示例#1
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	def test_loglikelihood(self):
		"""
		Tests whether 1-dimensional GSMs are normalized. Tests the log-likelihood
		of several instantiations of the GSM.
		"""

		# check whether the log-likelihood of 1D GSMs is normalized
		for num_scales in [1, 2, 3, 4, 5]:
			model = GSM(1, num_scales=num_scales)

			# implied probability density of model
			pdf = lambda x: exp(model.loglikelihood(array(x).reshape(1, -1)))

			# compute normalization constant and upper bound on error
			partf, err = integrate.quad(pdf, -inf, inf)

			self.assertTrue(partf - err <= 1.)
			self.assertTrue(partf + err >= 1.)

		# test the log-likelihood of a couple of GSMs
		for dim in [1, 2, 3, 4, 5]:
			for num_scales in [1, 2, 3, 4, 5]:
				# create Gaussian scale mixture
				model = GSM(dim, num_scales=num_scales)
				scales = model.scales.reshape(-1, 1)

				# create random data
				data = randn(model.dim, 100)

				# evaluate likelihood
				ll = logmeanexp(
					-0.5 * sum(square(data), 0) / square(scales)
					- model.dim * log(scales)
					- model.dim / 2. * log(2. * pi), 0)

				self.assertTrue(all(abs(ll - model.loglikelihood(data)) < 1E-6))

				# random scales
				scales = rand(num_scales, 1) + 0.5
				model.scales[:] = scales.flatten()

				# sample data from model
				data = model.sample(100)

				# evaluate likelihood
				ll = logmeanexp(
					-0.5 * sum(square(data), 0) / square(scales)
					- model.dim * log(scales)
					- model.dim / 2. * log(2. * pi), 0)

				self.assertTrue(all(abs(ll - model.loglikelihood(data)) < 1E-6))
示例#2
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文件: gsm_test.py 项目: afcarl/isa
    def test_loglikelihood(self):
        """
		Tests whether 1-dimensional GSMs are normalized. Tests the log-likelihood
		of several instantiations of the GSM.
		"""

        # check whether the log-likelihood of 1D GSMs is normalized
        for num_scales in [1, 2, 3, 4, 5]:
            model = GSM(1, num_scales=num_scales)

            # implied probability density of model
            pdf = lambda x: exp(model.loglikelihood(array(x).reshape(1, -1)))

            # compute normalization constant and upper bound on error
            partf, err = integrate.quad(pdf, -inf, inf)

            self.assertTrue(partf - err <= 1.)
            self.assertTrue(partf + err >= 1.)

        # test the log-likelihood of a couple of GSMs
        for dim in [1, 2, 3, 4, 5]:
            for num_scales in [1, 2, 3, 4, 5]:
                # create Gaussian scale mixture
                model = GSM(dim, num_scales=num_scales)
                scales = model.scales.reshape(-1, 1)

                # create random data
                data = randn(model.dim, 100)

                # evaluate likelihood
                ll = logmeanexp(
                    -0.5 * sum(square(data), 0) / square(scales) -
                    model.dim * log(scales) - model.dim / 2. * log(2. * pi), 0)

                self.assertTrue(
                    all(abs(ll - model.loglikelihood(data)) < 1E-6))

                # random scales
                scales = rand(num_scales, 1) + 0.5
                model.scales[:] = scales.flatten()

                # sample data from model
                data = model.sample(100)

                # evaluate likelihood
                ll = logmeanexp(
                    -0.5 * sum(square(data), 0) / square(scales) -
                    model.dim * log(scales) - model.dim / 2. * log(2. * pi), 0)

                self.assertTrue(
                    all(abs(ll - model.loglikelihood(data)) < 1E-6))
示例#3
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    def test_logjacobian(self):
        """
		Test log-Jacobian.
		"""

        gsm = GSM(3, 10)
        gsm.initialize('cauchy')

        # standard normal distribution
        gauss = GSM(3, 1)
        gauss.scales[0] = 1.

        # generate test data
        samples = gsm.sample(100)

        rg = RadialGaussianization(gsm)

        # after Gaussianization, samples should be Gaussian distributed
        loglik_gsm = gsm.loglikelihood(samples)
        loglik_gauss = gauss.loglikelihood(
            rg(samples)) + rg.logjacobian(samples)

        dist = abs(loglik_gsm - loglik_gauss)

        self.assertTrue(all(dist < 1E-6))

        ###

        # test one-dimensional Gaussian
        gsm = GSM(1, 10)
        gsm.initialize('cauchy')

        # standard normal distribution
        gauss = GSM(1, 1)
        gauss.scales[0] = 1.

        # generate test data
        samples = gsm.sample(100)

        rg = RadialGaussianization(gsm)

        # after Gaussianization, samples should be Gaussian distributed
        loglik_gsm = gsm.loglikelihood(samples)
        loglik_gauss = gauss.loglikelihood(
            rg(samples)) + rg.logjacobian(samples)

        dist = abs(loglik_gsm - loglik_gauss)

        self.assertTrue(all(dist < 1E-6))
示例#4
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    def test_logjacobian(self):
        isa = ISA(4, 4, 2)

        # standard normal distribution
        gauss = GSM(4, 1)
        gauss.scales[0] = 1.

        # generate test data
        samples = isa.sample(100)

        sg = SubspaceGaussianization(isa)

        # after Gaussianization, samples should be Gaussian distributed
        loglik_isa = isa.loglikelihood(samples)
        loglik_gauss = gauss.loglikelihood(
            sg(samples)) + sg.logjacobian(samples)

        dist = abs(loglik_isa - loglik_gauss)

        self.assertTrue(all(dist < 1E-6))

        ###

        # test ICA
        isa = ISA(3, 3, 1)

        # standard normal distribution
        gauss = GSM(3, 1)
        gauss.scales[0] = 1.

        # generate test data
        samples = isa.sample(100)

        sg = SubspaceGaussianization(isa)

        # after Gaussianization, samples should be Gaussian distributed
        loglik_isa = isa.loglikelihood(samples)
        loglik_gauss = gauss.loglikelihood(
            sg(samples)) + sg.logjacobian(samples)

        dist = abs(loglik_isa - loglik_gauss)

        self.assertTrue(all(dist < 1E-6))
	def test_logjacobian(self):
		ica = ICA(4)

		# standard normal distribution
		gauss = GSM(4, 1)
		gauss.scales[0] = 1.

		# generate test data
		samples = ica.sample(100)

		mg = MarginalGaussianization(ica)

		# after Gaussianization, samples should be Gaussian distributed
		loglik_ica = ica.loglikelihood(samples)
		loglik_gauss = gauss.loglikelihood(mg(samples)) + mg.logjacobian(samples)

		dist = abs(loglik_ica - loglik_gauss)

		self.assertTrue(all(dist < 1E-6))
示例#6
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	def test_sample(self):
		"""
		Compares model density with histogram obtained from samples.
		"""

		model = GSM(1, 3)
		model.scales = array([1., 3., 8.])

		data = model.sample(50000)

		try:
			hist, x = histogram(data, 100, density=True)
		except:
			# use deprecated method with older versions of Python
			hist, x = histogram(data, 100, normed=True)
		x = (x[1:] + x[:-1]) / 2.

		pdf = exp(model.loglikelihood(x.reshape(1, -1)))

		self.assertTrue(all(abs(pdf - hist) < 1E-1))
示例#7
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文件: gsm_test.py 项目: afcarl/isa
    def test_sample(self):
        """
		Compares model density with histogram obtained from samples.
		"""

        model = GSM(1, 3)
        model.scales = array([1., 3., 8.])

        data = model.sample(50000)

        try:
            hist, x = histogram(data, 100, density=True)
        except:
            # use deprecated method with older versions of Python
            hist, x = histogram(data, 100, normed=True)
        x = (x[1:] + x[:-1]) / 2.

        pdf = exp(model.loglikelihood(x.reshape(1, -1)))

        self.assertTrue(all(abs(pdf - hist) < 1E-1))
    def test_logjacobian(self):
        ica = ICA(4)

        # standard normal distribution
        gauss = GSM(4, 1)
        gauss.scales[0] = 1.

        # generate test data
        samples = ica.sample(100)

        mg = MarginalGaussianization(ica)

        # after Gaussianization, samples should be Gaussian distributed
        loglik_ica = ica.loglikelihood(samples)
        loglik_gauss = gauss.loglikelihood(
            mg(samples)) + mg.logjacobian(samples)

        dist = abs(loglik_ica - loglik_gauss)

        self.assertTrue(all(dist < 1E-6))