Train boosted fern regressor.
Boosted regression using random ferns as the weak regressor. See "Greedy
function approximation: A gradient boosting machine", Friedman, Annals of
Statistics 2001, for more details on boosted regression.
A few notes on the parameters: 'type' should in general be set to 'res'
(the 'ave' version is an undocumented variant that only performs well
under limited conditions). 'loss' determines the loss function being
optimized, in general the 'L2' version is the most robust and effective.
'reg' is a regularization term for the ferns, a low value such as .01 can
improve results. Setting the learning rate 'eta' is crucial in order to
achieve good performance, especially on noisy data. In general, eta
should decreased as M is increased.
Dimensions:
M - number ferns
R - number repeats
S - fern depth
N - number samples
F - number features
USAGE
[ferns,ysPr] = fernsRegTrain( data, hs, [varargin] )
INPUTS
data - [NxF] N length F feature vectors
ys - [Nx1] target output values
varargin - additional params (struct or name/value pairs)
.type - ['res'] options include {'res','ave'}
.loss - ['L2'] options include {'L1','L2','exp'}
.S - [2] fern depth (ferns are exponential in S)
.M - [50] number ferns (same as number phases)
.R - [10] number repetitions per fern
.thrr - [0 1] range for randomly generated thresholds
.reg - [0.01] fern regularization term in [0,1]
.eta - [1] learning rate in [0,1] (not used if type='ave')
.verbose - [0] if true output info to display
OUTPUTS
ferns - learned fern model w the following fields
.fids - [MxS] feature ids for each fern for each depth
.thrs - [MxS] threshold corresponding to each fid
.ysFern - [2^SxM] stored values at fern leaves
.loss - loss(ys,ysGt) computes loss of ys relateive to ysGt
ysPr - [Nx1] predicted output values
EXAMPLE
%% generate toy data
N=1000; sig=.5; f=@(x) cos(x*pi*4)+(x+1).^2;
xs0=rand(N,1); ys0=f(xs0)+randn(N,1)*sig;
xs1=rand(N,1); ys1=f(xs1)+randn(N,1)*sig;
%% train and apply fern regressor
prm=struct('type','res','loss','L2','eta',.05,...
'thrr',[-1 1],'reg',.01,'S',2,'M',1000,'R',3,'verbose',0);
tic, [ferns,ysPr0] = fernsRegTrain(xs0,ys0,prm); toc
tic, ysPr1 = fernsRegApply( xs1, ferns ); toc
fprintf('errors train=%f test=%f\n',...
ferns.loss(ysPr0,ys0),ferns.loss(ysPr1,ys1));
%% visualize results
figure(1); clf; hold on; plot(xs0,ys0,'.b'); plot(xs0,ysPr0,'.r');
figure(2); clf; hold on; plot(xs1,ys1,'.b'); plot(xs1,ysPr1,'.r');
See also fernsRegApply, fernsInds
Piotr's Computer Vision Matlab Toolbox Version 2.50
Copyright 2014 Piotr Dollar. [pdollar-at-gmail.com]
Licensed under the Simplified BSD License [see external/bsd.txt]