Probabilistic Typology: Deep Generative Models of Vowel Inventories

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Abstract

Linguistic typology studies the range of structures present in human language. The main goal of the field is to discover which sets of possible phenomena are universal, and which are merely frequent. For example, all languages have vowels, while most---but not all---languages have an /u/ sound. In this paper we present the first probabilistic treatment of a basic question in phonological typology: What makes a natural vowel inventory? We introduce a series of deep stochastic point processes, and contrast them with previous computational, simulation-based approaches. We provide a comprehensive suite of experiments on over 200 distinct languages.

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The coincidence approach to stochastic point processes

Odile Macchi (1975)

The structure of the probability space associated with a general point process, when regarded as a counting process, is reviewed using the coincidence formalism. The rest of the paper is devoted to the class of regular point processes for which all coincidence probabilities admit densities. It is shown that their distribution is completely specified by the system of coincidence densities. The specification formalism is stressed for ‘completely’ regular point processes. A construction theorem gives a characterization of the system of coincidence densities of such a process. It permits the study of most models of point processes. New results on the photon process, a particular type of conditioned Poisson process, are derived. New examples are exhibited, including the Gauss-Poisson process and the ‘fermion’ process that is suitable whenever the points are repulsive.

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Determinantal point processes for machine learning

, (2013)

Determinantal point processes (DPPs) are elegant probabilistic models of repulsion that arise in quantum physics and random matrix theory. In contrast to traditional structured models like Markov random fields, which become intractable and hard to approximate in the presence of negative correlations, DPPs offer efficient and exact algorithms for sampling, marginalization, conditioning, and other inference tasks. We provide a gentle introduction to DPPs, focusing on the intuitions, algorithms, and extensions that are most relevant to the machine learning community, and show how DPPs can be applied to real-world applications like finding diverse sets of high-quality search results, building informative summaries by selecting diverse sentences from documents, modeling non-overlapping human poses in images or video, and automatically building timelines of important news stories.