1,031 research outputs found
A Context-theoretic Framework for Compositionality in Distributional Semantics
Techniques in which words are represented as vectors have proved useful in
many applications in computational linguistics, however there is currently no
general semantic formalism for representing meaning in terms of vectors. We
present a framework for natural language semantics in which words, phrases and
sentences are all represented as vectors, based on a theoretical analysis which
assumes that meaning is determined by context.
In the theoretical analysis, we define a corpus model as a mathematical
abstraction of a text corpus. The meaning of a string of words is assumed to be
a vector representing the contexts in which it occurs in the corpus model.
Based on this assumption, we can show that the vector representations of words
can be considered as elements of an algebra over a field. We note that in
applications of vector spaces to representing meanings of words there is an
underlying lattice structure; we interpret the partial ordering of the lattice
as describing entailment between meanings. We also define the context-theoretic
probability of a string, and, based on this and the lattice structure, a degree
of entailment between strings.
We relate the framework to existing methods of composing vector-based
representations of meaning, and show that our approach generalises many of
these, including vector addition, component-wise multiplication, and the tensor
product.Comment: Submitted to Computational Linguistics on 20th January 2010 for
revie
Looking at Vector Space and Language Models for IR using Density Matrices
In this work, we conduct a joint analysis of both Vector Space and Language
Models for IR using the mathematical framework of Quantum Theory. We shed light
on how both models allocate the space of density matrices. A density matrix is
shown to be a general representational tool capable of leveraging capabilities
of both VSM and LM representations thus paving the way for a new generation of
retrieval models. We analyze the possible implications suggested by our
findings.Comment: In Proceedings of Quantum Interaction 201
The Bayesian Case Model: A Generative Approach for Case-Based Reasoning and Prototype Classification
We present the Bayesian Case Model (BCM), a general framework for Bayesian
case-based reasoning (CBR) and prototype classification and clustering. BCM
brings the intuitive power of CBR to a Bayesian generative framework. The BCM
learns prototypes, the "quintessential" observations that best represent
clusters in a dataset, by performing joint inference on cluster labels,
prototypes and important features. Simultaneously, BCM pursues sparsity by
learning subspaces, the sets of features that play important roles in the
characterization of the prototypes. The prototype and subspace representation
provides quantitative benefits in interpretability while preserving
classification accuracy. Human subject experiments verify statistically
significant improvements to participants' understanding when using explanations
produced by BCM, compared to those given by prior art.Comment: Published in Neural Information Processing Systems (NIPS) 2014,
Neural Information Processing Systems (NIPS) 201
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