Bayesian Inference
Probabilistic principles in unsupervised learning of visual structure: human data and a model
Edelman, Shimon, Hiles, Benjamin P., Yang, Hwajin, Intrator, Nathan
To find out how the representations of structured visual objects depend on the co-occurrence statistics of their constituents, we exposed subjects to a set of composite images with tight control exerted over (1) the conditional probabilities of the constituent fragments, and (2) the value of Barlow's criterion of "suspicious coincidence" (the ratio of joint probability to the product of marginals). We then compared the part verification response times for various probe/target combinations before and after the exposure. For composite probes, the speedup was much larger for targets that contained pairs of fragments perfectly predictive of each other, compared to those that did not. This effect was modulated by the significance of their co-occurrence as estimated by Barlow's criterion. For lone-fragment probes, the speedup in all conditions was generally lower than for composites. These results shed light on the brain's strategies for unsupervised acquisition of structural information in vision.
Adaptive Sparseness Using Jeffreys Prior
In this paper we introduce a new sparseness inducing prior which does not involve any (hyper)parameters thatneed to be adjusted or estimated. Although other applications are possible, we focus here on supervised learning problems: regression and classification. Experiments withseveral publicly available benchmark data sets show that the proposed approach yields state-of-the-art performance. In particular, our method outperforms support vector machines and performs competitively with the best alternative techniques, both in terms of error rates and sparseness, although it involves no tuning or adjusting of sparsenesscontrolling hyper-parameters.
TAP Gibbs Free Energy, Belief Propagation and Sparsity
Csatรณ, Lehel, Opper, Manfred, Winther, Ole
The adaptive TAP Gibbs free energy for a general densely connected probabilistic model with quadratic interactions and arbritary single site constraints is derived. We show how a specific sequential minimization of the free energy leads to a generalization of Minka's expectation propagation. Lastly,we derive a sparse representation version of the sequential algorithm. The usefulness of the approach is demonstrated on classification anddensity estimation with Gaussian processes and on an independent componentanalysis problem.
Intransitive Likelihood-Ratio Classifiers
Bilmes, Jeff, Ji, Gang, Meila, Marina
In this work, we introduce an information-theoretic based correction term to the likelihood ratio classification method for multiple classes. Under certain conditions, the term is sufficient for optimally correcting the difference betweenthe true and estimated likelihood ratio, and we analyze this in the Gaussian case. We find that the new correction term significantly improvesthe classification results when tested on medium vocabulary speechrecognition tasks. Moreover, the addition of this term makes the class comparisons analogous to an intransitive game and we therefore use several tournament-like strategies to deal with this issue. We find that further small improvements are obtained by using an appropriate tournament.Lastly, we find that intransitivity appears to be a good measure of classification confidence.
Bayesian Predictive Profiles With Applications to Retail Transaction Data
Cadez, Igor V., Smyth, Padhraic
Massive transaction data sets are recorded in a routine manner in telecommunications, retail commerce, and Web site management. In this paper we address the problem of inferring predictive individual profilesfrom such historical transaction data. We describe a generative mixture model for count data and use an an approximate Bayesian estimation framework that effectively combines anindividual's specific history with more general population patterns. We use a large real-world retail transaction data set to illustrate how these profiles consistently outperform non-mixture and non-Bayesian techniques in predicting customer behavior in out-of-sample data.
A Bayesian Network for Real-Time Musical Accompaniment
We describe a computer system that provides a real-time musical accompanimentfor a live soloist in a piece of non-improvised music for soloist and accompaniment. A Bayesian network is developed thatrepresents the joint distribution on the times at which the solo and accompaniment notes are played, relating the two parts through a layer of hidden variables. The network is first constructed usingthe rhythmic information contained in the musical score. The network is then trained to capture the musical interpretations ofthe soloist and accompanist in an off-line rehearsal phase. During live accompaniment the learned distribution of the network is combined with a real-time analysis of the soloist's acoustic signal, performedwith a hidden Markov model, to generate a musically principledaccompaniment that respects all available sources of knowledge. A live demonstration will be provided.
Using Vocabulary Knowledge in Bayesian Multinomial Estimation
Griffiths, Thomas L., Tenenbaum, Joshua B.
Recent approaches have used uncertainty over the vocabulary of symbols in a multinomial distribution as a means of accounting for sparsity. We present a Bayesian approach that allows weak prior knowledge, in the form of a small set of approximate candidate vocabularies, to be used to dramatically improve the resulting estimates. We demonstrate these improvements in applications to text compression andestimating distributions over words in newsgroup data. 1 Introduction Sparse multinomial distributions arise in many statistical domains, including natural languageprocessing and graphical models. Consequently, a number of approaches toparameter estimation for sparse multinomial distributions have been suggested [3]. These approaches tend to be domain-independent: they make little use of prior knowledge about a specific domain. In many domains where multinomial distributionsare estimated there is often at least weak prior knowledge about' the potential structure of distributions, such as a set of hypotheses about restricted vocabularies from which the symbols might be generated. Such knowledge can be solicited from experts or obtained from unlabeled data. We present a method for Bayesian_parameter estimation in sparse discrete domains that exploits this weak form of prior knowledge to improve estimates over knowledge-free approaches.
Learning Body Pose via Specialized Maps
Rosales, Rรณmer, Sclaroff, Stan
A nonlinear supervised learning model, the Specialized Mappings Architecture (SMA), is described and applied to the estimation of human body pose from monocular images. The SMA consists of several specialized forward mapping functions and an inverse mapping function.Each specialized function maps certain domains of the input space (image features) onto the output space (body pose parameters). The key algorithmic problems faced are those of learning the specialized domains and mapping functions in an optimal way,as well as performing inference given inputs and knowledge of the inverse function. Solutions to these problems employ the EM algorithm and alternating choices of conditional independence assumptions.Performance of the approach is evaluated with synthetic and real video sequences of human motion. 1 Introduction In everyday life, humans can easily estimate body part locations (body pose) from relatively low-resolution images of the projected 3D world (e.g., when viewing a photograph or a video). However, body pose estimation is a very difficult computer vision problem.
Learning Spike-Based Correlations and Conditional Probabilities in Silicon
Shon, Aaron P., Hsu, David, Diorio, Chris
We have designed and fabricated a VLSI synapse that can learn a conditional probability or correlation between spike-based inputs and feedback signals. The synapse is low power, compact, provides nonvolatile weight storage, and can perform simultaneous multiplication andadaptation. We can calibrate arrays of synapses to ensure uniform adaptation characteristics. Finally, adaptation in our synapse does not necessarily depend on the signals used for computation. Consequently,our synapse can implement learning rules that correlate past and present synaptic activity. We provide analysis andexperimental chip results demonstrating the operation in learning and calibration mode, and show how to use our synapse to implement various learning rules in silicon.