Location Dependent Dirichlet Processes

Dirichlet processes (DP) are widely applied in Bayesian nonparametric modeling. However, in their basic form they do not directly integrate dependency information among data arising from space and time. In this paper, we propose location dependent Dirichlet processes (LDDP) which incorporate nonparametric Gaussian processes in the DP modeling framework to model such dependencies. We develop the LDDP in the context of mixture modeling, and develop a mean field variational inference algorithm for this mixture model. The effectiveness of the proposed modeling framework is shown on an image segmentation task

Probabilistic machine learning and artificial intelligence.

How can a machine learn from experience? Probabilistic modelling provides a framework for understanding what learning is, and has therefore emerged as one of the principal theoretical and practical approaches for designing machines that learn from data acquired through experience. The probabilistic framework, which describes how to represent and manipulate uncertainty about models and predictions, has a central role in scientific data analysis, machine learning, robotics, cognitive science and artificial intelligence. This Review provides an introduction to this framework, and discusses some of the state-of-the-art advances in the field, namely, probabilistic programming, Bayesian optimization, data compression and automatic model discovery.The author acknowledges an EPSRC grant EP/I036575/1, the DARPA PPAML programme, a Google Focused Research Award for the Automatic Statistician and support from Microsoft Research.This is the author accepted manuscript. The final version is available from NPG at http://www.nature.com/nature/journal/v521/n7553/full/nature14541.html#abstract

Resolution of surface singularities : three lectures

v, 132 p. ; 25 cm

“Sophistical Fancies and Mear Chimaeras?” Traiano Boccalini’s Ragguagli di Parnaso and the Rosicrucian Enigma

Hidden Conditional Random Fields (HCRFs) are discriminative latent variable models which have been shown to successfully learn the hidden structure of a given classification problem. An infinite HCRF is an HCRF with a countably infinite number of hidden states, which rids us not only of the necessity to specify a priori a fixed number of hidden states available but also of the problem of overfitting. Markov chain Monte Carlo (MCMC) sampling algorithms are often employed for inference in such models. However, convergence of such algorithms is rather difficult to verify, and as the complexity of the task at hand increases, the computational cost of such algorithms often becomes prohibitive. These limitations can be overcome by variational techniques. In this paper, we present a generalized framework for infinite HCRF models, and a novel variational inference approach on a model based on coupled Dirichlet Process Mixtures, the HCRF–DPM. We show that the variational HCRF–DPM is able to converge to a correct number of represented hidden states, and performs as well as the best parametric HCRFs —chosen via cross–validation— for the difficult tasks of recognizing instances of agreement, disagreement, and pain in audiovisual sequences

An introduction to resolution of singularities via the multiplicity

In these notes, we study properties of the multiplicity at points of avariety X over a perfect field. We focus on properties that can be studiedusing ramification methods, such as discriminants and some generalizeddiscriminants that we shall introduce. We also show how these methodslead to an alternative proof of resolution of singularities for varieties overfields of characteristic zero.Fil: Sulca, Diego Armando. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaFil: Villamayor, Orlando. Universidad Autonoma de Madrid. Facultad de Ciencias. Departamento de Matemática; Españ

A Spatially-Constrained Normalized Gamma Process for Data Clustering

Part 9: ClusteringInternational audienceIn this work, we propose a novel nonparametric Bayesian method for clustering of data with spatial interdependencies. Specifically, we devise a novel normalized Gamma process, regulated by a simplified (pointwise) Markov random field (Gibbsian) distribution with a countably infinite number of states. As a result of its construction, the proposed model allows for introducing spatial dependencies in the clustering mechanics of the normalized Gamma process, thus yielding a novel nonparametric Bayesian method for spatial data clustering. We derive an efficient truncated variational Bayesian algorithm for model inference. We examine the efficacy of our approach by considering an image segmentation application using a real-world dataset. We show that our approach outperforms related methods from the field of Bayesian nonparametrics, including the infinite hidden Markov random field model, and the Dirichlet process prior