Question about GMM::probability_of

[eroehrig]

fast-gmm/src/gmm.cc

Lines 232 to 235 in 5b6940d

	real_t GMM::probability_of(std::vector<real_t> &x) {
	real_t prob = 0;
	for (int i = 0; i < nr_mixtures; i ++) {
	prob *= weights[i] * gaussians[i]->probability_of(x);

It should be prob += weights[i] * gaussians[i]->probability_of(x), shouldn't it be?

[zxytim]

No.
Probabilities are multiplicative, while log-probabilities are additive.
See

fast-gmm/src/gmm.cc

Line 244 in 5b6940d

prob += log_probability_of(x);

[eroehrig]

I think the probabilities of the different gaussians are additive (see at wikipedia).
The example you gave me, is the sum of the log_probability of more than one datapoint. That refers to

fast-gmm/src/gmm.cc

Lines 215 to 220 in 5b6940d

	real_t GMM::log_probability_of(std::vector<real_t> &x) {
	real_t prob = 0;
	for (int i = 0; i < nr_mixtures; i ++) {
	prob += weights[i] * gaussians[i]->probability_of(x);
	}
	return log(prob);

where it is done correctly. Because the probabilities are summed up before the log operation. There should be no difference to GMM::probability_of except of the log operation in the end.

[AlexanderFabisch]

A Gaussian mixture model is a weighted sum of Gaussians. I would say + is correct here.