Introduction to Hierarchical Model

- 8 mins

Data Mining Center, Renmin University of China

Introduction to Bayesian Framework

Priori, Likelihood and Posteriori

Types of Prior

What exactly is prior when we talk about it?

We can define three types of priors according to the information they contain

Common Types of Priors

What kinds of prior do we usally use?

Conjugate Prior

Why we use Conjugate Prior?

Non-informative Prior

Jeffrey Prior

Bayesian Hierarchical Model

How to set the Hyperparameters?

figure missing

Model Initialization

Toy Example

How to set the priors?

Fixed Prior Distribution

Informative Prior

Approximate estimate using Historical Data
Set the Hyperparameters without Data

Do we have to use data to set the hyperparameters?

Can we regard hyperparameters in prior as random variables?

Set one more level of Hierarchical Model

Regard $\alpha$ \& $\beta$ as Random Variables

Latent Dirichlet Allocation

Model Initialization

From Beta Distribution to Dirichlet

Notation and Assumption

Where is the “Latent” in LDA?

figure missing

Posteriorl Inference

Intractable Posterior

Reference

Ying Zhang

Ying Zhang

A statistician who gets lost in analysis.

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