Python GaussianKernel.obtain_from_generic方法代码示例

# 需要导入模块: from shogun.Kernel import GaussianKernel [as 别名]
# 或者: from shogun.Kernel.GaussianKernel import obtain_from_generic [as 别名]
def statistics_mmd_kernel_selection_single(m,distance,stretch,num_blobs,angle,selection_method):
	from shogun.Features import RealFeatures
	from shogun.Features import GaussianBlobsDataGenerator
	from shogun.Kernel import GaussianKernel, CombinedKernel
	from shogun.Statistics import LinearTimeMMD
	from shogun.Statistics import MMDKernelSelectionMedian
	from shogun.Statistics import MMDKernelSelectionMax
	from shogun.Statistics import MMDKernelSelectionOpt
	from shogun.Statistics import BOOTSTRAP, MMD1_GAUSSIAN
	from shogun.Distance import EuclideanDistance
	from shogun.Mathematics import Statistics, Math

	# init seed for reproducability
	Math.init_random(1)

	# note that the linear time statistic is designed for much larger datasets
	# results for this low number will be bad (unstable, type I error wrong)
	m=1000
	distance=10
	stretch=5
	num_blobs=3
	angle=pi/4

	# streaming data generator
	gen_p=GaussianBlobsDataGenerator(num_blobs, distance, 1, 0)
	gen_q=GaussianBlobsDataGenerator(num_blobs, distance, stretch, angle)
		
	# stream some data and plot
	num_plot=1000
	features=gen_p.get_streamed_features(num_plot)
	features=features.create_merged_copy(gen_q.get_streamed_features(num_plot))
	data=features.get_feature_matrix()
	
	#figure()
	#subplot(2,2,1)
	#grid(True)
	#plot(data[0][0:num_plot], data[1][0:num_plot], 'r.', label='$x$')
	#title('$X\sim p$')
	#subplot(2,2,2)
	#grid(True)
	#plot(data[0][num_plot+1:2*num_plot], data[1][num_plot+1:2*num_plot], 'b.', label='$x$', alpha=0.5)
	#title('$Y\sim q$')


	# create combined kernel with Gaussian kernels inside (shoguns Gaussian kernel is
	# different to the standard form, see documentation)
	sigmas=[2**x for x in range(-3,10)]
	widths=[x*x*2 for x in sigmas]
	combined=CombinedKernel()
	for i in range(len(sigmas)):
		combined.append_kernel(GaussianKernel(10, widths[i]))

	# mmd instance using streaming features, blocksize of 10000
	block_size=1000
	mmd=LinearTimeMMD(combined, gen_p, gen_q, m, block_size)
	
	# kernel selection instance (this can easily replaced by the other methods for selecting
	# single kernels
	if selection_method=="opt":
		selection=MMDKernelSelectionOpt(mmd)
	elif selection_method=="max":
		selection=MMDKernelSelectionMax(mmd)
	elif selection_method=="median":
		selection=MMDKernelSelectionMedian(mmd)
	
	# print measures (just for information)
	# in case Opt: ratios of MMD and standard deviation
	# in case Max: MMDs for each kernel
	# Does not work for median method
	if selection_method!="median":
		ratios=selection.compute_measures()
		#print "Measures:", ratios
		
	#subplot(2,2,3)
	#plot(ratios)
	#title('Measures')
	
	# perform kernel selection
	kernel=selection.select_kernel()
	kernel=GaussianKernel.obtain_from_generic(kernel)
	#print "selected kernel width:", kernel.get_width()
	
	# compute tpye I and II error (use many more trials). Type I error is only
	# estimated to check MMD1_GAUSSIAN method for estimating the null
	# distribution. Note that testing has to happen on difference data than
	# kernel selecting, but the linear time mmd does this implicitly
	mmd.set_kernel(kernel)
	mmd.set_null_approximation_method(MMD1_GAUSSIAN)
	
	# number of trials should be larger to compute tight confidence bounds
	num_trials=5;
	alpha=0.05 # test power
	typeIerrors=[0 for x in range(num_trials)]
	typeIIerrors=[0 for x in range(num_trials)]
	for i in range(num_trials):
		# this effectively means that p=q - rejecting is tpye I error
		mmd.set_simulate_h0(True)
		typeIerrors[i]=mmd.perform_test()>alpha
		mmd.set_simulate_h0(False)
		
#.........这里部分代码省略.........

# 需要导入模块: from shogun.Kernel import GaussianKernel [as 别名]
# 或者: from shogun.Kernel.GaussianKernel import obtain_from_generic [as 别名]
def quadratic_time_mmd_graphical():
	
	# parameters, change to get different results
	m=100
	dim=2
	
	# setting the difference of the first dimension smaller makes a harder test
	difference=0.5
	
	# number of samples taken from null and alternative distribution
	num_null_samples=500
	
	# streaming data generator for mean shift distributions
	gen_p=MeanShiftDataGenerator(0, dim)
	gen_q=MeanShiftDataGenerator(difference, dim)
	
	# Stream examples and merge them in order to compute MMD on joint sample
	# alternative is to call a different constructor of QuadraticTimeMMD
	features=gen_p.get_streamed_features(m)
	features=features.create_merged_copy(gen_q.get_streamed_features(m))
	
	# use the median kernel selection
	# create combined kernel with Gaussian kernels inside (shoguns Gaussian kernel is
	# compute median data distance in order to use for Gaussian kernel width
	# 0.5*median_distance normally (factor two in Gaussian kernel)
	# However, shoguns kernel width is different to usual parametrization
	# Therefore 0.5*2*median_distance^2
	# Use a subset of data for that, only 200 elements. Median is stable
	sigmas=[2**x for x in range(-3,10)]
	widths=[x*x*2 for x in sigmas]
	print "kernel widths:", widths
	combined=CombinedKernel()
	for i in range(len(sigmas)):
		combined.append_kernel(GaussianKernel(10, widths[i]))

	# create MMD instance, use biased statistic
	mmd=QuadraticTimeMMD(combined,features, m)
	mmd.set_statistic_type(BIASED)
	
	# kernel selection instance (this can easily replaced by the other methods for selecting
	# single kernels
	selection=MMDKernelSelectionMax(mmd)

	# perform kernel selection
	kernel=selection.select_kernel()
	kernel=GaussianKernel.obtain_from_generic(kernel)
	mmd.set_kernel(kernel);
	print "selected kernel width:", kernel.get_width()
	
	# sample alternative distribution (new data each trial)
	alt_samples=zeros(num_null_samples)
	for i in range(len(alt_samples)):
		# Stream examples and merge them in order to replace in MMD
		features=gen_p.get_streamed_features(m)
		features=features.create_merged_copy(gen_q.get_streamed_features(m))
		mmd.set_p_and_q(features)
		alt_samples[i]=mmd.compute_statistic()
	
	# sample from null distribution
	# bootstrapping, biased statistic
	mmd.set_null_approximation_method(BOOTSTRAP)
	mmd.set_statistic_type(BIASED)
	mmd.set_bootstrap_iterations(num_null_samples)
	null_samples_boot=mmd.bootstrap_null()
	
	# sample from null distribution
	# spectrum, biased statistic
	if "sample_null_spectrum" in dir(QuadraticTimeMMD):
			mmd.set_null_approximation_method(MMD2_SPECTRUM)
			mmd.set_statistic_type(BIASED)
			null_samples_spectrum=mmd.sample_null_spectrum(num_null_samples, m-10)
			
	# fit gamma distribution, biased statistic
	mmd.set_null_approximation_method(MMD2_GAMMA)
	mmd.set_statistic_type(BIASED)
	gamma_params=mmd.fit_null_gamma()
	# sample gamma with parameters
	null_samples_gamma=array([gamma(gamma_params[0], gamma_params[1]) for _ in range(num_null_samples)])
	
	# to plot data, sample a few examples from stream first
	features=gen_p.get_streamed_features(m)
	features=features.create_merged_copy(gen_q.get_streamed_features(m))
	data=features.get_feature_matrix()
	
	# plot
	figure()
	title('Quadratic Time MMD')
	
	# plot data of p and q
	subplot(2,3,1)
	grid(True)
	gca().xaxis.set_major_locator( MaxNLocator(nbins = 4) ) # reduce number of x-ticks
	gca().yaxis.set_major_locator( MaxNLocator(nbins = 4) ) # reduce number of x-ticks
	plot(data[0][0:m], data[1][0:m], 'ro', label='$x$')
	plot(data[0][m+1:2*m], data[1][m+1:2*m], 'bo', label='$x$', alpha=0.5)
	title('Data, shift in $x_1$='+str(difference)+'\nm='+str(m))
	xlabel('$x_1, y_1$')
	ylabel('$x_2, y_2$')
	
	# histogram of first data dimension and pdf
#.........这里部分代码省略.........

# 需要导入模块: from shogun.Kernel import GaussianKernel [as 别名]
# 或者: from shogun.Kernel.GaussianKernel import obtain_from_generic [as 别名]
def linear_time_mmd_graphical():

	
	# parameters, change to get different results
	m=1000 # set to 10000 for a good test result
	dim=2
	
	# setting the difference of the first dimension smaller makes a harder test
	difference=1
	
	# number of samples taken from null and alternative distribution
	num_null_samples=150
	
	# streaming data generator for mean shift distributions
	gen_p=MeanShiftDataGenerator(0, dim)
	gen_q=MeanShiftDataGenerator(difference, dim)
	
	# use the median kernel selection
	# create combined kernel with Gaussian kernels inside (shoguns Gaussian kernel is
	# compute median data distance in order to use for Gaussian kernel width
	# 0.5*median_distance normally (factor two in Gaussian kernel)
	# However, shoguns kernel width is different to usual parametrization
	# Therefore 0.5*2*median_distance^2
	# Use a subset of data for that, only 200 elements. Median is stable
	sigmas=[2**x for x in range(-3,10)]
	widths=[x*x*2 for x in sigmas]
	print "kernel widths:", widths
	combined=CombinedKernel()
	for i in range(len(sigmas)):
		combined.append_kernel(GaussianKernel(10, widths[i]))

	# mmd instance using streaming features, blocksize of 10000
	block_size=1000
	mmd=LinearTimeMMD(combined, gen_p, gen_q, m, block_size)
	
	# kernel selection instance (this can easily replaced by the other methods for selecting
	# single kernels
	selection=MMDKernelSelectionOpt(mmd)

	# perform kernel selection
	kernel=selection.select_kernel()
	kernel=GaussianKernel.obtain_from_generic(kernel)
	mmd.set_kernel(kernel);
	print "selected kernel width:", kernel.get_width()
	
	# sample alternative distribution, stream ensures different samples each run
	alt_samples=zeros(num_null_samples)
	for i in range(len(alt_samples)):
		alt_samples[i]=mmd.compute_statistic()
	
	# sample from null distribution
	# bootstrapping, biased statistic
	mmd.set_null_approximation_method(BOOTSTRAP)
	mmd.set_bootstrap_iterations(num_null_samples)
	null_samples_boot=mmd.bootstrap_null()
	
	# fit normal distribution to null and sample a normal distribution
	mmd.set_null_approximation_method(MMD1_GAUSSIAN)
	variance=mmd.compute_variance_estimate()
	null_samples_gaussian=normal(0,sqrt(variance),num_null_samples)
	
	# to plot data, sample a few examples from stream first
	features=gen_p.get_streamed_features(m)
	features=features.create_merged_copy(gen_q.get_streamed_features(m))
	data=features.get_feature_matrix()
	
	# plot
	figure()
	
	# plot data of p and q
	subplot(2,3,1)
	grid(True)
	gca().xaxis.set_major_locator( MaxNLocator(nbins = 4) ) # reduce number of x-ticks
	gca().yaxis.set_major_locator( MaxNLocator(nbins = 4) ) # reduce number of x-ticks
	plot(data[0][0:m], data[1][0:m], 'ro', label='$x$')
	plot(data[0][m+1:2*m], data[1][m+1:2*m], 'bo', label='$x$', alpha=0.5)
	title('Data, shift in $x_1$='+str(difference)+'\nm='+str(m))
	xlabel('$x_1, y_1$')
	ylabel('$x_2, y_2$')
	
	# histogram of first data dimension and pdf
	subplot(2,3,2)
	grid(True)
	gca().xaxis.set_major_locator( MaxNLocator(nbins = 3) ) # reduce number of x-ticks
	gca().yaxis.set_major_locator( MaxNLocator(nbins = 3) ) # reduce number of x-ticks
	hist(data[0], bins=50, alpha=0.5, facecolor='r', normed=True)
	hist(data[1], bins=50, alpha=0.5, facecolor='b', normed=True)
	xs=linspace(min(data[0])-1,max(data[0])+1, 50)
	plot(xs,normpdf( xs, 0, 1), 'r', linewidth=3)
	plot(xs,normpdf( xs, difference, 1), 'b', linewidth=3)
	xlabel('$x_1, y_1$')
	ylabel('$p(x_1), p(y_1)$')
	title('Data PDF in $x_1, y_1$')
	
	# compute threshold for test level
	alpha=0.05
	null_samples_boot.sort()
	null_samples_gaussian.sort()
	thresh_boot=null_samples_boot[floor(len(null_samples_boot)*(1-alpha))];
	thresh_gaussian=null_samples_gaussian[floor(len(null_samples_gaussian)*(1-alpha))];
#.........这里部分代码省略.........