mirror of
https://github.com/SheffieldML/GPy.git
synced 2026-05-08 19:42:39 +02:00
337 lines
14 KiB
Python
337 lines
14 KiB
Python
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
|
|
# Licensed under the BSD 3-clause license (see LICENSE.txt)
|
|
|
|
import numpy as np
|
|
import pylab as pb
|
|
import warnings
|
|
from .. import kern
|
|
from ..util.plot import gpplot, Tango, x_frame1D, x_frame2D
|
|
from ..util.linalg import dtrtrs
|
|
from model import Model
|
|
from parameterization import ObservableArray
|
|
from .. import likelihoods
|
|
from ..likelihoods.gaussian import Gaussian
|
|
from ..inference.latent_function_inference import exact_gaussian_inference
|
|
|
|
class GP(Model):
|
|
"""
|
|
General purpose Gaussian process model
|
|
|
|
:param X: input observations
|
|
:param Y: output observations
|
|
:param kernel: a GPy kernel, defaults to rbf+white
|
|
:param likelihood: a GPy likelihood
|
|
:rtype: model object
|
|
|
|
.. Note:: Multiple independent outputs are allowed using columns of Y
|
|
|
|
|
|
"""
|
|
def __init__(self, X, Y, kernel, likelihood, inference_method=None, name='gp'):
|
|
super(GP, self).__init__(name)
|
|
|
|
assert X.ndim == 2
|
|
self.X = ObservableArray(X)
|
|
self.num_data, self.input_dim = self.X.shape
|
|
|
|
assert Y.ndim == 2
|
|
self.Y = ObservableArray(Y)
|
|
assert Y.shape[0] == self.num_data
|
|
_, self.output_dim = self.Y.shape
|
|
|
|
assert isinstance(kernel, kern.kern)
|
|
self.kern = kernel
|
|
|
|
assert isinstance(likelihood, likelihoods.Likelihood)
|
|
self.likelihood = likelihood
|
|
|
|
#find a sensible inference method
|
|
if inference_method is None:
|
|
if isinstance(likelihood, likelihoods.Gaussian):
|
|
inference_method = exact_gaussian_inference.ExactGaussianInference()
|
|
else:
|
|
inference_method = expectation_propagation
|
|
print "defaulting to ", inference_method, "for latent function inference"
|
|
self.inference_method = inference_method
|
|
|
|
self.add_parameter(self.kern)
|
|
self.add_parameter(self.likelihood)
|
|
|
|
self.parameters_changed()
|
|
|
|
def parameters_changed(self):
|
|
self.posterior = self.inference_method.inference(self.kern, self.X, self.likelihood, self.Y)
|
|
|
|
def log_likelihood(self):
|
|
return self.posterior.log_marginal
|
|
|
|
def dL_dtheta_K(self):
|
|
return self.kern.dK_dtheta(self.posterior.dL_dK, self.X)
|
|
|
|
def _raw_predict(self, _Xnew, which_parts='all', full_cov=False, stop=False):
|
|
"""
|
|
Internal helper function for making predictions, does not account
|
|
for normalization or likelihood
|
|
|
|
full_cov is a boolean which defines whether the full covariance matrix
|
|
of the prediction is computed. If full_cov is False (default), only the
|
|
diagonal of the covariance is returned.
|
|
|
|
"""
|
|
Kx = self.kern.K(_Xnew, self.X, which_parts=which_parts).T
|
|
LiKx, _ = dtrtrs(self.posterior._woodbury_chol, np.asfortranarray(Kx), lower=1)
|
|
mu = np.dot(Kx.T, self.posterior._woodbury_vector)
|
|
if full_cov:
|
|
Kxx = self.kern.K(_Xnew, which_parts=which_parts)
|
|
var = Kxx - tdot(LiKx.T)
|
|
else:
|
|
Kxx = self.kern.Kdiag(_Xnew, which_parts=which_parts)
|
|
var = Kxx - np.sum(LiKx*LiKx, 0)
|
|
var = var.reshape(-1, 1)
|
|
return mu, var
|
|
|
|
def predict(self, Xnew, which_parts='all', full_cov=False, **likelihood_args):
|
|
"""
|
|
Predict the function(s) at the new point(s) Xnew.
|
|
|
|
:param Xnew: The points at which to make a prediction
|
|
:type Xnew: np.ndarray, Nnew x self.input_dim
|
|
:param which_parts: specifies which outputs kernel(s) to use in prediction
|
|
:type which_parts: ('all', list of bools)
|
|
:param full_cov: whether to return the full covariance matrix, or just the diagonal
|
|
:type full_cov: bool
|
|
:returns: mean: posterior mean, a Numpy array, Nnew x self.input_dim
|
|
:returns: var: posterior variance, a Numpy array, Nnew x 1 if full_cov=False, Nnew x Nnew otherwise
|
|
:returns: lower and upper boundaries of the 95% confidence intervals, Numpy arrays, Nnew x self.input_dim
|
|
|
|
|
|
If full_cov and self.input_dim > 1, the return shape of var is Nnew x Nnew x self.input_dim. If self.input_dim == 1, the return shape is Nnew x Nnew.
|
|
This is to allow for different normalizations of the output dimensions.
|
|
|
|
"""
|
|
# normalize X values
|
|
mu, var = self._raw_predict(Xnew, full_cov=full_cov, which_parts=which_parts)
|
|
|
|
# now push through likelihood
|
|
mean, var, _025pm, _975pm = self.likelihood.predictive_values(mu, var, full_cov, **likelihood_args)
|
|
return mean, var, _025pm, _975pm
|
|
|
|
def posterior_samples_f(self,X,size=10,which_parts='all',full_cov=True):
|
|
"""
|
|
Samples the posterior GP at the points X.
|
|
|
|
:param X: The points at which to take the samples.
|
|
:type X: np.ndarray, Nnew x self.input_dim.
|
|
:param size: the number of a posteriori samples to plot.
|
|
:type size: int.
|
|
:param which_parts: which of the kernel functions to plot (additively).
|
|
:type which_parts: 'all', or list of bools.
|
|
:param full_cov: whether to return the full covariance matrix, or just the diagonal.
|
|
:type full_cov: bool.
|
|
:returns: Ysim: set of simulations, a Numpy array (N x samples).
|
|
"""
|
|
m, v = self._raw_predict(X, which_parts=which_parts, full_cov=full_cov)
|
|
v = v.reshape(m.size,-1) if len(v.shape)==3 else v
|
|
if not full_cov:
|
|
Ysim = np.random.multivariate_normal(m.flatten(), np.diag(v.flatten()), size).T
|
|
else:
|
|
Ysim = np.random.multivariate_normal(m.flatten(), v, size).T
|
|
|
|
return Ysim
|
|
|
|
def posterior_samples(self,X,size=10,which_parts='all',full_cov=True,noise_model=None):
|
|
"""
|
|
Samples the posterior GP at the points X.
|
|
|
|
:param X: the points at which to take the samples.
|
|
:type X: np.ndarray, Nnew x self.input_dim.
|
|
:param size: the number of a posteriori samples to plot.
|
|
:type size: int.
|
|
:param which_parts: which of the kernel functions to plot (additively).
|
|
:type which_parts: 'all', or list of bools.
|
|
:param full_cov: whether to return the full covariance matrix, or just the diagonal.
|
|
:type full_cov: bool.
|
|
:param noise_model: for mixed noise likelihood, the noise model to use in the samples.
|
|
:type noise_model: integer.
|
|
:returns: Ysim: set of simulations, a Numpy array (N x samples).
|
|
"""
|
|
Ysim = self.posterior_samples_f(X, size, which_parts=which_parts, full_cov=full_cov)
|
|
if isinstance(self.likelihood, Gaussian):
|
|
noise_std = np.sqrt(self.likelihood._get_params())
|
|
Ysim += np.random.normal(0,noise_std,Ysim.shape)
|
|
elif isinstance(self.likelihood, Gaussian_Mixed_Noise):
|
|
assert noise_model is not None, "A noise model must be specified."
|
|
noise_std = np.sqrt(self.likelihood._get_params()[noise_model])
|
|
Ysim += np.random.normal(0,noise_std,Ysim.shape)
|
|
else:
|
|
Ysim = self.likelihood.noise_model.samples(Ysim)
|
|
|
|
return Ysim
|
|
|
|
def plot_f(self, *args, **kwargs):
|
|
"""
|
|
Plot the GP's view of the world, where the data is normalized and before applying a likelihood.
|
|
|
|
This is a convenience function: we simply call self.plot with the
|
|
argument use_raw_predict set True. All args and kwargs are passed on to
|
|
plot.
|
|
|
|
see also: gp.plot
|
|
"""
|
|
kwargs['plot_raw'] = True
|
|
self.plot(*args, **kwargs)
|
|
|
|
def plot(self, plot_limits=None, which_data_rows='all',
|
|
which_data_ycols='all', which_parts='all', fixed_inputs=[],
|
|
levels=20, samples=0, fignum=None, ax=None, resolution=None,
|
|
plot_raw=False,
|
|
linecol=Tango.colorsHex['darkBlue'],fillcol=Tango.colorsHex['lightBlue']):
|
|
"""
|
|
Plot the posterior of the GP.
|
|
- In one dimension, the function is plotted with a shaded region identifying two standard deviations.
|
|
- In two dimsensions, a contour-plot shows the mean predicted function
|
|
- In higher dimensions, use fixed_inputs to plot the GP with some of the inputs fixed.
|
|
|
|
Can plot only part of the data and part of the posterior functions
|
|
using which_data_rowsm which_data_ycols and which_parts
|
|
|
|
:param plot_limits: The limits of the plot. If 1D [xmin,xmax], if 2D [[xmin,ymin],[xmax,ymax]]. Defaluts to data limits
|
|
:type plot_limits: np.array
|
|
:param which_data_rows: which of the training data to plot (default all)
|
|
:type which_data_rows: 'all' or a slice object to slice self.X, self.Y
|
|
:param which_data_ycols: when the data has several columns (independant outputs), only plot these
|
|
:type which_data_rows: 'all' or a list of integers
|
|
:param which_parts: which of the kernel functions to plot (additively)
|
|
:type which_parts: 'all', or list of bools
|
|
:param fixed_inputs: a list of tuple [(i,v), (i,v)...], specifying that input index i should be set to value v.
|
|
:type fixed_inputs: a list of tuples
|
|
:param resolution: the number of intervals to sample the GP on. Defaults to 200 in 1D and 50 (a 50x50 grid) in 2D
|
|
:type resolution: int
|
|
:param levels: number of levels to plot in a contour plot.
|
|
:type levels: int
|
|
:param samples: the number of a posteriori samples to plot
|
|
:type samples: int
|
|
:param fignum: figure to plot on.
|
|
:type fignum: figure number
|
|
:param ax: axes to plot on.
|
|
:type ax: axes handle
|
|
:type output: integer (first output is 0)
|
|
:param linecol: color of line to plot.
|
|
:type linecol:
|
|
:param fillcol: color of fill
|
|
:param levels: for 2D plotting, the number of contour levels to use is ax is None, create a new figure
|
|
"""
|
|
#deal with optional arguments
|
|
if which_data_rows == 'all':
|
|
which_data_rows = slice(None)
|
|
if which_data_ycols == 'all':
|
|
which_data_ycols = np.arange(self.output_dim)
|
|
if len(which_data_ycols)==0:
|
|
raise ValueError('No data selected for plotting')
|
|
if ax is None:
|
|
fig = pb.figure(num=fignum)
|
|
ax = fig.add_subplot(111)
|
|
|
|
#work out what the inputs are for plotting (1D or 2D)
|
|
fixed_dims = np.array([i for i,v in fixed_inputs])
|
|
free_dims = np.setdiff1d(np.arange(self.input_dim),fixed_dims)
|
|
|
|
#one dimensional plotting
|
|
if len(free_dims) == 1:
|
|
|
|
#define the frame on which to plot
|
|
resolution = resolution or 200
|
|
Xnew, xmin, xmax = x_frame1D(self.X[:,free_dims], plot_limits=plot_limits)
|
|
Xgrid = np.empty((Xnew.shape[0],self.input_dim))
|
|
Xgrid[:,free_dims] = Xnew
|
|
for i,v in fixed_inputs:
|
|
Xgrid[:,i] = v
|
|
|
|
#make a prediction on the frame and plot it
|
|
if plot_raw:
|
|
m, v = self._raw_predict(Xgrid, which_parts=which_parts)
|
|
lower = m - 2*np.sqrt(v)
|
|
upper = m + 2*np.sqrt(v)
|
|
Y = self.Y
|
|
else:
|
|
m, v, lower, upper = self.predict(Xgrid, which_parts=which_parts)
|
|
Y = self.Y
|
|
for d in which_data_ycols:
|
|
gpplot(Xnew, m[:, d], lower[:, d], upper[:, d], axes=ax, edgecol=linecol, fillcol=fillcol)
|
|
ax.plot(self.X[which_data_rows,free_dims], Y[which_data_rows, d], 'kx', mew=1.5)
|
|
|
|
#optionally plot some samples
|
|
if samples: #NOTE not tested with fixed_inputs
|
|
Ysim = self.posterior_samples(Xgrid, samples, which_parts=which_parts)
|
|
for yi in Ysim.T:
|
|
ax.plot(Xnew, yi[:,None], Tango.colorsHex['darkBlue'], linewidth=0.25)
|
|
#ax.plot(Xnew, yi[:,None], marker='x', linestyle='--',color=Tango.colorsHex['darkBlue']) #TODO apply this line for discrete outputs.
|
|
|
|
#set the limits of the plot to some sensible values
|
|
ymin, ymax = min(np.append(Y[which_data_rows, which_data_ycols].flatten(), lower)), max(np.append(Y[which_data_rows, which_data_ycols].flatten(), upper))
|
|
ymin, ymax = ymin - 0.1 * (ymax - ymin), ymax + 0.1 * (ymax - ymin)
|
|
ax.set_xlim(xmin, xmax)
|
|
ax.set_ylim(ymin, ymax)
|
|
|
|
#2D plotting
|
|
elif len(free_dims) == 2:
|
|
|
|
#define the frame for plotting on
|
|
resolution = resolution or 50
|
|
Xnew, _, _, xmin, xmax = x_frame2D(self.X[:,free_dims], plot_limits, resolution)
|
|
Xgrid = np.empty((Xnew.shape[0],self.input_dim))
|
|
Xgrid[:,free_dims] = Xnew
|
|
for i,v in fixed_inputs:
|
|
Xgrid[:,i] = v
|
|
x, y = np.linspace(xmin[0], xmax[0], resolution), np.linspace(xmin[1], xmax[1], resolution)
|
|
|
|
#predict on the frame and plot
|
|
if plot_raw:
|
|
m, _ = self._raw_predict(Xgrid, which_parts=which_parts)
|
|
Y = self.likelihood.Y
|
|
else:
|
|
m, _, _, _ = self.predict(Xgrid, which_parts=which_parts,sampling=False)
|
|
Y = self.likelihood.data
|
|
for d in which_data_ycols:
|
|
m_d = m[:,d].reshape(resolution, resolution).T
|
|
ax.contour(x, y, m_d, levels, vmin=m.min(), vmax=m.max(), cmap=pb.cm.jet)
|
|
ax.scatter(self.X[which_data_rows, free_dims[0]], self.X[which_data_rows, free_dims[1]], 40, Y[which_data_rows, d], cmap=pb.cm.jet, vmin=m.min(), vmax=m.max(), linewidth=0.)
|
|
|
|
#set the limits of the plot to some sensible values
|
|
ax.set_xlim(xmin[0], xmax[0])
|
|
ax.set_ylim(xmin[1], xmax[1])
|
|
|
|
if samples:
|
|
warnings.warn("Samples are rather difficult to plot for 2D inputs...")
|
|
|
|
else:
|
|
raise NotImplementedError, "Cannot define a frame with more than two input dimensions"
|
|
|
|
|
|
|
|
def _getstate(self):
|
|
"""
|
|
Get the current state of the class, here we return everything that is needed to recompute the model.
|
|
"""
|
|
return Model._getstate(self) + [self.X,
|
|
self.num_data,
|
|
self.input_dim,
|
|
self.kern,
|
|
self.likelihood,
|
|
self.output_dim,
|
|
self._Xoffset,
|
|
self._Xscale,
|
|
]
|
|
|
|
def _setstate(self, state):
|
|
self._Xscale = state.pop()
|
|
self._Xoffset = state.pop()
|
|
self.output_dim = state.pop()
|
|
self.likelihood = state.pop()
|
|
self.kern = state.pop()
|
|
self.input_dim = state.pop()
|
|
self.num_data = state.pop()
|
|
self.X = state.pop()
|
|
Model._setstate(self, state)
|
|
|
|
|