1.Density Estimation Basic concepts 1 Density estimation:estimating the probability density function p(x)based on a given set of training samples D={x1,x2,...,xN}. 2 Estimated density:denoted by p(x). 3 Training samples are i.i.d.and distributed according to p(x). 4 Parametric estimation:parameter vector 0 ofp(x;0) 5 Non-parametric estimation:a function p:X->R 6 Finite number of training samples meaning that there will be some errors in the function(density)estimation. 3/451. Density Estimation Basic concepts 1 Density estimation: estimating the probability density function p(x) based on a given set of training samples D = {x1, x2, ..., xN}. 2 Estimated density: denoted by pˆ(x). 3 Training samples are i.i.d. and distributed according to p(x). 4 Parametric estimation: parameter vector θ of p(x; θ) 5 Non-parametric estimation: a function p : X → R 6 Finite number of training samples meaning that there will be some errors in the function (density) estimation. 3 / 45