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Iccs_Pind.m
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Iccs_Pind.m
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function Iccs = Iccs_Pind(A, Pjoint)
% calculate redundancy between a set of sources
% from pointwise common change in surprise
% using conditional independent joint-source distribution
%
% A - cell array of sources
% Pjoint - full joint distribution (S last axis)
isclosefp = @(a,b) abs(a - b) <= eps(max(abs(a), abs(b)));
s = size(Pjoint);
Sm = s(end); % number of target values
Nx = length(s)-1; % number of dependent variables
vars = 1:Nx;
NA = length(A);
if NA>3
error('Iccs: only 3 sources supported')
end
PA(NA).Pa = []; % intialize struct
Am = zeros(1,NA); % number of symbols in each element
% Ps
Ps = Pjoint;
for xi=1:Nx
Ps = squeeze(sum(Ps,1));
end
% sort variables within each source
A = cellfun(@sort, A, 'Unif',false);
% build distributions for each source
for ai=1:NA
thsA = A{ai};
Nv = length(thsA);
% vars to sum over
sumover = setdiff(vars, thsA);
Pas = Pjoint;
for ii=1:length(sumover)
Pas = sum(Pas, sumover(ii));
end
% joint distribution P(a,s)
Pas = squeeze(Pas);
% target first axis to collapse over non-target axes
% Pas = permute(Pas, [Nv+1 1:Nv]);
% Pas = Pas(:,:)';
s = size(Pas);
Pas = reshape(Pas, [prod(s(1:end-1)) s(end)]);
PA(ai).Pas = Pas;
% unconditional distribution P(a)
PA(ai).Pa = squeeze(sum(Pas,2));
% conditional distribution P(a|s)
PA(ai).Pacs = bsxfun(@rdivide, PA(ai).Pas, Ps);
Am(ai) = size(Pas,1);
end
% build pairwise joint source distributions
if NA==2
pairs = nchoosek(1:NA,2);
Npair = size(pairs,1);
Ppair(Npair).Paa = []; % intialize struct
for pi=1:Npair
p1 = pairs(pi,1);
p2 = pairs(pi,2);
Ppair(pi).Paacs = zeros(Am(p1),Am(p2),Sm);
for si=1:Sm
Paacs(:,:,si) = PA(p1).Pacs(:,si) * PA(p2).Pacs(:,si)';
end
Ppair(pi).Paacs = Paacs;
Paas = bsxfun(@times, Paacs, reshape(Ps,[1 1 Sm]));
Ppair(pi).Paas = Paas;
Ppair(pi).Paa = nansum(Paas,3);
end
end
% build triplewise joint source distributions
if NA==3
Paaacs = zeros(Am(1),Am(2),Am(3),Sm);
for si=1:Sm
Paac = PA(1).Pacs(:,si) * PA(2).Pacs(:,si)';
Paaacs(:,:,:,si) = bsxfun(@times, Paac, reshape(PA(3).Pacs(:,si), [1 1 Am(3)]));
end
Ptrip(1).Paaacs = Paaacs;
Paaas = bsxfun(@times, Paaacs, reshape(Ps,[1 1 1 Sm]));
Ptrip(1).Paaas = Paaas;
Ptrip(1).Paaa = nansum(Paaas,4);
% now build pairwise distributions from this maxent solution
pairs = nchoosek(1:3,2);
Npair = size(pairs,1);
Ppair(Npair).Paa = []; % intialize struct
for pi=1:Npair
keepax = [pairs(pi,1) pairs(pi,2)];
% collapse variables we don't need
sumover = setdiff(1:3, keepax);
Paas = Paaas;
for ii=1:length(sumover)
Paas = sum(Paas, sumover(ii));
end
Paas = squeeze(Paas);
Ppair(pi).Paas = Paas;
Ppair(pi).Paa = squeeze(sum(Paas,3));
end
end
% pointwise interaction information
cds = zeros([Am Sm]);
if NA==1
for a1=1:Am(1)
for si=1:Sm
ds1 = log2( PA(1).Pas(a1,si) ./ (PA(1).Pa(a1)*Ps(si)) );
cds(a1,si) = ds1;
end
end
% keyboard
cds = PA(1).Pas .* cds;
elseif NA==2
for a1=1:Am(1)
for a2=1:Am(2)
for si=1:Sm
dsj = log2( Ppair(1).Paas(a1,a2,si) / (Ppair(1).Paa(a1,a2)*Ps(si)) );
ds1 = log2( PA(1).Pas(a1,si) ./ (PA(1).Pa(a1)*Ps(si)) );
ds2 = log2( PA(2).Pas(a2,si) ./ (PA(2).Pa(a2)*Ps(si)) );
overlap = ds1 + ds2 - dsj;
if isfinite(overlap) && (abs(overlap)-min(abs([ds1 ds2])))>2*eps(abs(overlap))
fprintf(1,'Warning [%d %d %d] : Overlap larger than individuals. overlap: %6.3f ds1: %6.3f ds2: %6.3f\n',a1,a2,si,overlap,ds1,ds2)
fprintf(1,'overlap: %d ds1: %d ds2: %d\n',sign(overlap),sign(ds1),sign(ds2))
end
if sign(ds1)==sign(ds2)
% change of surprise has same size so possibility of
% overlap
if sign(dsj)~=sign(ds1)
% fprintf(1,'Warning [%d %d %d] : DSJ sign flip dsj: %6.3f ds1: %6.3f ds2: %6.3f\n',a1,a2,si,dsj,ds1,ds2)
% keyboard
continue
end
overlap = ds1 + ds2 - dsj;
if sign(overlap)==sign(ds1)
% redundant (mis)information
if isfinite(overlap) && (abs(overlap)-min(abs([ds1 ds2])))>2*eps(abs(overlap))
fprintf(1,'Warning [%d %d %d] : Overlap larger than individuals. overlap: %6.3f ds1: %6.3f ds2: %6.3f\n',a1,a2,si,overlap,ds1,ds2)
end
cds(a1,a2,si) = overlap;
end
end
end
end
end
cds = Ppair(1).Paas .* cds;
elseif NA==3
for a1=1:Am(1)
for a2=1:Am(2)
for a3=1:Am(3)
for si=1:Sm
ds123 = log2( Ptrip(1).Paaas(a1,a2,a3,si) / (Ptrip(1).Paaa(a1,a2,a3)*Ps(si)) );
ds1 = log2( PA(1).Pas(a1,si) ./ (PA(1).Pa(a1)*Ps(si)) );
ds2 = log2( PA(2).Pas(a2,si) ./ (PA(2).Pa(a2)*Ps(si)) );
ds3 = log2( PA(3).Pas(a3,si) ./ (PA(3).Pa(a3)*Ps(si)) );
ds12 = log2( Ppair(1).Paas(a1,a2,si) / (Ppair(1).Paa(a1,a2)*Ps(si)) );
ds13 = log2( Ppair(2).Paas(a1,a3,si) / (Ppair(2).Paa(a1,a3)*Ps(si)) );
ds23 = log2( Ppair(3).Paas(a2,a3,si) / (Ppair(3).Paa(a2,a3)*Ps(si)) );
if (sign(ds1)==sign(ds2)) && (sign(ds2)==sign(ds3))
% change of surprise has same sign for all 3
% variables, so possibility of overlap
if sign(ds123)~=sign(ds1)
% fprintf(1,'Warning [%d %d %d %d] : DSJ sign flip dsj: %6.3f ds1: %6.3f ds2: %6.3f ds3: %6.3f\n',a1,a2,a3,si,ds123,ds1,ds2,ds3)
continue
end
overlap = ds1 + ds2 + ds3 - ds12 - ds13 - ds23 + ds123;
if sign(overlap)==sign(ds1)
% redundant (mis)information
if isfinite(overlap) && (abs(overlap)-max(abs([ds1 ds2 ds3])))>6*eps(min(abs([overlap ds1 ds2 ds3])))
fprintf(1,'Warning [%d %d %d %d] : Overlap larger than individual overlap: %6.3f ds1: %6.3f ds2: %6.3f ds3: %6.3f\n',a1,a2,a3,si,overlap,ds1,ds2,ds3)
end
cds(a1,a2,a3,si) = overlap;
end
end
end
end
end
end
cds = Ptrip(1).Paaas .* cds;
end
locred = nansum(cds(:));
Iccs = locred;