I am developing a classification task where I generate a gaussian distribution (its mean and standard deviation) from a set of 3-dimensional data. My question is: would the classifier give same outputs if I use three uni variate normal distributions or one 3-dimensional multivariate distribution? When getting the probability of a test point belonging to either the 3D distribution or the three separate distributions, would the number be the same?
2025-01-12 19:21:39.1736709699
Multivariate Gaussian vs univariate
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A 3-d multivariate distribution would be the same as the 3 independent 1-d distributions if, you guessed, the dimensions are statistically independent of each other. If they are correlated, then you have to introduce that correlation one way or another.