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rmlr_train.m
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function [W, Xi, Diagnostics] = rmlr_train(X, Y, Cslack, varargin)
%[W, Xi, D] = rmlr_train(X, Y, C, LOSS, k, REG, Diagonal, stochastic, lam, STRUCTREG)
%
% [W, Xi, D] = rmlr_train(X, Y, C,...)
%
% X = d*n data matrix
% Y = either n-by-1 label of vectors
% OR
% n-by-2 cell array where
% Y{q,1} contains relevant indices for q, and
% Y{q,2} contains irrelevant indices for q
%
% C >= 0 slack trade-off parameter (default=1)
%
% W = the learned metric
% Xi = slack value on the learned metric
% D = diagnostics
%
% Optional arguments:
%
% [W, Xi, D] = rmlr_train(X, Y, C, LOSS)
% where LOSS is one of:
% 'AUC': Area under ROC curve (default)
% 'KNN': KNN accuracy
% 'Prec@k': Precision-at-k
% 'MAP': Mean Average Precision
% 'MRR': Mean Reciprocal Rank
% 'NDCG': Normalized Discounted Cumulative Gain
%
% [W, Xi, D] = rmlr_train(X, Y, C, LOSS, k)
% where k is the number of neighbors for Prec@k or NDCG
% (default=3)
%
% [W, Xi, D] = rmlr_train(X, Y, C, LOSS, k, REG)
% where REG defines the regularization on W, and is one of:
% 0: no regularization
% 1: 1-norm: trace(W) (default)
% 2: 2-norm: trace(W' * W)
% 3: Kernel: trace(W * X), assumes X is square and positive-definite
%
% [W, Xi, D] = rmlr_train(X, Y, C, LOSS, k, REG, Diagonal)
% Not implemented as learning a diagonal W metric just reduces to MLR because ||W||_2,1 = trace(W) when W is diagonal.
%
% [W, Xi, D] = rmlr_train(X, Y, C, LOSS, k, REG, Diagonal, B)
% where B > 0 enables stochastic optimization with batch size B
%
% [W, Xi, D] = rmlr_train(X, Y, C, LOSS, k, REG, Diagonal, B, lambda)
% lambda is the desired value of the hyperparameter which is the coefficient of ||W||_2,1. Default is 1 if lambda is not set
TIME_START = tic();
global C;
C = Cslack;
[d,n,m] = size(X);
if m > 1
MKL = 1;
else
MKL = 0;
end
if nargin < 3
C = 1;
end
%%%
% Default options:
global CP SO PSI REG FEASIBLE LOSS DISTANCE SETDISTANCE CPGRADIENT STRUCTKERNEL DUALW THRESH INIT;
global RHO;
% </modified>
global FEASIBLE_COUNT;
FEASIBLE_COUNT = 0;
CP = @cuttingPlaneFull;
SO = @separationOracleAUC;
PSI = @metricPsiPO;
if ~MKL
INIT = @initializeFull;
REG = @regularizeTraceFull;
STRUCTKERNEL= @structKernelLinear;
DUALW = @dualWLinear;
FEASIBLE = @feasibleFull;
THRESH = @threshFull_mixed;
CPGRADIENT = @cpGradientFull;
DISTANCE = @distanceFull;
SETDISTANCE = @setDistanceFull;
LOSS = @lossHinge;
Regularizer = 'Trace';
else
INIT = @initializeFullMKL;
REG = @regularizeMKLFull;
STRUCTKERNEL= @structKernelMKL;
DUALW = @dualWMKL;
FEASIBLE = @feasibleFullMKL;
THRESH = @threshFull_mixed;
CPGRADIENT = @cpGradientFullMKL;
DISTANCE = @distanceFullMKL;
SETDISTANCE = @setDistanceFullMKL;
LOSS = @lossHingeFullMKL;
Regularizer = 'Trace';
end
Loss = 'AUC';
Feature = 'metricPsiPO';
%%%
% Default k for prec@k, ndcg
k = 3;
%%%
% Stochastic violator selection?
STOCHASTIC = 0;
batchSize = n;
SAMPLES = 1:n;
if nargin > 3
switch lower(varargin{1})
case {'auc'}
SO = @separationOracleAUC;
PSI = @metricPsiPO;
Loss = 'AUC';
Feature = 'metricPsiPO';
case {'knn'}
SO = @separationOracleKNN;
PSI = @metricPsiPO;
Loss = 'KNN';
Feature = 'metricPsiPO';
case {'prec@k'}
SO = @separationOraclePrecAtK;
PSI = @metricPsiPO;
Loss = 'Prec@k';
Feature = 'metricPsiPO';
case {'map'}
SO = @separationOracleMAP;
PSI = @metricPsiPO;
Loss = 'MAP';
Feature = 'metricPsiPO';
case {'mrr'}
SO = @separationOracleMRR;
PSI = @metricPsiPO;
Loss = 'MRR';
Feature = 'metricPsiPO';
case {'ndcg'}
SO = @separationOracleNDCG;
PSI = @metricPsiPO;
Loss = 'NDCG';
Feature = 'metricPsiPO';
otherwise
error('MLR:LOSS', ...
'Unknown loss function: %s', varargin{1});
end
end
if nargin > 4
k = varargin{2};
end
Diagonal = 0;
%Diagonal case is not implemented. Use mlr_train for that.
if nargin > 5
switch(varargin{3})
case {0}
REG = @regularizeNone;
Regularizer = 'None';
THRESH = @threshFull_mixed;
case {1}
if MKL
REG = @regularizeMKLFull;
STRUCTKERNEL= @structKernelMKL;
DUALW = @dualWMKL;
else
REG = @regularizeTraceFull;
STRUCTKERNEL= @structKernelLinear;
DUALW = @dualWLinear;
end
Regularizer = 'Trace';
case {2}
REG = @regularizeTwoFull;
Regularizer = '2-norm';
error('MLR:REGULARIZER', '2-norm regularization no longer supported');
case {3}
if MKL
REG = @regularizeMKLFull;
STRUCTKERNEL= @structKernelMKL;
DUALW = @dualWMKL;
else
REG = @regularizeKernel;
STRUCTKERNEL= @structKernelMKL;
DUALW = @dualWMKL;
end
Regularizer = 'Kernel';
otherwise
error('MLR:REGULARIZER', ...
'Unknown regularization: %s', varargin{3});
end
end
% Are we in stochastic optimization mode?
if nargin > 7 && varargin{5} > 0
if varargin{5} < n
STOCHASTIC = 1;
CP = @cuttingPlaneRandom;
batchSize = varargin{5};
end
end
% Algorithm
%
% Working <- []
%
% repeat:
% (W, Xi) <- solver(X, Y, C, Working)
%
% for i = 1:|X|
% y^_i <- argmax_y^ ( Delta(y*_i, y^) + w' Psi(x_i, y^) )
%
% Working <- Working + (y^_1,y^_2,...,y^_n)
% until mean(Delta(y*_i, y_i)) - mean(w' (Psi(x_i,y_i) - Psi(x_i,y^_i)))
% <= Xi + epsilon
if nargin > 8
lam = varargin{6};
else
lam = 1;
end
disp(['lam = ' num2str(lam)])
global DEBUG;
if isempty(DEBUG)
DEBUG = 0;
end
DEBUG = 1;
%%%
% Max calls to seperation oracle
MAX_CALLS = 200;
MIN_CALLS = 10;
%%%
% Timer to eliminate old constraints
ConstraintClock = 500;
%%%
% Convergence criteria for worst-violated constraint
E = 1e-3;
%XXX: 2012-01-31 21:29:50 by Brian McFee <[email protected]>
% no longer belongs here
% Initialize
W = INIT(X);
global ADMM_Z ADMM_V ADMM_UW ADMM_UV;
ADMM_Z = W;
ADMM_V = W;
ADMM_UW = 0 * ADMM_Z;
ADMM_UV = 0 * ADMM_Z;
ClassScores = [];
if isa(Y, 'double')
Ypos = [];
Yneg = [];
ClassScores = synthesizeRelevance(Y);
elseif isa(Y, 'cell') && size(Y,1) == n && size(Y,2) == 2
dbprint(1, 'Using supplied Ypos/Yneg');
Ypos = Y(:,1);
Yneg = Y(:,2);
% Compute the valid samples
SAMPLES = find( ~(cellfun(@isempty, Y(:,1)) | cellfun(@isempty, Y(:,2))));
elseif isa(Y, 'cell') && size(Y,1) == n && size(Y,2) == 1
dbprint(1, 'Using supplied Ypos/synthesized Yneg');
Ypos = Y(:,1);
Yneg = [];
SAMPLES = find( ~(cellfun(@isempty, Y(:,1))));
else
error('MLR:LABELS', 'Incorrect format for Y.');
end
%%
% If we don't have enough data to make the batch, cut the batch
batchSize = min([batchSize, length(SAMPLES)]);
Diagnostics = struct( 'loss', Loss, ... % Which loss are we optimizing?
'feature', Feature, ... % Which ranking feature is used?
'k', k, ... % What is the ranking length?
'regularizer', Regularizer, ... % What regularization is used?
'diagonal', Diagonal, ... % 0 for full metric, 1 for diagonal
'num_calls_SO', 0, ... % Calls to separation oracle
'num_calls_solver', 0, ... % Calls to solver
'time_SO', 0, ... % Time in separation oracle
'time_solver', 0, ... % Time in solver
'time_total', 0, ... % Total time
'f', [], ... % Objective value
'num_steps', [], ... % Number of steps for each solver run
'num_constraints', [], ... % Number of constraints for each run
'Xi', [], ... % Slack achieved for each run
'Delta', [], ... % Mean loss for each SO call
'gap', [], ... % Gap between loss and slack
'C', C, ... % Slack trade-off
'epsilon', E, ... % Convergence threshold
'feasible_count', FEASIBLE_COUNT, ... % Counter for # svd's
'constraint_timer', ConstraintClock); % Time before evicting old constraints
global PsiR;
global PsiClock;
PsiR = {};
PsiClock = [];
Xi = -Inf;
Margins = [];
H = [];
Q = [];
if STOCHASTIC
dbprint(1, 'STOCHASTIC OPTIMIZATION: Batch size is %d/%d', batchSize, n);
end
dbprint(1,['Regularizer is "' Regularizer '"']);
while 1
if Diagnostics.num_calls_solver > MAX_CALLS
dbprint(1,['Calls to SO >= ' num2str(MAX_CALLS)]);
break;
end
dbprint(1, 'Round %03d', Diagnostics.num_calls_solver);
% Generate a constraint set
Termination = -Inf;
dbprint(2, 'Calling separation oracle...');
[PsiNew, Mnew, SO_time] = CP(k, X, W, Ypos, Yneg, batchSize, SAMPLES, ClassScores);
Termination = LOSS(W, PsiNew, Mnew, 0);
Diagnostics.num_calls_SO = Diagnostics.num_calls_SO + 1;
Diagnostics.time_SO = Diagnostics.time_SO + SO_time;
Margins = cat(1, Margins, Mnew);
PsiR = cat(1, PsiR, PsiNew);
PsiClock = cat(1, PsiClock, 0);
H = expandKernel(H);
Q = expandRegularizer(Q, X, W);
dbprint(2, '\n\tActive constraints : %d', length(PsiClock));
dbprint(2, '\t Mean loss : %0.4f', Mnew);
dbprint(2, '\t Current loss Xi : %0.4f', Xi);
dbprint(2, '\t Termination -Xi < E : %0.4f <? %.04f\n', Termination - Xi, E);
Diagnostics.gap = cat(1, Diagnostics.gap, Termination - Xi);
Diagnostics.Delta = cat(1, Diagnostics.Delta, Mnew);
%if Termination <= Xi + E
if Termination <= Xi + E && Diagnostics.num_calls_solver > MIN_CALLS
%if Termination - Xi <= E
dbprint(1, 'Done.');
break;
end
dbprint(1, 'Calling solver...');
PsiClock = PsiClock + 1;
Solver_time = tic();
% disp('Robust MLR')
[W, Xi, Dsolver] = rmlr_admm(C, X, Margins, H, Q, lam);
Diagnostics.time_solver = Diagnostics.time_solver + toc(Solver_time);
Diagnostics.num_calls_solver = Diagnostics.num_calls_solver + 1;
Diagnostics.Xi = cat(1, Diagnostics.Xi, Xi);
Diagnostics.f = cat(1, Diagnostics.f, Dsolver.f);
Diagnostics.num_steps = cat(1, Diagnostics.num_steps, Dsolver.num_steps);
%%%
% Cull the old constraints
GC = PsiClock < ConstraintClock;
Margins = Margins(GC);
PsiR = PsiR(GC);
PsiClock = PsiClock(GC);
H = H(GC, GC);
Q = Q(GC);
Diagnostics.num_constraints = cat(1, Diagnostics.num_constraints, length(PsiR));
end
% Finish diagnostics
Diagnostics.time_total = toc(TIME_START);
Diagnostics.feasible_count = FEASIBLE_COUNT;
end
function H = expandKernel(H)
global STRUCTKERNEL;
global PsiR;
m = length(H);
H = padarray(H, [1 1], 0, 'post');
for i = 1:m+1
H(i,m+1) = STRUCTKERNEL( PsiR{i}, PsiR{m+1} );
H(m+1, i) = H(i, m+1);
end
end
function Q = expandRegularizer(Q, K, W)
% FIXME: 2012-01-31 21:34:15 by Brian McFee <[email protected]>
% does not support unregularized learning
global PsiR;
global STRUCTKERNEL REG;
m = length(Q);
Q(m+1,1) = STRUCTKERNEL(REG(W,K,1), PsiR{m+1});
end
function ClassScores = synthesizeRelevance(Y)
classes = unique(Y);
nClasses = length(classes);
ClassScores = struct( 'Y', Y, ...
'classes', classes, ...
'Ypos', [], ...
'Yneg', []);
Ypos = cell(nClasses, 1);
Yneg = cell(nClasses, 1);
for c = 1:nClasses
Ypos{c} = (Y == classes(c));
Yneg{c} = ~Ypos{c};
end
ClassScores.Ypos = Ypos;
ClassScores.Yneg = Yneg;
end