diff --git a/gp/demo_epinf.m b/gp/demo_epinf.m index d49e765a..d1c997f4 100644 --- a/gp/demo_epinf.m +++ b/gp/demo_epinf.m @@ -1,12 +1,21 @@ -%DEMO_EPINF Demonstration of input dependent noise and magnitude model +%DEMO_EPINF Demonstration of input dependent noise and magnitude model with EP % -% Description -% Uses toy data sets to demonstrate heteroscedastic noise with input -% dependent noise and magnitude model. Compare with results from -% DEMO_INPUTDEPENDENTNOISE. +% Description +% Uses toy data sets to demonstrate heteroscedastic noise with +% input dependent noise and magnitude model using EP +% inference. Compare with results from +% DEMO_INPUTDEPENDENTNOISE. % -% See also -% DEMO_INPUTDEPENDENTNOISE, LIK_EPGAUSSIAN +% Reference: +% Ville Tolvanen, Pasi Jylänki and Aki Vehtari (2014). Expectation +% propagation for nonstationary heteroscedastic Gaussian process +% regression. In Machine Learning for Signal Processing (MLSP), +% 2014 IEEE International Workshop on, +% DOI:10.1109/MLSP.2014.6958906. +% +% +% See also +% DEMO_INPUTDEPENDENTNOISE, DEMO_STOCHASTICVOLATILITY, LIK_EPGAUSSIAN % % % Copyright (c) Ville Tolvanen 2011-2014 diff --git a/gp/demo_inputdependentnoise.m b/gp/demo_inputdependentnoise.m index 71baf42e..9b291f37 100644 --- a/gp/demo_inputdependentnoise.m +++ b/gp/demo_inputdependentnoise.m @@ -1,11 +1,20 @@ %DEMO_INPUTDEPENDENTNOISE Demonstration of input dependent-noise -% model using Gaussian process prior +% model using Gaussian process prior and Laplace approx % % Description % Uses toy data sets to demonstrate how inferring % heteroscedastic noise with input dependent noise model % differs from standard noise models (Gaussian, Student-t). % +% Reference: +% Ville Tolvanen, Pasi Jylänki and Aki Vehtari (2014). Expectation +% propagation for nonstationary heteroscedastic Gaussian process +% regression. In Machine Learning for Signal Processing (MLSP), +% 2014 IEEE International Workshop on, +% DOI:10.1109/MLSP.2014.6958906. +% +% +% See also DEMO_EPINF, DEMO_STOCHASTICVOLATILITY % % Copyright (c) Ville Tolvanen 2011-2012 diff --git a/gp/demo_regression_additive1.m b/gp/demo_regression_additive1.m index eddbe23c..42b568b0 100644 --- a/gp/demo_regression_additive1.m +++ b/gp/demo_regression_additive1.m @@ -119,7 +119,7 @@ warning('GPstuff:SuiteSparseMissing',... ['SuiteSparse is not properly installed. (in BECS try ''use suitesparse'')\n' ... 'Using gpcf_sexp (non-compact support) instead of gpcf_ppcs2 (compact support)']); - gpcf2 = gpcf_sexp('lengthScale', 5, 'magnSigma2', 1, 'lengthScale_prior', pl2, 'magnSigma2_prior', pm); + gpcf2 = gpcf_sexp('lengthScale', 5, 'magnSigma2', 1, 'lengthScale_prior', pl2, 'magnSigma2_prior', pm2); end lik = lik_gaussian('sigma2', 0.1, 'sigma2_prior', pn); diff --git a/gp/demo_stochasticvolatility.m b/gp/demo_stochasticvolatility.m new file mode 100644 index 00000000..6cfedf16 --- /dev/null +++ b/gp/demo_stochasticvolatility.m @@ -0,0 +1,125 @@ +%DEMO_STOCHASTICVOLATILITY Demonstration of input dependent-noise +% model using Gaussian process prior, which corresponds to a +% stochastic volatility model +% +% Description +% Demonstrates stochastic volatility model for S&P 500 +% weekly closing value. +% +% Reference: +% Ville Tolvanen, Pasi Jylänki and Aki Vehtari (2014). Expectation +% propagation for nonstationary heteroscedastic Gaussian process +% regression. In Machine Learning for Signal Processing (MLSP), +% 2014 IEEE International Workshop on, +% DOI:10.1109/MLSP.2014.6958906. +% +% +% See also DEMO_INPUTDEPENDENTNOISE, DEMO_EPINF +% +% Copyright (c) Aki Vehtari 2015 + +% This software is distributed under the GNU General Public +% License (version 3 or later); please refer to the file +% License.txt, included with the software, for details. + + +%% Data +% Stochastic volatility model for change in +% S&P 500 stock index weekly closing value from 2001-01-02 to 2014-12-29 +S = which('demo_stochasticvolatility'); +L = strrep(S,'demo_stochasticvolatility.m','demodata/sp500_weekly.csv'); +d=dataset('File',L,'Delimiter',','); +d.Datenum=datenum(d.Date); +% order from oldest to newest +x=flipud(d.Datenum); +x=x(2:end)-x(1); +% normalise +[xn,nd.xmean,nd.xstd]=normdata(x); +% order from oldest to newest +y=flipud(d.Close); +% change in closing price +y=diff(y); +% normalise +[yn,nd.ymean,nd.ystd]=normdata(y); +% +n=numel(y); + +%% Covariance functions +pl = prior_t('s2',1); +pm = prior_t('s2',1); +gpcf1 = gpcf_sexp('lengthScale', 1, 'magnSigma2', 0.5, ... + 'lengthScale_prior', pl, 'magnSigma2_prior', pm); +gpcf2 = gpcf_exp('lengthScale', 1, 'magnSigma2', 0.1, ... + 'lengthScale_prior', pl, 'magnSigma2_prior', pm); + +%% Inference using Laplace approximate + +% Create the likelihood structure. Don't set prior for sigma2 if covariance +% function magnitude for noise process has a prior. +lik = lik_inputdependentnoise('sigma2', 0.1, 'sigma2_prior', prior_fixed()); + +% NOTE! if multiple covariance functions per latent is used, define +% gp.comp_cf as follows: +% gp = gp_set(..., 'comp_cf' {[1 2] [5 6]}; +gp = gp_set('lik', lik, 'cf', {gpcf1 gpcf2}, 'jitterSigma2', 1e-9, 'comp_cf', {[1] [2]}); + +% Set the approximate inference method to Laplace +gp = gp_set(gp, 'latent_method', 'Laplace'); +% For more complex problems, maxiter in latent_opt should be increased. +% gp.latent_opt.maxiter=1e6; + +% Set the options for the optimization +opt=optimset('TolFun',1e-3,'TolX',1e-3,'Derivativecheck','off','Display','iter'); +% Optimize with the scaled conjugate gradient method +gp=gp_optim(gp,xn,yn,'opt',opt); + +% make prediction to the data points +[Ef, Varf,lpyt, Ey, Vary] = gp_pred(gp, xn, yn); +Ef11=Ef(1:n);Ef12=Ef(n+1:end); +Varf11=diag(Varf(1:n,1:n)); +prctmus=[Ef11-1.645*sqrt(Varf11) Ef11 Ef11+1.645*sqrt(Varf11)].*nd.ystd+nd.ymean; +prctys=[Ey-1.645*sqrt(Vary) Ey Ey+1.645*sqrt(Vary)].*nd.ystd+nd.ymean; + +figure; +a4 +% plot mean and 5% and 95% quantiles +subplot(2,1,1) +plot(x,prctmus(:,2),'b',x,prctmus(:,1),'r',x,prctmus(:,3),'r',x,prctys(:,1),'r--',x,prctys(:,3),'r--',x,y,'.') +datetick('x',11) +title('Input dependent noise model -- Laplace approximation'); +legend('Mean','5% f','95% f','5% y','95% y','location','southwest') + + +%% Inference using EP + +% note that lik_epgaussian could be used to include input dependent +% magnitude, too, see demo_epinf +sigma2=1; +lik = lik_epgaussian('sigma2', sigma2, 'sigma2_prior', prior_fixed(), ... + 'int_likparam', true, 'inputparam', true); + +% Set latent options +latent_opt = struct('maxiter',1000, 'df',0.8, 'df2',0.6, 'tol',1e-6, ... + 'parallel', 'on', 'init_prev','off', 'display','off'); + +% NOTE! if multiple covariance functions per latent is used, define +% gp.comp_cf as follows: +% gp = gp_set(..., 'comp_cf' {[1 2] [5 6]}; +gp2 = gp_set('lik', lik, 'cf', {gpcf1 gpcf2}, ... + 'jitterSigma2', 1e-9, 'comp_cf', {1 2}, ... + 'latent_method', 'EP', 'latent_opt', latent_opt); + +gp2 = gp_optim(gp2,xn,yn,'opt',opt, 'optimf', @fminscg); +[Ef, Varf, lpyt, Ey, Vary] = gp_pred(gp2, xn, yn); +prctmus=[Ef(:,1)-1.645*sqrt(Varf(:,1)) ... + Ef(:,1) ... + Ef(:,1)+1.645*sqrt(Varf(:,1))].*nd.ystd+nd.ymean; +prctys=[Ey(:,1)-1.645*sqrt(Vary(:,1)) ... + Ey(:,1) ... + Ey(:,1)+1.645*sqrt(Vary(:,1))].*nd.ystd+nd.ymean; + +subplot(2,1,2) +plot(x,prctmus(:,2),'b',x,prctmus(:,1),'r',x,prctmus(:,3),'r',x,prctys(:,1),'r--',x,prctys(:,3),'r--',x,y,'.') +datetick('x',11) +title('Input dependent noise model -- EP approximation'); +legend('Mean','5% f','95% f','5% y','95% y','location','southwest') diff --git a/gp/demodata/sp500_weekly.csv b/gp/demodata/sp500_weekly.csv new file mode 100644 index 00000000..3b234d49 --- /dev/null +++ b/gp/demodata/sp500_weekly.csv @@ -0,0 +1,731 @@ 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isequal(gpmf.interactions,'on') diff --git a/gp/lgpdens.m b/gp/lgpdens.m index 1a505a83..73631f2e 100644 --- a/gp/lgpdens.m +++ b/gp/lgpdens.m @@ -3,7 +3,7 @@ % % Description % LGPDENS(X,OPTIONS) Compute and plot LGP density estimate. X is -% 1D or 2D point data. For 1D data plot the mean and 95% region. +% 1D or 2D point data. For 1D data plot the mean and 90% region. % For 2D data plot the density contours. % % [P,PQ,XT] = LGPDENS(X,OPTIONS) Compute LGP density estimate @@ -52,6 +52,8 @@ % bounded - in 1D case tells if the density is bounded from left % or right (default is [0 0]). In unbounded case, % decreasing tails are assumed. +% percentiles - the percentiles [x_low x_high] for the LGP density +% estimate. Default is [5, 95]. % % Reference % @@ -86,6 +88,7 @@ ip.addParamValue('cond_dens',[], @(x) ismember(x,{'on' 'off'})); ip.addParamValue('basis','gaussian', @(x) ismember(x,{'gaussian' 'exp' 'off'})); ip.addParamValue('bounded',[0 0], @(x) isnumeric(x) && min(size(x))==1 && max(size(x))==2); + ip.addParamValue('percentiles', [5 95], @(x) isnumeric(x) && min(size(x))==1 && max(size(x))==2); % additional undocumented parameters for importance sampling ip.addParamValue('n_is',8000, @(x) isnumeric(x) && x>=0); @@ -108,6 +111,7 @@ cond_dens=ip.Results.cond_dens; basis=ip.Results.basis; bounded=ip.Results.bounded; + percentiles=ip.Results.percentiles; % additional undocumented parameters for importance sampling @@ -469,10 +473,10 @@ if ~strcmpi(imp_sampling,'off') pp=wmean(pjr',ws)'; - ppq=wprctile(pjr', [5 95], ws)'; + ppq=wprctile(pjr', percentiles, ws)'; else pp=mean(pjr')'; - ppq=prctile(pjr',[5 95])'; + ppq=prctile(pjr',percentiles)'; end if nargout<1 @@ -823,10 +827,10 @@ if ~strcmpi(imp_sampling,'off') pp=wmean(pjr',ws)'; - ppq=wprctile(pjr', [5 95], ws)'; + ppq=wprctile(pjr', percentiles, ws)'; else pp=mean(pjr')'; - ppq=prctile(pjr',[5 95])'; + ppq=prctile(pjr',percentiles)'; end if nargout<1 diff --git a/gp/lik_epgaussian.m b/gp/lik_epgaussian.m index 71ed8c49..79d20b7e 100644 --- a/gp/lik_epgaussian.m +++ b/gp/lik_epgaussian.m @@ -8,7 +8,7 @@ % See also % GP_SET, LIK_* % - +% % Copyright (c) 2013 Ville Tolvanen % This software is distributed under the GNU General Public