Probability density functions can be initially thought of as a kind of distance measure that we learn from the data.
From distance measures to probability distributions
It's time to shift up a gear and start thinking probabilistically.
The Gaussian as a model of data
Instead of storing data, we will distill it into a model: a probability density function.
Variance and covariance of the Gaussian
Modelling multivariate data requires more parameters, especially if the dimensions are correlated.
Using Gaussians to perform classification
We can construct a classifier from two Gaussian probability density functions.
Estimating the parameters of the Gaussian from data
Straightforward, provided we have data that we can assume was generated by this Gaussian.
