function [B, ll] = drbmc(varargin)
%DRBMC Trainable classifier by Discriminative Restricted Boltzmann Machine
%
% W = DRBMC(A,N,L)
% W = A*DRBMC([],N,L)
% W = A*DRBMC(N,L)
%
% INPUT
% A Dataset
% N Number of hidden units
% L Regularization parameter (L2)
%
% OUTPUT
% W Discriminative Restricted Boltzmann Machine classifier
%
% DESCRIPTION
% The classifier trains a discriminative Restricted Boltzmann Machine (RBM)
% on dataset A. The discriminative RBM can be viewed as a logistic
% regressor with hidden units. The discriminative RBM has N hidden units
% (default = 5). It is trained with L2 regularization using regularization
% parameter L (default = 0).
%
% New objects are classified in the same way as in a logistic regressor,
% using a softmax function over the labels.
%
% REFERENCE
% H. Larochelle and Y. Bengio. Classification using Discriminative Restricted
% Boltzmann Machines. Proceedings of the 25th International Conference on
% Machine Learning (ICML), pages 536?543, 2008.
%
% SEE ALSO (<a href="http://37steps.com/prtools">PRTools Guide</a>)
% DATASETS, MAPPINGS, LOGLC
% (C) Laurens van der Maaten, 2010
% University of California, San Diego
% 28 Jan 2013, debugged, default N = 5, PRTools call tests
name = 'Discr. RBM';
argin = shiftargin(varargin,'scalar');
argin = setdefaults(argin,[],5,0,1e-3);
% Handle untrained calls like W = drbmc([]);
if mapping_task(argin,'definition')
B = define_mapping(argin,'untrained',name);
%B = prmapping(mfilename);
%B = setname(B, name);
return;
% Handle training on dataset A (use A * drbmc, A * drbmc([]), and drbmc(A))
elseif mapping_task(argin,'training')
[A,W,L,I] = deal(argin{:});
if ~isa(L, 'double')
error('Illegal call');
end
if ~isa(I, 'double')
error('Illegal call');
end
islabtype(A, 'crisp');
isvaldfile(A, 1, 2);
A = testdatasize(A, 'features');
A = setprior(A, getprior(A));
[m, k, c] = getsize(A);
% Normalize data and add extra feature
train_X = +A;
data.min_X = min(train_X(:));
train_X = train_X - data.min_X;
data.max_X = max(train_X(:));
train_X = train_X / data.max_X;
train_X = (train_X * 2) - 1;
data.max_radius = max(sum(train_X .^ 2, 2));
train_X = [train_X sqrt(data.max_radius - sum(train_X .^ 2, 2))];
% Train the dRBM
[data.machine, ll] = train_drbm(train_X, getnlab(A), W, 100, L, I);
B = prmapping(mfilename, 'trained', data, getlablist(A), k, c);
B = setname(B, name);
% Handle evaluation of a trained dRBM W for a dataset A
elseif mapping_task(argin,'execution')
[A,W] = deal(argin{1:2});
% Normalize data and add extra feature
test_X = +A;
test_X = test_X - W.data.min_X;
test_X = test_X / W.data.max_X;
test_X = (test_X * 2) - 1;
test_X = [test_X sqrt(W.data.max_radius - sum(test_X .^ 2, 2))];
% Evaluate dRBM
[test_labels, test_post] = predict_ff(W.data.machine, test_X, length(W.labels));
A = prdataset(A);
B = setdata(A, real(test_post), getlabels(W));
ll = [];
% This should not happen
else
error('Illegal call');
end
end
function [machine, ll] = train_drbm(X, labels, h, max_iter, weight_cost, variance)
%TRAIN_DRBM Trains a discrimative RBM using gradient descent
%
% machine = train_drbm(X, labels, h, max_iter, weight_cost, variance)
%
% Trains a discriminative Restricted Boltzmann Machine on dataset X. The RBM
% has h hidden nodes (default = 100). The training is performed by means of
% the gradient descent. The visible and hidden units are binary stochastic,
% whereas the label layer has softmax units. The maximum number of
% iterations can be specified through max_iter (default = 30).
% The trained RBM is returned in the machine struct.
%
%
% (C) Laurens van der Maaten
% University of California San Diego, 2010
% Process inputs
if ischar(X)
load(X);
end
if ~exist('h', 'var') || isempty(h)
h = 100;
end
if ~exist('max_iter', 'var') || isempty(max_iter)
max_iter = 15;
end
if ~exist('weight_cost', 'var') || isempty(weight_cost)
weight_cost = 0;
end
% Randomly permute data
ind = randperm(size(X, 1));
X = X(ind,:);
labels = labels(ind);
% Convert labels to binary matrix
no_labels = length(unique(labels));
label_matrix = zeros(length(labels), no_labels);
label_matrix(sub2ind(size(label_matrix), (1:length(labels))', labels)) = 1;
% Initialize some variables
[n, v] = size(X);
machine.W = randn(v, h) * variance;
machine.labW = randn(no_labels, h) * variance;
machine.bias_upW = zeros(1, h);
machine.bias_labW = zeros(1, no_labels);
% Main loop
for iter=1:max_iter
% Encode current solution
x = [machine.W(:); machine.labW(:); machine.bias_upW(:); machine.bias_labW(:)];
% Run conjugate gradients using five linesearches
% checkgrad('drbm_grad', x, 1e-7, machine, cur_X, cur_lab, cur_labmat, weight_cost)
x = minimize(x, 'drbm_grad', 9, machine, X, labels, label_matrix, weight_cost);
% Process the updated solution
ii = 1;
machine.W = reshape(x(ii:ii - 1 + numel(machine.W)), size(machine.W));
ii = ii + numel(machine.W);
machine.labW = reshape(x(ii:ii - 1 + numel(machine.labW)), size(machine.labW));
ii = ii + numel(machine.labW);
machine.bias_upW = reshape(x(ii:ii - 1 + numel(machine.bias_upW)), size(machine.bias_upW));
ii = ii + numel(machine.bias_upW);
machine.bias_labW = reshape(x(ii:ii - 1 + numel(machine.bias_labW)), size(machine.bias_labW));
end
machine.type = 'drbm';
ll = drbm_grad(x, machine, X, labels, label_matrix, weight_cost);
end
function [test_labels, test_post] = predict_ff(machine, test_X, no_labels)
%PREDICT_FF Perform label predictions in a feed-forward neural network
%
% [test_labels, test_post] = predict_ff(network, test_X, no_labels)
%
% The function performs label prediction in the feed-forward neural net
% specified in network (trained using TRAIN_DBN) on dataset test_X. The
% predicted labels are returned in test_labels. The class posterior is
% returned in test_post.
%
%
% (C) Laurens van der Maaten
% University of California San Diego, 2010
% Precompute W dot X + bias
Wx = bsxfun(@plus, test_X * machine.W, machine.bias_upW);
% Loop over all labels to compute p(y|x)
n = size(test_X, 1);
energy = zeros(n, size(machine.labW, 2), no_labels);
label_logpost = zeros(n, no_labels);
for i=1:no_labels
% Clamp current label
lab = zeros(1, no_labels);
lab(i) = 1;
% Compute log-posterior probability for current class
energy(:,:,i) = bsxfun(@plus, lab * machine.labW, Wx);
label_logpost(:,i) = machine.bias_labW(i) + sum(log(1 + exp(energy(:,:,i))), 2);
end
test_post = exp(bsxfun(@minus, label_logpost, max(label_logpost, [], 2)));
test_post = bsxfun(@rdivide, test_post, sum(test_post, 2));
[foo, test_labels] = max(test_post, [], 2);
end
function [C, dC] = drbm_grad(x, machine, X, labels, label_matrix, weight_cost)
%DRBM_GRAD Computes gradient for training a discriminative RBM
%
% [C, dC] = drbm_grad(x, machine, X, labels, label_matrix)
%
% Computes gradient for training a discriminative RBM.
%
%
% (C) Laurens van der Maaten
% University of California San Diego, 2010
% Decode the current solution
if ~isempty(x)
ii = 1;
machine.W = reshape(x(ii:ii - 1 + numel(machine.W)), size(machine.W));
ii = ii + numel(machine.W);
machine.labW = reshape(x(ii:ii - 1 + numel(machine.labW)), size(machine.labW));
ii = ii + numel(machine.labW);
machine.bias_upW = reshape(x(ii:ii - 1 + numel(machine.bias_upW)), size(machine.bias_upW));
ii = ii + numel(machine.bias_upW);
machine.bias_labW = reshape(x(ii:ii - 1 + numel(machine.bias_labW)), size(machine.bias_labW));
end
no_labels = size(label_matrix, 2);
n = size(X, 1);
% Precompute W dot X + bias
Wx = bsxfun(@plus, X * machine.W, machine.bias_upW);
% Loop over all labels to compute p(y|x)
energy = zeros(n, size(machine.labW, 2), no_labels);
label_logpost = zeros(n, no_labels);
for i=1:no_labels
% Clamp current label
lab = zeros(1, no_labels);
lab(i) = 1;
% Compute log-posterior probability for current class
energy(:,:,i) = bsxfun(@plus, lab * machine.labW, Wx);
label_logpost(:,i) = machine.bias_labW(i) + sum(log(1 + exp(energy(:,:,i))), 2);
end
label_post = exp(bsxfun(@minus, label_logpost, max(label_logpost, [], 2)));
label_post = bsxfun(@rdivide, label_post, sum(label_post, 2));
% Compute cost function -sum(log p(y|x))
Pyx = log(sum(label_matrix .* label_post, 2));
C = -sum(Pyx) + weight_cost * sum(machine.W(:) .^ 2);
% Only compute gradients if they are requested
if nargout > 1
% Precompute sigmoids of energies, and products with label posterior
sigmoids = 1 ./ (1 + exp(-energy));
sigmoids_label_post = sigmoids;
for i=1:no_labels
sigmoids_label_post(:,:,i) = bsxfun(@times, sigmoids_label_post(:,:,i), label_post(:,i));
end
% Initialize gradients
grad_W = zeros(size(machine.W));
grad_labW = zeros(size(machine.labW));
grad_bias_upW = zeros(size(machine.bias_upW));
% Sum gradient with respect to the data-hidden weights
for i=1:no_labels
ind = find(labels == i);
grad_W = grad_W + X(ind,:)' * sigmoids(ind,:,i) - X' * sigmoids_label_post(:,:,i);
end
grad_W = grad_W - 2 * weight_cost * machine.W;
% Compute gradient with respect to bias on label-hidden weights
for i=1:no_labels
grad_labW(i,:) = sum(sigmoids(labels == i,:,i), 1) - sum(sigmoids_label_post(:,:,i), 1);
end
% Compute gradient with respect to bias on hidden units
for i=1:no_labels
grad_bias_upW = grad_bias_upW + sum(sigmoids(labels == i,:,i), 1) - sum(sigmoids_label_post(:,:,i), 1);
end
% Compute the gradient with respect to bias on labels
grad_bias_labW = sum(label_matrix - label_post, 1);
% Encode the gradient
dC = -[grad_W(:); grad_labW(:); grad_bias_upW(:); grad_bias_labW(:)];
end
end
function [X, fX, i] = minimize(X, f, length, P1, P2, P3, P4, P5);
% Minimize a continuous differentialble multivariate function. Starting point
% is given by "X" (D by 1), and the function named in the string "f", must
% return a function value and a vector of partial derivatives. The Polack-
% Ribiere flavour of conjugate gradients is used to compute search directions,
% and a line search using quadratic and cubic polynomial approximations and the
% Wolfe-Powell stopping criteria is used together with the slope ratio method
% for guessing initial step sizes. Additionally a bunch of checks are made to
% make sure that exploration is taking place and that extrapolation will not
% be unboundedly large. The "length" gives the length of the run: if it is
% positive, it gives the maximum number of line searches, if negative its
% absolute gives the maximum allowed number of function evaluations. You can
% (optionally) give "length" a second component, which will indicate the
% reduction in function value to be expected in the first line-search (defaults
% to 1.0). The function returns when either its length is up, or if no further
% progress can be made (ie, we are at a minimum, or so close that due to
% numerical problems, we cannot get any closer). If the function terminates
% within a few iterations, it could be an indication that the function value
% and derivatives are not consistent (ie, there may be a bug in the
% implementation of your "f" function). The function returns the found
% solution "X", a vector of function values "fX" indicating the progress made
% and "i" the number of iterations (line searches or function evaluations,
% depending on the sign of "length") used.
%
% Usage: [X, fX, i] = minimize(X, f, length, P1, P2, P3, P4, P5)
%
% Copyright (C) 2001 and 2002 by Carl Edward Rasmussen. Date 2002-02-13
RHO = 0.01; % a bunch of constants for line searches
SIG = 0.5; % RHO and SIG are the constants in the Wolfe-Powell conditions
INT = 0.1; % don't reevaluate within 0.1 of the limit of the current bracket
EXT = 3.0; % extrapolate maximum 3 times the current bracket
MAX = 20; % max 20 function evaluations per line search
RATIO = 100; % maximum allowed slope ratio
argstr = [f, '(X']; % compose string used to call function
for i = 1:(nargin - 3)
argstr = [argstr, ',P', int2str(i)];
end
argstr = [argstr, ')'];
if max(size(length)) == 2, red=length(2); length=length(1); else red=1; end
if length>0, S=['Linesearch']; else S=['Function evaluation']; end
i = 0; % zero the run length counter
ls_failed = 0; % no previous line search has failed
fX = [];
[f1 df1] = eval(argstr); % get function value and gradient
i = i + (length<0); % count epochs?!
s = -df1; % search direction is steepest
d1 = -s'*s; % this is the slope
z1 = red/(1-d1); % initial step is red/(|s|+1)
while i < abs(length) % while not finished
i = i + (length>0); % count iterations?!
X0 = X; f0 = f1; df0 = df1; % make a copy of current values
X = X + z1*s; % begin line search
[f2 df2] = eval(argstr);
i = i + (length<0); % count epochs?!
d2 = df2'*s;
f3 = f1; d3 = d1; z3 = -z1; % initialize point 3 equal to point 1
if length>0, M = MAX; else M = min(MAX, -length-i); end
success = 0; limit = -1; % initialize quanteties
while 1
while ((f2 > f1+z1*RHO*d1) | (d2 > -SIG*d1)) & (M > 0)
limit = z1; % tighten the bracket
if f2 > f1
z2 = z3 - (0.5*d3*z3*z3)/(d3*z3+f2-f3); % quadratic fit
else
A = 6*(f2-f3)/z3+3*(d2+d3); % cubic fit
B = 3*(f3-f2)-z3*(d3+2*d2);
z2 = (sqrt(B*B-A*d2*z3*z3)-B)/A; % numerical error possible - ok!
end
if isnan(z2) | isinf(z2)
z2 = z3/2; % if we had a numerical problem then bisect
end
z2 = max(min(z2, INT*z3),(1-INT)*z3); % don't accept too close to limits
z1 = z1 + z2; % update the step
X = X + z2*s;
[f2 df2] = eval(argstr);
M = M - 1; i = i + (length<0); % count epochs?!
d2 = df2'*s;
z3 = z3-z2; % z3 is now relative to the location of z2
end
if f2 > f1+z1*RHO*d1 | d2 > -SIG*d1
break; % this is a failure
elseif d2 > SIG*d1
success = 1; break; % success
elseif M == 0
break; % failure
end
A = 6*(f2-f3)/z3+3*(d2+d3); % make cubic extrapolation
B = 3*(f3-f2)-z3*(d3+2*d2);
z2 = -d2*z3*z3/(B+sqrt(B*B-A*d2*z3*z3)); % num. error possible - ok!
if ~isreal(z2) | isnan(z2) | isinf(z2) | z2 < 0 % num prob or wrong sign?
if limit < -0.5 % if we have no upper limit
z2 = z1 * (EXT-1); % the extrapolate the maximum amount
else
z2 = (limit-z1)/2; % otherwise bisect
end
elseif (limit > -0.5) & (z2+z1 > limit) % extraplation beyond max?
z2 = (limit-z1)/2; % bisect
elseif (limit < -0.5) & (z2+z1 > z1*EXT) % extrapolation beyond limit
z2 = z1*(EXT-1.0); % set to extrapolation limit
elseif z2 < -z3*INT
z2 = -z3*INT;
elseif (limit > -0.5) & (z2 < (limit-z1)*(1.0-INT)) % too close to limit?
z2 = (limit-z1)*(1.0-INT);
end
f3 = f2; d3 = d2; z3 = -z2; % set point 3 equal to point 2
z1 = z1 + z2; X = X + z2*s; % update current estimates
[f2 df2] = eval(argstr);
M = M - 1; i = i + (length<0); % count epochs?!
d2 = df2'*s;
end % end of line search
if success % if line search succeeded
f1 = f2; fX = [fX' f1]';
s = (df2'*df2-df1'*df2)/(df1'*df1)*s - df2; % Polack-Ribiere direction
tmp = df1; df1 = df2; df2 = tmp; % swap derivatives
d2 = df1'*s;
if d2 > 0 % new slope must be negative
s = -df1; % otherwise use steepest direction
d2 = -s'*s;
end
z1 = z1 * min(RATIO, d1/(d2-realmin)); % slope ratio but max RATIO
d1 = d2;
ls_failed = 0; % this line search did not fail
else
X = X0; f1 = f0; df1 = df0; % restore point from before failed line search
if ls_failed | i > abs(length) % line search failed twice in a row
break; % or we ran out of time, so we give up
end
tmp = df1; df1 = df2; df2 = tmp; % swap derivatives
s = -df1; % try steepest
d1 = -s'*s;
z1 = 1/(1-d1);
ls_failed = 1; % this line search failed
end
end
end
function d = checkgrad(f, X, e, P1, P2, P3, P4, P5, P6);
% checkgrad checks the derivatives in a function, by comparing them to finite
% differences approximations. The partial derivatives and the approximation
% are printed and the norm of the diffrence divided by the norm of the sum is
% returned as an indication of accuracy.
%
% usage: checkgrad('f', X, e, P1, P2, ...)
%
% where X is the argument and e is the small perturbation used for the finite
% differences. and the P1, P2, ... are optional additional parameters which
% get passed to f. The function f should be of the type
%
% [fX, dfX] = f(X, P1, P2, ...)
%
% where fX is the function value and dfX is a vector of partial derivatives.
%
% Carl Edward Rasmussen, 2001-08-01.
argstr = [f, '(X']; % assemble function call strings
argstrd = [f, '(X+dx'];
for i = 1:(nargin - 3)
argstr = [argstr, ',P', int2str(i)];
argstrd = [argstrd, ',P', int2str(i)];
end
argstr = [argstr, ')'];
argstrd = [argstrd, ')'];
[y dy] = eval(argstr); % get the partial derivatives dy
dh = zeros(length(X),1) ;
for j = 1:length(X)
dx = zeros(length(X),1);
dx(j) = dx(j) + e; % perturb a single dimension
y2 = eval(argstrd);
dx = -dx ;
y1 = eval(argstrd);
dh(j) = (y2 - y1)/(2*e);
end
disp([dy dh]) % print the two vectors
d = norm(dh-dy)/norm(dh+dy); % return norm of diff divided by norm of sum
end