Permutation invariant matrix statistics and computational language tasks
The Linguistic Matrix Theory programme introduced by Kartsaklis, Ramgoolam and Sadrzadeh is an approach to the statistics of matrices that are generated in type-driven distributional semantics, based on permutation invariant polynomial functions which are regarded as the key observables encoding the significant statistics. In this paper we generalize the previous results on the approximate Gaussianity of matrix distributions arising from compositional distributional semantics. We also introduce a geometry of observable vectors for words, defined by exploiting the graph-theoretic basis for the permutation invariants and the statistical characteristics of the ensemble of matrices associated with the words. We describe successful applications of this unified framework to a number of tasks in computational linguistics, associated with the distinctions between synonyms, antonyms, hypernyms and hyponyms.
Code (1)
Similar Papers 제목 키워드 기반
Permutation Invariant Gaussian Matrix Models
Permutation invariant Gaussian matrix models were recently developed for applications in computational linguistics. A 5-parameter family of models was solved. In this paper, we use a representation theoretic approach to …
Linguistic Matrix Theory
Recent research in computational linguistics has developed algorithms which associate matrices with adjectives and verbs, based on the distribution of words in a corpus of text. These matrices are linear operators on a v…
Gaussianity and typicality in matrix distributional semantics
Constructions in type-driven compositional distributional semantics associate large collections of matrices of size $D$ to linguistic corpora. We develop the proposal of analysing the statistical characteristics of this …
Permutation invariant Gaussian matrix models for financial correlation matrices
We construct an ensemble of correlation matrices from high-frequency foreign exchange market data, with one matrix for every day for 446 days. The matrices are symmetric and have vanishing diagonal elements after subtrac…
Anomaly DetectionMulti-talker Speech Separation with Utterance-level Permutation Invariant Training of Deep Recurrent Neural Networks
In this paper we propose the utterance-level Permutation Invariant Training (uPIT) technique. uPIT is a practically applicable, end-to-end, deep learning based solution for speaker independent multi-talker speech separat…
ClusteringDeep ClusteringSpeech Separation