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Bayesian models of cognition
"... For over 200 years, philosophers and mathematicians have been using probability theory to describe human cognition. While the theory of probabilities was first developed as a means of analyzing games of chance, it quickly took on a larger and deeper significance as a formal account of how rational a ..."
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For over 200 years, philosophers and mathematicians have been using probability theory to describe human cognition. While the theory of probabilities was first developed as a means of analyzing games of chance, it quickly took on a larger and deeper significance as a formal account of how rational agents should reason in situations of uncertainty
Discovering latent patterns with hierarchical Bayesian mixedmembership models and the issue of model choice
 In Data Mining Patterns: New Methods and Applications (P. Poncelet, F. Masseglia and M. Teisseire, eds.) 240–275. Idea Group Inc
, 2006
"... There has been an explosive growth of datamining models involving latent structure for clustering and classification. While having related objectives these models use different parameterizations and often very different specifications and constraints. Model choice is thus a major methodological iss ..."
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Cited by 13 (5 self)
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There has been an explosive growth of datamining models involving latent structure for clustering and classification. While having related objectives these models use different parameterizations and often very different specifications and constraints. Model choice is thus a major methodological issue and a crucial practical one for applications. In this paper, we work from a general formulation of hierarchical Bayesian mixedmembership models in Erosheva [15] and Erosheva, Fienberg, and Lafferty [19] and present several model specifications and variations, both parametric and nonparametric, in the context of the learning the number of latent groups and associated patterns for clustering units. Model choice is an issue within specifications, and becomes a component of the larger issue of model comparison. We elucidate strategies for comparing models and specifications by producing novel analyses of two data sets: (1) a corpus of scientific publications from the Proceedings of the National Academy of Sciences (PNAS) examined earlier by Erosheva, Fienberg, and Lafferty [19] and Griffiths and Steyvers [22]; (2) data on functionally disabled American seniors from the National
Classifying Dynamic Objects: An Unsupervised Learning Approach
"... Abstract — For robots operating in realworld environments, the ability to deal with dynamic entities such as humans, animals, vehicles, or other robots is of fundamental importance. The variability of dynamic objects, however, is large in general, which makes it hard to manually design suitable mod ..."
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Abstract — For robots operating in realworld environments, the ability to deal with dynamic entities such as humans, animals, vehicles, or other robots is of fundamental importance. The variability of dynamic objects, however, is large in general, which makes it hard to manually design suitable models for their appearance and dynamics. In this paper, we present an unsupervised learning approach to this modelbuilding problem. We describe an exemplarbased model for representing the timevarying appearance of objects in planar laser scans as well as a clustering procedure that builds a set of object classes from given training sequences. Extensive experiments in real environments demonstrate that our system is able to autonomously learn useful models for, e.g., pedestrians, skaters, or cyclists without being provided with external class information. I.
InformationGeometric Optimization Algorithms: A Unifying Picture via Invariance Principles
"... We present a canonical way to turn any smooth parametric family of probability distributions on an arbitrary search space ..."
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Cited by 5 (2 self)
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We present a canonical way to turn any smooth parametric family of probability distributions on an arbitrary search space
Uniqueness of Tensor Decompositions with Applications to Polynomial Identifiability. ArXiv 1304.8087
, 2013
"... We give a robust version of the celebrated result of Kruskal on the uniqueness of tensor decompositions: we prove that given a tensor whose decomposition satisfies a robust form of Kruskal’s rank condition, it is possible to approximately recover the decomposition if the tensor is known up to a suff ..."
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Cited by 3 (1 self)
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We give a robust version of the celebrated result of Kruskal on the uniqueness of tensor decompositions: we prove that given a tensor whose decomposition satisfies a robust form of Kruskal’s rank condition, it is possible to approximately recover the decomposition if the tensor is known up to a sufficiently small (inverse polynomial) error. Kruskal’s theorem has found many applications in proving the identifiability of parameters for various latent variable models and mixture models such as Hidden Markov models, topic models etc. Our robust version immediately implies identifiability using only polynomially many samples in many of these settings. This polynomial identifiability is an essential first step towards efficient learning algorithms for these models. Recently, algorithms based on tensor decompositions have been used to estimate the parameters of various hidden variable models efficiently in special cases as long as they satisfy certain “nondegeneracy ” properties. Our methods give a way to go beyond this nondegeneracy barrier, and establish polynomial identifiablity of the parameters under much milder conditions. Given the importance of Kruskal’s theorem in the tensor literature, we expect that this robust version will have several applications beyond the settings we explore in this work.
Bayesian clustering of huge friendship networks
, 2007
"... Because of the recent growth in popularity of social websites, such as MySpace, Facebook and Last.fm, there is an increasing interest in ways to analyze extremely large friendship networks with even millions of nodes. These huge networks provide a practical test ground for new network algorithms. Th ..."
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Because of the recent growth in popularity of social websites, such as MySpace, Facebook and Last.fm, there is an increasing interest in ways to analyze extremely large friendship networks with even millions of nodes. These huge networks provide a practical test ground for new network algorithms. The network analysis methods can also be applied to other networks than social networks, such as interactions between proteins and links between web pages. Social networks have typically structure: there are dense groups of nodes and some nodes have disproportionately many connections. The structure emerges, because friendships are not formed randomly. Instead, people tend to become friends with those who are similar to themselves. This can be called homophily. There are also other factors that guide the formation of friendships, such as geographical location and membership in common activities. The M0 algorithm finds clustering structure in networks with homophily by Bayesian statistical inference. The algorithm is based on a generative model for creating the edges
Model selection for mixtures of mutagenetic trees
 Genetics Statistical Applications in Genetics and Molecular Biology, 5, Article 17
, 2006
"... Abstract The evolution of drug resistance in HIV is characterized by the accumulation of resistanceassociated mutations in the HIV genome. Mutagenetic trees, a family of restricted Bayesian tree models, have been applied to infer the order and rate of occurrence of these mutations. Understanding an ..."
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Abstract The evolution of drug resistance in HIV is characterized by the accumulation of resistanceassociated mutations in the HIV genome. Mutagenetic trees, a family of restricted Bayesian tree models, have been applied to infer the order and rate of occurrence of these mutations. Understanding and predicting this evolutionary process is an important prerequisite for the rational design of antiretroviral therapies. In practice, mixtures models of K mutagenetic trees provide more flexibility and are often more appropriate for modelling observed mutational patterns. Here, we investigate the model selection problem for Kmutagenetic trees mixture models. We evaluate several classical model selection criteria including crossvalidation, the Bayesian Information Criterion (BIC), and the Akaike Information Criterion. We also use the empirical Bayes method by constructing a prior probability distribution for the parameters of a mutagenetic trees mixture model and deriving the posterior probability of the model. In addition to the model dimension, we consider the redundancy of a mixture model, which is measured by comparing the topologies of trees within a mixture model. Based on the redundancy, we propose a new model selection criterion, which is a modification of the BIC. Experimental results on simulated and on real HIV data show that the classical criteria tend to select models with far too many tree components. Only crossvalidation and the modified BIC recover the correct number of trees and the tree topologies most of the time. At the same optimal performance, the runtime of the new BIC modification is about one order of magnitude lower. Thus, this model selection criterion can also be used for large data sets for which crossvalidation becomes computationally infeasible.
Intelligent Planning for Autonomous Underwater Vehicles
, 2007
"... The aim of my PhD is to develop novel algorithms to allow an Autonomous Underwater Vehicle (AUV) to locate hydrothermal vents on the ocean floor. Hydrothermal vents are tectonicallydriven outgassings of mineralrich superheated water, and they produce a chemicaladvecting plume that can be detected ..."
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Cited by 2 (2 self)
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The aim of my PhD is to develop novel algorithms to allow an Autonomous Underwater Vehicle (AUV) to locate hydrothermal vents on the ocean floor. Hydrothermal vents are tectonicallydriven outgassings of mineralrich superheated water, and they produce a chemicaladvecting plume that can be detected from kilometres away. Finding vents is challenging firstly because detecting a chemical tracer from a plume gives very little information on the bearing or range to the source, and secondly because tracers from different vents combine in an additive way, and there is no a priori way of telling how many vents have contributed to a measured signal. I have decomposed the task of finding vents into a mapping problem, where a probabilistic map of nearby vents is constructed, and a planning problem, which uses the uncertain map to determine actions the AUV should take to allow it to find as many vents as possible on a mission, subject to the limited power resources it has. Both problems will require the development of new methods to solve them. The mapping problem is novel because sensors do not provide even an approximate range to their target, there are potentially multiple targets, and