Latent Variable Models

Many phenomena are observed only incompletely or indirectly, which complicates their analysis. Their statistical modeling must therefore include unobserved variables—known as latent variables—that are linked in some way to the observed variables. This course introduces the various ways to incorporate latent variables into a model depending on their type (qualitative or quantitative), and to estimate the model’s parameters.

Provide training in statistical modeling involving unobserved or indirectly observed variables.

Course on Multidimensional Data Analysis (ACP & CA). Course on Multivariate Analysis. Course on Inferential Statistics.

Recommended prerequisites: A very strong grasp of matrix algebra, vector calculus, and constrained optimization.

Introduction.

Contexts and typologies of latent variables: continuous / nominal; random / non-random.

I - Non-random VL models

  1. Nominal VL: Clustering Models

    a) Gaussian model.

    b) Multinomial model.

  2. Continuous VL: Component-Based Models

    a) PCA model.

    b) ACPVI model.

    c) PLS model.

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

II - Models with Random VLs

  1. The EM Algorithm

  2. Nominal VL: Mixing Models

    a) Gaussian mixture.

    b) Multinomial mixture: latent class analysis.

  3. Continuous VL: Factor Models

    a) Factor model for 1 block.

    b) Structural equation models.

  4. Hidden Markov Chain Models

Hourly volumes:

            CM: 21

            TD:

            Practical Work: 

            Lot: