topics {maptpx} | R Documentation |
Estimation for Topic Models
Description
MAP estimation of Topic models
Usage
topics(counts, K, shape=NULL, initopics=NULL,
tol=0.1, bf=FALSE, kill=2, ord=TRUE, verb=1, ...)
Arguments
counts |
A matrix of multinomial response counts in |
K |
The number of latent topics. If |
shape |
Optional argument to specify the Dirichlet prior concentration parameter as |
initopics |
Optional start-location for |
tol |
Convergence tolerance: optimization stops, conditional on some extra checks, when the absolute posterior increase over a full paramater set update is less than |
bf |
An indicator for whether or not to calculate the Bayes factor for univariate |
kill |
For choosing from multiple |
ord |
If |
verb |
A switch for controlling printed output. |
... |
Additional arguments to the undocumented internal |
Details
A latent topic model represents each i'th document's term-count vector X_i
(with \sum_{j} x_{ij} = m_i
total phrase count)
as having been drawn from a mixture of K
multinomials, each parameterized by topic-phrase
probabilities \theta_i
, such that
X_i \sim MN(m_i, \omega_1 \theta_1 + ... + \omega_K\theta_K).
We assign a K-dimensional Dirichlet(1/K) prior to each document's topic weights
[\omega_{i1}...\omega_{iK}]
, and the prior on each \theta_k
is Dirichlet with concentration \alpha
.
The topics
function uses quasi-newton accelerated EM, augmented with sequential quadratic programming
for conditional \Omega | \Theta
updates, to obtain MAP estimates for the topic model parameters.
We also provide Bayes factor estimation, from marginal likelihood
calculations based on a Laplace approximation around the converged MAP parameter estimates. If input length(K)>1
, these
Bayes factors are used for model selection. Full details are in Taddy (2011).
Value
An topics
object list with entries
K |
The number of latent topics estimated. If input |
theta |
The |
omega |
The |
BF |
The log Bayes factor for each number of topics in the input |
D |
Residual dispersion: for each element of |
X |
The input count matrix, in |
Note
Estimates are actually functions of the MAP (K-1 or p-1)-dimensional logit transformed natural exponential family parameters.
Author(s)
Matt Taddy mataddy@gmail.com
References
Taddy (2012), On Estimation and Selection for Topic Models. http://arxiv.org/abs/1109.4518
See Also
plot.topics, summary.topics, predict.topics, wsjibm, congress109, we8there
Examples
## Simulation Parameters
K <- 10
n <- 100
p <- 100
omega <- t(rdir(n, rep(1/K,K)))
theta <- rdir(K, rep(1/p,p))
## Simulated counts
Q <- omega%*%t(theta)
counts <- matrix(ncol=p, nrow=n)
totals <- rpois(n, 100)
for(i in 1:n){ counts[i,] <- rmultinom(1, size=totals[i], prob=Q[i,]) }
## Bayes Factor model selection (should choose K or nearby)
summary(simselect <- topics(counts, K=K+c(-5:5)), nwrd=0)
## MAP fit for given K
summary( simfit <- topics(counts, K=K, verb=2), n=0 )
## Adjust for label switching and plot the fit (color by topic)
toplab <- rep(0,K)
for(k in 1:K){ toplab[k] <- which.min(colSums(abs(simfit$theta-theta[,k]))) }
par(mfrow=c(1,2))
tpxcols <- matrix(rainbow(K), ncol=ncol(theta), byrow=TRUE)
plot(theta,simfit$theta[,toplab], ylab="fitted values", pch=21, bg=tpxcols)
plot(omega,simfit$omega[,toplab], ylab="fitted values", pch=21, bg=tpxcols)
title("True vs Fitted Values (color by topic)", outer=TRUE, line=-2)
## The S3 method plot functions
par(mfrow=c(1,2))
plot(simfit, lgd.K=2)
plot(simfit, type="resid")