67,577 research outputs found
Probabilistic Constraint Logic Programming
This paper addresses two central problems for probabilistic processing
models: parameter estimation from incomplete data and efficient retrieval of
most probable analyses. These questions have been answered satisfactorily only
for probabilistic regular and context-free models. We address these problems
for a more expressive probabilistic constraint logic programming model. We
present a log-linear probability model for probabilistic constraint logic
programming. On top of this model we define an algorithm to estimate the
parameters and to select the properties of log-linear models from incomplete
data. This algorithm is an extension of the improved iterative scaling
algorithm of Della-Pietra, Della-Pietra, and Lafferty (1995). Our algorithm
applies to log-linear models in general and is accompanied with suitable
approximation methods when applied to large data spaces. Furthermore, we
present an approach for searching for most probable analyses of the
probabilistic constraint logic programming model. This method can be applied to
the ambiguity resolution problem in natural language processing applications.Comment: 35 pages, uses sfbart.cl
Precise n-gram Probabilities from Stochastic Context-free Grammars
We present an algorithm for computing n-gram probabilities from stochastic
context-free grammars, a procedure that can alleviate some of the standard
problems associated with n-grams (estimation from sparse data, lack of
linguistic structure, among others). The method operates via the computation of
substring expectations, which in turn is accomplished by solving systems of
linear equations derived from the grammar. We discuss efficient implementation
of the algorithm and report our practical experience with it.Comment: 12 pages, to appear in ACL-9
Stochastic Attribute-Value Grammars
Probabilistic analogues of regular and context-free grammars are well-known
in computational linguistics, and currently the subject of intensive research.
To date, however, no satisfactory probabilistic analogue of attribute-value
grammars has been proposed: previous attempts have failed to define a correct
parameter-estimation algorithm.
In the present paper, I define stochastic attribute-value grammars and give a
correct algorithm for estimating their parameters. The estimation algorithm is
adapted from Della Pietra, Della Pietra, and Lafferty (1995). To estimate model
parameters, it is necessary to compute the expectations of certain functions
under random fields. In the application discussed by Della Pietra, Della
Pietra, and Lafferty (representing English orthographic constraints), Gibbs
sampling can be used to estimate the needed expectations. The fact that
attribute-value grammars generate constrained languages makes Gibbs sampling
inapplicable, but I show how a variant of Gibbs sampling, the
Metropolis-Hastings algorithm, can be used instead.Comment: 23 pages, 21 Postscript figures, uses rotate.st
Constrained Optimization for a Subset of the Gaussian Parsimonious Clustering Models
The expectation-maximization (EM) algorithm is an iterative method for
finding maximum likelihood estimates when data are incomplete or are treated as
being incomplete. The EM algorithm and its variants are commonly used for
parameter estimation in applications of mixture models for clustering and
classification. This despite the fact that even the Gaussian mixture model
likelihood surface contains many local maxima and is singularity riddled.
Previous work has focused on circumventing this problem by constraining the
smallest eigenvalue of the component covariance matrices. In this paper, we
consider constraining the smallest eigenvalue, the largest eigenvalue, and both
the smallest and largest within the family setting. Specifically, a subset of
the GPCM family is considered for model-based clustering, where we use a
re-parameterized version of the famous eigenvalue decomposition of the
component covariance matrices. Our approach is illustrated using various
experiments with simulated and real data
A robust approach to model-based classification based on trimming and constraints
In a standard classification framework a set of trustworthy learning data are
employed to build a decision rule, with the final aim of classifying unlabelled
units belonging to the test set. Therefore, unreliable labelled observations,
namely outliers and data with incorrect labels, can strongly undermine the
classifier performance, especially if the training size is small. The present
work introduces a robust modification to the Model-Based Classification
framework, employing impartial trimming and constraints on the ratio between
the maximum and the minimum eigenvalue of the group scatter matrices. The
proposed method effectively handles noise presence in both response and
exploratory variables, providing reliable classification even when dealing with
contaminated datasets. A robust information criterion is proposed for model
selection. Experiments on real and simulated data, artificially adulterated,
are provided to underline the benefits of the proposed method
- …