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show_mc_jester_plots.m
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show_mc_jester_plots.m
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function show_mc_jester_plots()
% This file is part of RSOpt package.
%
% Created by H.Kasai and B.Mishra on Sep. 13, 2018
clc; close all; clear
%% set parameters
maxepoch = 36;
N = 100;
d = 24983;
r = 5;
tolgradnorm = 1e-8;
batchsize = 1;
inner_repeat = 1;
srg_varpi = 0.5;
%% generate dataset
[samples, samples_test, samples_valid, values, indicator, values_test, indicator_test, data_ls, data_test, ~] = generate_mc_data_jester();
%% set manifold
problem.M = grassmannfactory(d, r);
problem.ncostterms = N;
%% define problem
% cost function
problem.cost = @mc_cost;
function f = mc_cost(U)
W = mylsqfit(U, samples);
f = 0.5*norm(indicator.*(U*W') - values, 'fro')^2;
f = f/N;
end
% Euclidean gradient of the cost function
problem.egrad = @mc_egrad;
function g = mc_egrad(U)
W = mylsqfit(U, samples);
g = (indicator.*(U*W') - values)*W;
g = g/N;
end
% Euclidean stochastic gradient of the cost function
problem.partialegrad = @mc_partialegrad;
function g = mc_partialegrad(U, idx_batchsize)
g = zeros(d, r);
m_batchsize = length(idx_batchsize);
for ii = 1 : m_batchsize
colnum = idx_batchsize(ii);
w = mylsqfit(U, samples(colnum));
indicator_vec = indicator(:, colnum);
values_vec = values(:, colnum);
g = g + (indicator_vec.*(U*w') - values_vec)*w;
end
g = g/m_batchsize;
end
function W = mylsqfit(U, currentsamples)
W = zeros(length(currentsamples), size(U, 2));
for ii = 1 : length(currentsamples)
% Pull out the relevant indices and revealed entries for this column
IDX = currentsamples(ii).indicator;
values_Omega = currentsamples(ii).values;
U_Omega = U(IDX,:);
% Solve a simple least squares problem to populate U
W(ii,:) = (U_Omega\values_Omega)';
end
end
% % Consistency checks
% checkgradient(problem)
% pause;
%% run algorithms
% Initialize
Uinit = problem.M.rand();
% R-SD
clear options;
options.maxiter = maxepoch;
options.tolgradnorm = tolgradnorm;
options.statsfun = @mc_mystatsfun;
[~, ~, infos_sd, options_sd] = steepestdescent(problem, Uinit, options);
% R-CG
clear options;
options.maxiter = maxepoch;
options.tolgradnorm = tolgradnorm;
options.statsfun = @mc_mystatsfun;
[~, ~, infos_cg, options_cg] = conjugategradient(problem, Uinit, options);
% R-SGD with decay step-size
clear options;
options.verbosity = 1;
options.batchsize = batchsize;
options.update_type='sgd';
options.maxepoch = maxepoch;
options.tolgradnorm = tolgradnorm;
options.stepsize_type = 'decay';
options.stepsize = 1e-7;
options.stepsize_lambda = 1e-3;
options.transport = 'ret_vector';
options.maxinneriter = N;
options.statsfun = @mc_mystatsfun;
[~, ~, infos_sgd, options_sgd] = Riemannian_svrg(problem, Uinit, options);
% R-SVRG
clear options;
options.verbosity = 1;
options.batchsize = batchsize;
options.update_type='svrg';
options.maxepoch = maxepoch / (1 + 2 * inner_repeat);
options.tolgradnorm = tolgradnorm;
options.svrg_type = 1;
options.stepsize_type = 'fix';
options.stepsize = 1e-6;
options.boost = 0;
options.svrg_type = 1; % effective only for R-SVRG variants
options.transport = 'ret_vector';
options.maxinneriter = inner_repeat * N;
options.statsfun = @mc_mystatsfun;
[~, ~, infos_svrg, options_svrg] = Riemannian_svrg(problem, Uinit, options);
% R-SRG
clear options;
options.verbosity = 1;
options.batchsize = batchsize;
options.update_type='srg';
options.maxepoch = maxepoch / (1 + 2 * inner_repeat);
options.tolgradnorm = tolgradnorm;
options.stepsize_type = 'fix';
options.stepsize = 1e-6;
options.transport = 'ret_vector';
options.maxinneriter = inner_repeat * N;
options.statsfun = @mc_mystatsfun;
[~, ~, infos_srg, options_srg] = Riemannian_srg(problem, Uinit, options);
% R-SRG+
clear options;
options.verbosity = 1;
options.batchsize = batchsize;
options.update_type='srg';
options.maxepoch = maxepoch / (1 + 2 * inner_repeat);
options.tolgradnorm = tolgradnorm;
options.stepsize_type = 'fix';
options.stepsize = 1e-6;
options.transport = 'ret_vector';
options.maxinneriter = inner_repeat * N;
options.gamma = srg_varpi;
options.statsfun = @mc_mystatsfun;
[~, ~, infos_srg_plus, options_srg_plus] = Riemannian_srg(problem, Uinit, options);
% Calculate # of gradient evaluations
num_grads_sd = (1:length([infos_sd.cost])) - 1; % N*options_sd.maxiter;
num_grads_cg = (1:length([infos_cg.cost])) - 1; % N*options_sd.maxiter;
num_grads_sgd = ceil(options_sgd.maxinneriter/N)*((1:length([infos_sgd.cost])) - 1); % options.maxepoch*(options_sgd.maxinneriter);
num_grads_svrg = ceil((N + 2*options_svrg.maxinneriter)/N)*((1:length([infos_svrg.cost])) - 1); %options.maxepoch*(N + options_svrg.maxinneriter); % Per epoch we compute equivalent of 2 batch grads.
for kk = 1 : size(infos_srg,2)
num_grads_srg(kk) = infos_srg(kk).grad_cnt;
end
num_grads_srg = num_grads_srg/N;
for kk = 1 : size(infos_srg_plus,2)
num_grads_srg_plus(kk) = infos_srg_plus(kk).grad_cnt;
end
num_grads_srg_plus = num_grads_srg_plus/N;
%% plots
fs = 20;
% Train MSE versus #grads/N
figure;
semilogy(num_grads_sd, [infos_sd.cost] * 2 * N / data_ls.nentries,'-','LineWidth',2,'Color', [255, 128, 0]/255); hold on;
semilogy(num_grads_cg, [infos_cg.cost] * 2 * N / data_ls.nentries,'-','LineWidth',2,'Color', [76, 153, 0]/255); hold on;
semilogy(num_grads_sgd, [infos_sgd.cost] * 2 * N / data_ls.nentries,'-','LineWidth',2,'Color', [255,0,255]/255); hold on;
semilogy(num_grads_svrg, [infos_svrg.cost] * 2 * N / data_ls.nentries, '-', 'LineWidth',2,'Color', [255, 0, 0]/255); hold on;
semilogy(num_grads_srg, [infos_srg.cost] * 2 * N / data_ls.nentries, '-', 'LineWidth',2,'Color', [0, 0, 255]/255); hold on;
semilogy(num_grads_srg_plus, [infos_srg_plus.cost] * 2 * N / data_ls.nentries, '-.', 'LineWidth',2,'Color', [0, 0, 255]/255); hold on;
hold off;
ax1 = gca;
set(ax1,'FontSize',fs);
xlabel(ax1,'#grad/N','FontName','Arial','FontSize',fs,'FontWeight','bold');
ylabel(ax1,'Means square error on train set \Gamma','FontName','Arial','FontSize',fs,'FontWeight','bold');
legend('R-SD', 'R-CG', 'R-SGD', 'R-SVRG', 'R-SRG', 'R-SRG+');
% Train MSE versus #grads/N
fs = 20;
figure;
semilogy(num_grads_sd, [infos_sd.cost_test] * 2 * N / data_test.nentries,'-','LineWidth',2,'Color', [255, 128, 0]/255); hold on;
semilogy(num_grads_cg, [infos_cg.cost_test] * 2 * N / data_test.nentries,'-','LineWidth',2,'Color', [76, 153, 0]/255); hold on;
semilogy(num_grads_sgd, [infos_sgd.cost_test] * 2 * N / data_test.nentries,'-','LineWidth',2,'Color', [255,0,255]/255); hold on;
semilogy(num_grads_svrg, [infos_svrg.cost_test] * 2 * N / data_test.nentries, '-', 'LineWidth',2,'Color', [255, 0, 0]/255); hold on;
semilogy(num_grads_srg, [infos_srg.cost_test] * 2 * N / data_test.nentries, '-', 'LineWidth',2,'Color', [0, 0, 255]/255); hold on;
semilogy(num_grads_srg_plus, [infos_srg_plus.cost_test] * 2 * N / data_test.nentries, '-.', 'LineWidth',2,'Color', [0, 0, 255]/255); hold on;
hold off;
ax1 = gca;
set(ax1,'FontSize',fs);
xlabel(ax1,'#grad/N','FontName','Arial','FontSize',fs,'FontWeight','bold');
ylabel(ax1,'Means square error on test set \Phi','FontName','Arial','FontSize',fs,'FontWeight','bold');
legend('R-SD', 'R-CG', 'R-SGD', 'R-SVRG', 'R-SRG', 'R-SRG+');
% Train MSE versus #grads/N
fs = 20;
figure;
semilogy([infos_sd.time], [infos_sd.cost_test] * 2 * N / data_test.nentries,'-','LineWidth',2,'Color', [255, 128, 0]/255); hold on;
semilogy([infos_cg.time], [infos_cg.cost_test] * 2 * N / data_test.nentries,'-','LineWidth',2,'Color', [76, 153, 0]/255); hold on;
semilogy([infos_sgd.time], [infos_sgd.cost_test] * 2 * N / data_test.nentries,'-','LineWidth',2,'Color', [255,0,255]/255); hold on;
semilogy([infos_svrg.time], [infos_svrg.cost_test] * 2 * N / data_test.nentries, '-', 'LineWidth',2,'Color', [255, 0, 0]/255); hold on;
semilogy([infos_srg.time], [infos_srg.cost_test] * 2 * N / data_test.nentries, '-', 'LineWidth',2,'Color', [0, 0, 255]/255); hold on;
semilogy([infos_srg_plus.time], [infos_srg_plus.cost_test] * 2 * N / data_test.nentries, '-.', 'LineWidth',2,'Color', [0, 0, 255]/255); hold on;
hold off;
ax1 = gca;
set(ax1,'FontSize',fs);
xlabel(ax1,'Time [sec]','FontName','Arial','FontSize',fs,'FontWeight','bold');
ylabel(ax1,'Means square error on test set \Phi','FontName','Arial','FontSize',fs,'FontWeight','bold');
legend('R-SD', 'R-CG', 'R-SGD', 'R-SVRG', 'R-SRG', 'R-SRG+');
function [samples, samples_test, samples_valid, values, indicator, values_test, indicator_test, data_ls, data_test, data_valid] = generate_mc_data_jester()
load('./dataset/jester/jester_mat.mat'); % Original size [24983,100]
samples_valid = [];
data_valid = [];
%% ------ [start] BM code from Scaled SGD -----
%% Randomly select nu rows and creat the data structure
nu = d; % Number of users selected
p = randperm(size(A,1), nu);
A = A(p, :); % Matrix of size nu-by-100
Avec = A(:);
Avecindices = 1:length(Avec);
Avecindices = Avecindices';
i = ones(length(Avec),1);
i(Avec == 99) = 0;
Avecindices_final = Avecindices(logical(i));
[I, J] = ind2sub([size(A,1) 100],Avecindices_final);
Avecsfinall = Avec(logical(i));
[Isort, indI] = sort(I,'ascend');
data_real.rows = Isort;
data_real.cols = J(indI);
data_real.entries = Avecsfinall(indI);
data_real.nentries = length(data_real.entries);
% Test data: two ratings per user
[~,IA,~] = unique(Isort,'stable');
data_ts_ind = [];
for ii = 1 : length(IA)
if ii < length(IA)
inneridx = randperm(IA(ii+1) - IA(ii), 2);
else
inneridx = randperm(length(data_real.entries) +1 - IA(ii), 2);
end
data_ts_ind = [data_ts_ind; IA(ii) + inneridx' - 1];
end
data_test.rows = data_real.rows(data_ts_ind);
data_test.cols = data_real.cols(data_ts_ind);
data_test.entries = data_real.entries(data_ts_ind);
data_test.nentries = length(data_test.rows);
% Train data
data_ls = data_real;
data_ls.rows(data_ts_ind) = [];
data_ls.cols(data_ts_ind) = [];
data_ls.entries(data_ts_ind) = [];
data_ls.nentries = length(data_ls.rows);
% Permute train data
random_order = randperm(length(data_ls.rows));
data_ls.rows = data_ls.rows(random_order);
data_ls.cols = data_ls.cols(random_order);
data_ls.entries = data_ls.entries(random_order);
% Dimensions and options
n = size(A, 1);
m = size(A, 2);
%% ------ [end] BM code from Scaled SGD -----
%% for train set
values = sparse(data_ls.rows, data_ls.cols, data_ls.entries, n, m);
indicator = sparse(data_ls.rows, data_ls.cols, 1, n, m);
% Creat the cells
samples(m).colnumber = []; % Preallocate memory.
for k = 1 : m
% Pull out the relevant indices and revealed entries for this column
idx = find(indicator(:, k)); % find known row indices
values_col = values(idx, k); % the non-zero entries of the column
samples(k).indicator = idx;
samples(k).values = values_col;
samples(k).colnumber = k;
end
%% for test set
values_test = sparse(data_test.rows, data_test.cols, data_test.entries, n, m);
indicator_test = sparse(data_test.rows, data_test.cols, 1, n, m);
samples_test(m).colnumber = [];
for k = 1 : m
% Pull out the relevant indices and revealed entries for this column
idx = find(indicator_test(:, k)); % find known row indices
values_col = values_test(idx, k); % the non-zero entries of the column
samples_test(k).indicator = idx;
samples_test(k).values = values_col;
samples_test(k).colnumber = k;
end
d = n;
N = m;
end
function stats = mc_mystatsfun(problem, U, stats)
global indicator_valid;
global values_valid;
W = mylsqfit(U, samples_test);
f_test = 0.5*norm(indicator_test.*(U*W') - values_test, 'fro')^2;
f_test = f_test/N;
stats.cost_test = f_test;
if ~isempty(samples_valid)
W = mylsqfit(U, samples_valid);
f_valid = 0.5*norm(indicator_valid.*(U*W') - values_valid, 'fro')^2;
f_valid = f_valid/N;
stats.cost_valid = f_valid;
end
end
end