irm.Rmd

---
title: "Final Lecture: Infinite Relational Model"
author: "Jesse Mu"
date: "November 2, 2016"
output:
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---

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```{r echo=FALSE, message=FALSE}
knitr::opts_chunk$set(fig.align = 'center', message = FALSE)
library(knitr)
library(ggplot2)
library(cowplot)
library(reshape)
```

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# The Infinite Relational Model

What happens when you want to cluster your data, but the number of clusters is
unknown? While some approaches involve fitting several models with a varying
number of clusters to your data and comparing model fit statistics, the Bayesian
approach is to specify a model which is allowed to dynamically grow the number
of clusters as the complexity of the data warrants.

The **Infinite Relational Model** is the prototypical example of such a model.

> [Kemp et al. (2006). Learning Systems of Concepts with an Infinite Relational Model](http://web.mit.edu/cocosci/Papers/Kemp-etal-AAAI06.pdf)

For this last project, I coded up a simple version of Charles Kemp's Infinite
Relational Model (IRM) in `irm.R` to co-cluster rows and columns of a simple
2-dimensional binary relation.

## Demo

```{r}
source('irm.R')
```

### Sanity check

As a sanity check, we use the toy matrix in the original paper:

```{r}
R = rbind(
  c(0, 0, 1, 0, 1, 0, 0, 1, 0),
  c(0, 0, 0, 0, 0, 0, 1, 0, 1),
  c(0, 0, 1, 0, 0, 0, 1, 0, 1),
  c(0, 1, 1, 0, 0, 0, 0, 1, 1),
  c(0, 0, 0, 0, 0, 0, 1, 0, 1),
  c(0, 1, 1, 0, 1, 0, 0, 1, 0),
  c(1, 0, 0, 0, 0, 1, 0, 0, 0),
  c(0, 0, 0, 0, 0, 1, 1, 0, 1),
  c(1, 0, 0, 1, 0, 1, 0, 0, 0)
)
plot.R(R)
```

```{r}
Z = irm(R, sweeps = 1000)
top.n(Z)
plot.R(R, mode.irm(Z))
```

This successfully finds the clusters of rows and columns that correspond to the original paper.

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