What is a population minimizer?

Question

I am reading into statistics in combination with machine learning and I came across the expression "population minimizer". I found no good explanation on what a population minimizer exactly means, so what exactly is it?

May help: ftp://ftp.stat.math.ethz.ch/Manuscripts/buhlmann/loss-functions.pdf — 高田航, Jul 06 '17 at 20:15
It is a prediction function which minimizes expected loss on a population level for a given loss function. Also called a risk minimizer — Henry, Jul 06 '17 at 20:21

score 2 · Accepted Answer · edited Jul 06 '17 at 21:02

A loss function

$$l(y, f)$$ measures how good we can use $f$ to predict $y$.

The smaller the result of the loss function $l$ is, the better the function $f$ is in performing the prediction task.

Expectation values are used since in practice, $Y$ and $X$ are random.

$$f_{pop}(.) = \arg\min_{f(.)} \mathbb{E}[l(Y,f(X)]$$

The population minimizer is the function $f$ that best approximates $Y$ and thus minimizes the expectation value $\mathbb{E}$ of the loss function $l$.

What is a population minimizer?

1 Answers1