Latent variable models

Many phenomena are only incompletely or indirectly observed, which complicates their analysis. Their statistical modeling must therefore include unobserved variables, known as latent variables, which are linked in one way or another to the observed variables. This course introduces the various ways of introducing latent variables into a model, depending on their type (qualitative or quantitative), and of estimating model parameters.

Training in statistical modeling in the presence of unobserved or indirectly observed variables.

Multidimensional data analysis course (PCA & CA). Multivariate analysis course. Inferential statistics course.

Recommended prerequisites: Very good command of matrix algebra, vector derivation and constrained optimization.

Introduction.

Situations and typology of latent variables: continuous / nominal; random / non-random.

I - Non-random LV models

  1. Nominal VL: clustering models

    a) Gaussian model.

    b) Multinomial model.

  2. Continuous VL: component models

    a) PCA model.

    b) PCAVI model.

    c) PLS model.

    d) Multi-block explanatory models: THEME and SCGLR.

II - Random VL models

  1. The EM algorithm

  2. VL nominal: mixing models

    a) Gaussian mixture.

    b) Multinomial mixture: latent class analysis.

  3. VL Continues: factor models

    a) 1-block factor model.

    b) Structural equation models.

  4. Hidden Markov chain models

Hourly volumes :

            CM: 21

            TD :

            TP : 

            Terrain :