Section: Overall Objectives

Context

In several respects, modern society has strengthened the need for statistical analysis, even if other related names are sometimes preferably used depending on methods, communities and applications, as data analysis, machine learning or artificial intelligence. The genesis comes from the easier availability of data thanks to technological breakthroughs (storage, transfer, computing), and are now so widespread that they are no longer limited to large human organizations. The more or less conscious goal of such data availability is the expectation to improving the quality of “since the dawn of time” statistical stories which are namely discovering new knowledge or doing better predictions. These both central tasks can be referred respectively as unsupervised learning or supervised learning, even if it is not limited to them or other names exist depending on communities. Somewhere, it pursues the following hope: “more data for better quality and more numerous results”.

However, today's data are increasingly complex. They gather mixed type features (for instance continuous data mixed with categorical data), missing or partially missing items (like intervals) and numerous variables (high dimensional situation). As a consequence, the target “better quality and more numerous results” of the previous adage (both words are important: “better quality” and also “more numerous”) could not be reached through a somewhat “handwork” way, but should inevitably rely on some theoretical formalization and guarantee. Indeed, data can be so numerous and so complex (data can live in quite abstract spaces) that the “empirical” statistician is quickly outdated. However, data being subject by nature to randomness, the probabilistic framework is a very sensible theoretical environment to serve as a general guide for modern statistical analysis.