# Topic Models¶

## Supported Data Formats¶

Topic models can be applied to any dataset that has group structure.

## Supported Learning Algorithms¶

• FiniteTopicModel supports VB, soVB, moVB
• HDPTopicModel supports VB, soVB, and moVB. * with birth/merge/delete moves for moVB

## Possible Implementations¶

• FiniteTopicModel: stuff here
• HDPTopicModel: more stuff here

There are two types of mixture model supported. Both define the model in terms of a global parameter vector $$\beta$$, where $$\beta_k$$ gives the probability of topic k, and local assignments $$z$$, where $$z_n$$ indicates which state {1, 2, 3, ... K} is assigned to data item n.

The FiniteMixtureModel has a generative process:

$\begin{split}[\beta_1, \beta_2, \ldots \beta_K] \sim \mbox{Dir}(\gamma, \gamma, \ldots \gamma) \\ z_n \sim \mbox{Discrete}(\beta)\end{split}$

while the DPMixtureModel has generative process:

$\begin{split}[\beta_1, \beta_2, \ldots \beta_K \ldots] \sim \mbox{StickBreaking}(\gamma_0) \\ z_n \sim \mbox{Discrete}(\beta)\end{split}$

If we let K grow to infinity, these two models converge if $$\gamma = \gamma_0 /K$$.