A BAYESIAN MALLOWS APPROACH TO NONTRANSITIVE PAIR COMPARISON DATA : HOW HUMAN ARE SOUNDS?

We are interested in learning how listeners perceive sounds as having human origins. An experiment was performed with a series of electronically synthesized sounds, and listeners were asked to compare them in pairs. We propose a Bayesian probabilistic method to learn individual preferences from nontransitive pairwise comparison data, as happens when one (or more) individual preferences in the data contradicts what is implied by the others. We build a Bayesian Mallows model in order to handle nontransitive data, with a latent layer of uncertainty which captures the generation of preference misreporting. We then develop a mixture extension of the Mallows model, able to learn individual preferences in a heterogeneous population. The results of our analysis of the musicology experiment are of interest to electroacoustic composers and sound designers, and to the audio industry in general, whose aim is to understand how computer generated sounds can be produced in order to sound more human.Peer reviewe

Probabilistic Models over Ordered Partitions with Application in Learning to Rank

This paper addresses the general problem of modelling and learning rank data with ties. We propose a probabilistic generative model, that models the process as permutations over partitions. This results in super-exponential combinatorial state space with unknown numbers of partitions and unknown ordering among them. We approach the problem from the discrete choice theory, where subsets are chosen in a stagewise manner, reducing the state space per each stage significantly. Further, we show that with suitable parameterisation, we can still learn the models in linear time. We evaluate the proposed models on the problem of learning to rank with the data from the recently held Yahoo! challenge, and demonstrate that the models are competitive against well-known rivals.Comment: 19 pages, 2 figure

Learning mixed membership models with a separable latent structure: theory, provably efficient algorithms, and applications

In a wide spectrum of problems in science and engineering that includes hyperspectral imaging, gene expression analysis, and machine learning tasks such as topic modeling, the observed data is high-dimensional and can be modeled as arising from a data-specific probabilistic mixture of a small collection of latent factors. Being able to successfully learn the latent factors from the observed data is important for efficient data representation, inference, and prediction. Popular approaches such as variational Bayesian and MCMC methods exhibit good empirical performance on some real-world datasets, but make heavy use of approximations and heuristics for dealing with the highly non-convex and computationally intractable optimization objectives that accompany them. As a consequence, consistency or efficiency guarantees for these algorithms are rather weak. This thesis develops a suite of algorithms with provable polynomial statistical and computational efficiency guarantees for learning a wide class of high-dimensional Mixed Membership Latent Variable Models (MMLVMs). Our approach is based on a natural separability property of the shared latent factors that is known to be either exactly or approximately satisfied by the estimates produced by variational Bayesian and MCMC methods. Latent factors are called separable when each factor contains a novel part that is predominantly unique to that factor. For a broad class of problems, we establish that separability is not only an algorithmically convenient structural condition, but is in fact an inevitable consequence of a having a relatively small number of latent factors in a high-dimensional observation space. The key insight underlying our algorithms is the identification of novel parts of each latent factor as extreme points of certain convex polytopes in a suitable representation space. We show that this can be done efficiently through appropriately defined random projections in the representation space. We establish statistical and computational efficiency bounds that are both polynomial in all the model parameters. Furthermore, the proposed random-projections-based algorithm turns out to be naturally amenable to a low-communication-cost distributed implementation which is attractive for modern web-scale distributed data mining applications. We explore in detail two distinct classes of MMLVMs in this thesis: learning topic models for text documents based on their empirical word frequencies and learning mixed membership ranking models based on pairwise comparison data. For each problem, we demonstrate that separability is inevitable when the data dimension scales up and then establish consistency and efficiency guarantees for identifying all novel parts and estimating the latent factors. As a by-product of this analysis, we obtain the first asymptotic consistency and polynomial sample and computational complexity results for learning permutation-mixture and Mallows-mixture models for rankings based on pairwise comparison data. We demonstrate empirically that the performance of our approach is competitive with the current state-of-the-art on a number of real-world datasets