| MMGAUSS | |
Minimax estimation of Gaussian distribution.
Synopsis:
model = mmgauss(X)
model = mmgauss(X,options)
model = mmgauss(X,options,init_model)
Description:
This function computes the minimax estimation of Gaussian
parameters. The minimax estimation (reffer to [SH10]) for
Gaussian model is defined as:
(Mean,Cov) = argmax min( pdfgauss(X, Mean, Cov) ).
Mean,Cov
The sample data X should be good representatives of the
distribution. In contrast to maximum-likelihood estimation,
the data do not have to be i.i.d.
An itrative algorithm is used for estimation. It iterates
until
upper_bound - lower_bound < eps,
where eps is prescribed precission and upper_bound, lower_bound
are bounds on the optimal solution
upper_bound > max min( pdfgauss(X, Mean, Cov) ) > lower_bound
Mean,Cov
Input:
X [dim x num_data] Data sample.
options [struct] Control parameters:
.eps [1x1] Precision of found estimate (default 0.1).
.tmax [1x1] Maximal number of iterations (default inf).
.cov_type [int] Type of estimated covariance matrix:
cov_type = 'full' full covariance matrix (default)
cov_type = 'diag' diagonal covarinace matrix
cov_type = 'spherical' spherical covariance matrix
.verb [int] If 1 then info is printed (default 0).
init_model [struct] Initial model:
.Alpha [1xnum_data] Weights of training vectors.
.t [1x1] (optional) Counter of iterations.
Output:
model [struct] Gaussian distribution:
.Mean [dim x 1] Estimated mean vector.
.Cov [dim x dim] Estimated covariance matrix.
.t [1x1] Number of iterations.
.exitflag [1x1] 1 ... (upper_bound - lower_bound) < eps
0 ... maximal number of iterations tmax exceeded.
.upper_bound [1x1] Upper bound on the optimized criterion.
.lower_bound [1x1] Lower bound on the optimized criterion.
.Alpha [1 x num_data] Data weights. The minimax estimate
is equal to maximum-likelihood estimate of weighted data.
.options [struct] Copy of used options.
Example:
X = [[0;0] [1;0] [0;1]];
mm_model = mmgauss(X);
figure; ppatterns(X);
pgauss(mm_model, struct('p',exp(mm_model.lower_bound')));
See also
PDFGAUSS, MLCGMM, EMGMM.
About: Statistical Pattern Recognition Toolbox
(C) 1999-2003, Written by Vojtech Franc and Vaclav Hlavac
Czech Technical University Prague
Faculty of Electrical Engineering
Center for Machine Perception
Modifications:
26-may-2004, VF
30-apr-2004, VF
19-sep-2003, VF
27-feb-2003, VF
24. 6.00 V. Hlavac, comments polished.