blogreg Bayesian logistic regression.
 
    DESCRIPTION
    Multivariate Laplace prior supports spatiotemporal interactions,
    multitask and mixed effects models. The scale property specifies the
    regularization. The bigger the scale, the less the regression
    coefficients will be regularized towards zero. If multiple scales are
    used then the optimal one will be selected based on the log model
    evidence (recorded by the logp property). Note: a bias term is added
    to the model and should not be included explicitly
 
    EXAMPLE
    In the following examples we work with the following input data:
 
    rand('seed',1); randn('seed',1);
    X1 = rand(10,5,10); X2 = X1 + 0.1*randn(size(X1));
    Y1 = [1 1 1 1 1 2 2 2 2 2]'; Y2 = [1 1 1 1 2 1 2 2 2 2]';
 
    Sometimes we assume the input data is just a region of interest that is
    specified by some mask. E.g.
 
    rand('seed',1); randn('seed',1);
    mask = rand(5,10)>0.3;
    X1m = rand(10,sum(mask(:))); X2m = X1m + 0.1*randn(size(X1m)); % create a subset of the data
 
    creates data X1 (and X2) whose columns stand for those elements in the
    mask that are equal to one. The representation for the output stays the
    same.
 
    In the examples use spy(f.prior) to look at the structure of the coupling
    matrix
 
    f = dml.blogreg('scale',logspace(-3,0,4));
    f = f.train(X1,Y1);
    f.test(X1)
 
    Blogreg allows features to become coupled. This is done through the
    coupling property, which specifies for each input dimension the coupling
    strength in that dimension. E.g. coupling = [100 0 100] will strongly couple
    neighboring features in the first and second input dimension. Also,
    the input dimensions of the original data must be specified through the indims property.
 
    f = dml.blogreg('indims',[5 10],'coupling',[100 100]);
    f = f.train(X1,Y1);
    f.test(X1)
 
    In case the input data X is just a region of interest then we can use a
    mask to indicate which features from the original volume of data are
    represented by X. This still allows us to use the above approach to
    specify the coupling.
 
    f = dml.blogreg('indims',[5 10],'coupling',[100 100],'mask',mask);
    f = f.train(X1m,Y1);
    f.test(X1m)
 
    In the following we discuss some more exotic uses of blogreg, which
    is not required by the typical user.
 
    Multitask learning (multitask = true) is implemented by augmenting the data matrix as
    [ T1     0   ]
    [ 0      T2  ]
    etc and coupling the tasks through the taskcoupling property. Data X and Y must be given by a cell-array.
 
    f = dml.blogreg('multitask',1);
    f = f.train({X1 X2},{Y1 Y2});
    f.test({X1 X2})
 
    This can also be combined with coupling of the features themselves.
 
    f = dml.blogreg('multitask',1,'indims',[5 10],'coupling',[100 100],'mask',mask);
    f = f.train({X1m X2m},{Y1 Y2});
    f.test({X1m X2m})
 
    Blogreg also supports a mixed effects model (mixed = true)
    of the form
    [ M1 M1 0 ]
    [ M2 0 M2 ]
    where the first column contains the "fixed effects" and the remaining
    columns the "random effects". The basic idea is that if prediction is
    supported by a fixed effect then it will be chosen since this incurs the
    smallest penalty in terms of sparseness. Data should be given by a
    cell-array.
 
    f = dml.blogreg('mixed',1);
    f = f.train({X1 X2}',{Y1 Y2}');
    f.test({X1 X2})
 
    This can also be combined with coupling of the features themselves.
    If a coupling is specified then this coupling will only operate on the
    fixed effects using mixed=1 and on both the fixed and random effects
    using mixed=2.
 
    f = dml.blogreg('mixed',1,'indims',[5 10],'coupling',[100 100],'mask',mask);
    f = f.train({X1m X2m}',{Y1 Y2}');
    f.test({X1m X2m})
 
    If the input data is a cell-array of cell-arrays then we assume a mixed
    effects model for multiple tasks. The output will have the same
    structure. E.g. model{i}{j,k} will be the j-th model for the k-th mixed
    effect in the i-th subject. Note that k=1 is the fixed effect and k>1 are
    the random effects.
 
    f = dml.blogreg('mixed',1,'multitask',1);
    f = f.train({{X1 X2} {X1 X2}},{{Y1 Y2} {Y1 Y2}});
    f.test({{X1 X2} {X1 X2}})
 
    If mixed = 1 then the only coupling  (spatial or multitask) will be for
    the fixed effects part. For mixed = 2, also the random effects will be coupled.
 
    f = dml.blogreg('mixed',1,'multitask',1,'coupling',[100 100],'indims',[5 10],'mask',mask);
    f = f.train({ {X1m X2m} {X1m X2m} },{ {Y1 Y2} {Y1 Y2} });
    f.test({{X1m X2m} {X1m X2m}})
 
 
    REFERENCE
 
    When using this method please refer to the following:
 
    van Gerven et al. Efficient Bayesian multivariate fMRI analysis using a
    sparsifying spatio-temporal prior. Neuroimage, 2010
 
    van Gerven & Simanova. Concept classification with Bayesian multitask
    learning, NAACL, 2010
 
    DEVELOPER
    Marcel van Gerven (m.vangerven@donders.ru.nl)