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Toggle# Multidimensional statistics video lectures

**Multidimensional statistics theory **is very useful in many fields. It relies on measure and probability theories and gives the first insights for machine learning. As an example, you will learn to build confidence intervals for your estimators.

## I Basic statistics

**PDF**, **Vidéo**

We aim in this lecture to present some basic results from statistics underlying machine learning theory. In forthcoming lectures we shall present more involved results from multivariate statistics.

**Outline**:

Statistical estimation

Statistical framework

Mean squared error of an estimator

Estimators of expectation and variance

Confidence interval

Hypothesis testing

Hypothesis tests

Hypothesis tests for Gaussian random variables

Statistic and test statistic

The p-value

Likelihood

## II Linear fitting and regression

**PDF**, **Vidéo**

Linear fitting and regression are classical problems in statistics, which permit to illustrate the basic ideas underlying machine learning theory. Indeed, linear fitting is one of the simplest examples of machine learning problems.

**Outline**:

Unidimensional input

Linear fitting

Linear regression

Linear prediction

Multidimensional input

Multidimensional linear fitting

Multidimensional linear regression

Multidimensional linear prediction

Gaussian model

Maximum likelihood estimators

## III Logistic regression

**PDF**, **Vidéo**

Logistic regression is also one of the simplest examples of machine learning problems. It permits to illustrate the ideas underlying some machine learning algorithms. It is an adaptation of linear regression to the case when the output variable is discrete.

**Outline**:

Binary logistic regression

Binary logistic regression model

Binary logistic prediction

Multiclass logistic regression

Multiclass logistic regression model

Multiclass logistic prediction

## IV Principal component and factor analysis

**PDF**

We shall present two techniques, called ‘principal component analysis’ and ‘factor analysis’, which aim to reduce the eventual redundancy among some observed random variables Y1, Y2, . . . , Yp by using a smaller number of components (or factors). The objective is the same, but each of these techniques has its own specificities, as we shall see.

**Outline**:

Principal component analysis (PCA)

PCA for random observed variables

PCA for deterministic observed variables

Factor analysis

Existence of factor analysis model

Scaling in factor analysis

Rotation of factors

Factors interpretation

Estimating loadings