Latent variable models

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

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

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

Recommended prerequisites: Very good command of matrix algebra, vector differentiation, and optimization under constraints.

Introduction.

Situations and types 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 VLs: component models

    a) PBA model.

    b) ACPVI model.

    c) PLS model.

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

II - Random VL models

  1. The EM algorithm

  2. Nominal VL: mixing models

    a) Gaussian mixture.

    b) Multinomial mixture: latent class analysis.

  3. VL Continues: factor models

    a) Factor model for 1 block.

    b) Structural equation models.

  4. Hidden Markov models

Hourly volumes:

            CM: 21

            TD:

            TP: 

            Land: