)
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mapping = GPy.mappings.Kernel(X=data['Y'], output_dim=2, kernel=back_kernel)
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@ -559,8 +572,9 @@ def bcgplvm_stick(kernel=None, optimize=True, verbose=True, plot=True):
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def robot_wireless(optimize=True, verbose=True, plot=True):
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from matplotlib import pyplot as plt
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import GPy
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import pods
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data = GPy.util.datasets.robot_wireless()
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data = pods.datasets.robot_wireless()
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# optimize
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m = GPy.models.BayesianGPLVM(data['Y'], 4, num_inducing=25)
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if optimize: m.optimize(messages=verbose, max_f_eval=10000)
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@ -574,8 +588,9 @@ def stick_bgplvm(model=None, optimize=True, verbose=True, plot=True):
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from matplotlib import pyplot as plt
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import numpy as np
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import GPy
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import pods
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data = GPy.util.datasets.osu_run1()
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data = pods.datasets.osu_run1()
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Q = 6
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kernel = GPy.kern.RBF(Q, lengthscale=np.repeat(.5, Q), ARD=True)
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m = BayesianGPLVM(data['Y'], Q, init="PCA", num_inducing=20, kernel=kernel)
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@ -605,8 +620,9 @@ def stick_bgplvm(model=None, optimize=True, verbose=True, plot=True):
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def cmu_mocap(subject='35', motion=['01'], in_place=True, optimize=True, verbose=True, plot=True):
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import GPy
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import pods
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data = GPy.util.datasets.cmu_mocap(subject, motion)
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data = pods.datasets.cmu_mocap(subject, motion)
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if in_place:
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# Make figure move in place.
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data['Y'][:, 0:3] = 0.0
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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()
|
||||
|
||||
# create simple GP Model
|
||||
m = GPy.models.GPRegression(data['Y'], data['X'], kernel=kernel)
|
||||
|
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# optimize
|
||||
if optimize:
|
||||
m.optimize(messages=True, max_iters=max_iters)
|
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m.optimize(max_iters=max_iters)
|
||||
|
||||
Xpredict = m.predict(data['Ytest'])[0]
|
||||
if plot:
|
||||
|
|
@ -372,13 +371,12 @@ def robot_wireless(max_iters=100, kernel=None, optimize=True, plot=True):
|
|||
|
||||
sse = ((data['Xtest'] - Xpredict)**2).sum()
|
||||
|
||||
print m
|
||||
print('Sum of squares error on test data: ' + str(sse))
|
||||
return m
|
||||
|
||||
def silhouette(max_iters=100, optimize=True, plot=True):
|
||||
"""Predict the pose of a figure given a silhouette. This is a task from Agarwal and Triggs 2004 ICML paper."""
|
||||
data = GPy.util.datasets.silhouette()
|
||||
data = pods.datasets.silhouette()
|
||||
|
||||
# create simple GP Model
|
||||
m = GPy.models.GPRegression(data['X'], data['Y'])
|
||||
|
|
@ -390,7 +388,7 @@ def silhouette(max_iters=100, optimize=True, plot=True):
|
|||
print m
|
||||
return m
|
||||
|
||||
def sparse_GP_regression_1D(num_samples=400, num_inducing=5, max_iters=100, optimize=True, plot=True, checkgrad=True):
|
||||
def sparse_GP_regression_1D(num_samples=400, num_inducing=5, max_iters=100, optimize=True, plot=True, checkgrad=False):
|
||||
"""Run a 1D example of a sparse GP regression."""
|
||||
# sample inputs and outputs
|
||||
X = np.random.uniform(-3., 3., (num_samples, 1))
|
||||
|
|
@ -401,10 +399,10 @@ def sparse_GP_regression_1D(num_samples=400, num_inducing=5, max_iters=100, opti
|
|||
m = GPy.models.SparseGPRegression(X, Y, kernel=rbf, num_inducing=num_inducing)
|
||||
|
||||
if checkgrad:
|
||||
m.checkgrad(verbose=1)
|
||||
m.checkgrad()
|
||||
|
||||
if optimize:
|
||||
m.optimize('tnc', messages=1, max_iters=max_iters)
|
||||
m.optimize('tnc', max_iters=max_iters)
|
||||
|
||||
if plot:
|
||||
m.plot()
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue