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    Metadata details:
    filename: VBA_classification.m
    path of file: ./repos/VBA-toolbox/modules/classification
    
    the code of the file until where you have to start completion: function [all] = VBA_classification(X,y,k,verbose,options,sparse)

    
function [all] = VBA_classification(X,y,k,verbose,options,sparse)
% performs binary classification using VBA
% function [pv,stat,df,all] = VBA_classification(X,y,k,verbose,options)
% In brief, this function fits the following logistic regresion model:
%   p(y=1) = s(X*beta)
% where y is the binary data, s is the standard sigmoid mapping, X is the
% design matrix and beta are unknown weight parameters.
% Statistical testing is performed using cross-validation scheme, such that
% the p-value computes the probability of the test score under the null H0.
% In cross-validation, the test score is the binary accuracy outcome
% sampled across test sets. The null distribution accounts for potential
% imbalance in the data in that the first-order moment of the corresponding
% binomial distribution is specified in terms of the sample mean of the
% data. VBA_classification uses a k-fold cross-validation scheme, which
% involves partitioning the data into k subsamples of equal size, each of
% which is used as the test set in turn.
% Note: VBA_classification also performs a fully Bayesian model inversion
% on the entire dataset (full-data inversion).
% IN:
%   - X: nXp design matrix
%   - y: nX1 binary data matrix
%   - k: the number of folds for the k-fold cross-validation scheme. If k
%   is set to n (default), then VBA_classification uses a leave-one-out
%   scheme. If k is set to 0, then the cross-validation scheme is entirely
%   skipped (only the full-data inversion is performed).
%   - verbose: flag for displaying results (default is 0)
%   - options: structure containing VBA's options (can be used for passing,
%   e.g., priors on classification weight parameters)
%   - sparse: when sparse=1, VBA_classification uses sparsifying priors
%   (default=0).
% OUT:
%   - all: structure array with fields:
%       .stat: structure of summary statistics:
%           .pv: classical p-value on classifier accuracy
%           .success: nx1 vector of successful classifications
%           .pa: cross-validation prediction accuracy
%           .bpa: balanced prediction accuracy
%           .pBayes: Bayesian exceedance prob. on prediction accuracy
%       .P: pxk matrix of estimated classification weights
%       .r: data imbalance (r=0.5 means balanced data)
%       .in: structure storing the inputs to VBA_classification
%       .date: date stamp
%       .dt: computing time
%       .handles: a structure containing the handles of the graphical
%       objects (filled-in by VBA_classication_display.m)
% Note: cross-validation results can be displayed using the following
% command line: VBA_classification_display(all).

% fill in default I/O
tStart = tic;
all = [];
[n,m] = size(y);
[n0,p] = size(X);

try,k;catch,k=n;end