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Fast Kernel Density Estimator (Multivariate)

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Fast Kernel Density Estimator (Multivariate)



09 Apr 2013 (Updated )

A very fast multivariate bandwidth calculation for KDE that can even be calculated from a GMM.

gaussian_prob(x, m, C, use_log)
function p = gaussian_prob(x, m, C, use_log)
% GAUSSIAN_PROB Evaluate a multivariate Gaussian density.
% p = gaussian_prob(X, m, C)
% p(i) = N(X(:,i), m, C) where C = covariance matrix and each COLUMN of x is a datavector

% p = gaussian_prob(X, m, C, 1) returns log N(X(:,i), m, C) (to prevents underflow).
% If X has size dxN, then p has size Nx1, where N = number of examples

if nargin < 4, use_log = 0; end

if length(m)==1 % scalar
  x = x(:)';
[d N] = size(x);
%assert(length(m)==d); % slow
m = m(:);
M = m*ones(1,N); % replicate the mean across columns
denom = (2*pi)^(d/2)*sqrt(abs(det(C)));
mahal = sum(((x-M)'*inv(C)).*(x-M)',2);   % Chris Bregler's trick
if any(mahal<0)
  warning('mahal < 0 => C is not psd')
if use_log
  p = -0.5*mahal - log(denom);
  p = exp(-0.5*mahal) / (denom+eps);

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