We introduce a new discrepancy score between two distributions that gives an indication on their \emph{similarity}. While much research has been done to determine if two samples come from exactly the same distribution, much less research considered the problem of determining if two finite samples come from similar distributions. The new score gives an intuitive interpretation of similarity; it optimally perturbs the distributions so that they best fit each other. The score is defined between distributions, and can be efficiently estimated from samples. We provide convergence bounds of the estimated score, and develop hypothesis testing procedures that test if two data sets come from similar distributions. The statistical power of this procedures is presented in simulations. We also compare the score's capacity to detect similarity with that of other known measures on real data.

Characterizing the information carried by neural populations in the brain requires accurate statistical models of neural spike responses. The negative-binomial distribution provides a convenient model for over-dispersed spike counts, that is, responses with greater-than-Poisson variability. Here we describe a powerful data-augmentation framework for fully Bayesian inference in neural models with negative-binomial spiking. Our approach relies on a recently described latent-variable representation of the negative-binomial distribution, which equates it to a Polya-gamma mixture of normals. This framework provides a tractable, conditionally Gaussian representation of the posterior that can be used to design efficient EM and Gibbs sampling based algorithms for inference in regression and dynamic factor models. We apply the model to neural data from primate retina and show that it substantially outperforms Poisson regression on held-out data, and reveals latent structure underlying spike count correlations in simultaneously recorded spike trains.

We describe the tradeoff between the performance in a visual recognition problem and the control authority that the agent can exercise on the sensing process. We focus on the problem of "visual search" of an object in an otherwise known and static scene, propose a measure of control authority, and relate it to the expected risk and its proxy (conditional entropy of the posterior density). We show this analytically, as well as empirically by simulation using the simplest known model that captures the phenomenology of image formation, including scaling and occlusions. We show that a "passive" agent given a training set can provide no guarantees on performance beyond what is afforded by the priors, and that an "omnipotent" agent, capable of infinite control authority, can achieve arbitrarily good performance (asymptotically). In between these limiting cases, the tradeoff can be characterized empirically.

We explore the hypothesis that the neuronal spike generation mechanism is an analog-to-digital converter, which rectifies low-pass filtered summed synaptic currents and encodes them into spike trains linearly decodable in post-synaptic neurons. To digitally encode an analog current waveform, the sampling rate of the spike generation mechanism must exceed its Nyquist rate. Such oversampling is consistent with the experimental observation that the precision of the spike-generation mechanism is an order of magnitude greater than the cut-off frequency of dendritic low-pass filtering. To achieve additional reduction in the error of analog-to-digital conversion, electrical engineers rely on noise-shaping. If noise-shaping were used in neurons, it would introduce correlations in spike timing to reduce low-frequency (up to Nyquist) transmission error at the cost of high-frequency one (from Nyquist to sampling rate). Using experimental data from three different classes of neurons, we demonstrate that biological neurons utilize noise-shaping. We also argue that rectification by the spike-generation mechanism may improve energy efficiency and carry out de-noising. Finally, the zoo of ion channels in neurons may be viewed as a set of predictors, various subsets of which are activated depending on the statistics of the input current.

The ability to predict action content from neural signals in real time before the action occurshas been long sought in the neuroscientific study of decision-making, agency and volition. Online real-time (ORT) prediction is important for understanding therelation between neural correlates of decision-making and conscious, voluntary action as well as for brain-machine interfaces. Here, epilepsy patients, implanted with intracranial depth microelectrodes or subdural grid electrodes for clinical purposes, participated in a "matching-pennies" game against an opponent. In each trial, subjects were given a 5 s countdown, after which they had to raise their left or right hand immediately as the "go" signal appeared on a computer screen. They won a fixed amount of money if they raised a different hand than their opponent and lost that amount otherwise.

Multi-dimensional latent variable models can capture the many latent factors in a text corpus, such as topic, author perspective and sentiment. We introduce factorial LDA, a multi-dimensional latent variable model in which a document is influenced by K different factors, and each word token depends on a K-dimensional vector of latent variables. Our model incorporates structured word priors and learns a sparse product of factors. Experiments on research abstracts show that our model can learn latent factors such as research topic, scientific discipline, and focus (e.g. methods vs. applications.) Our modeling improvements reduce test perplexity and improve human interpretability of the discovered factors.

We consider sequential prediction algorithms that are given the predictions from a set of models as inputs. If the nature of the data is changing over time in that different models predict well on different segments of the data, then adaptivity is typically achieved by mixing into the weights in each round a bit of the initial prior (kind of like a weak restart). However, what if the favored models in each segment are from a small subset, i.e. the data is likely to be predicted well by models that predicted well before? Curiously, fitting such ''sparse composite models'' is achieved by mixing in a bit of all the past posteriors. This self-referential updating method is rather peculiar, but it is efficient and gives superior performance on many natural data sets. Also it is important because it introduces a long-term memory: any model that has done well in the past can be recovered quickly. While Bayesian interpretations can be found for mixing in a bit of the initial prior, no Bayesian interpretation is known for mixing in past posteriors. We build atop the ''specialist'' framework from the online learning literature to give the Mixing Past Posteriors update a proper Bayesian foundation. We apply our method to a well-studied multitask learning problem and obtain a new intriguing efficient update that achieves a significantly better bound.

In many large economic markets, goods are sold through sequential auctions. Such domains include eBay, online ad auctions, wireless spectrum auctions, and the Dutch flower auctions. Bidders in these domains face highly complex decision-making problems, as their preferences for outcomes in one auction often depend on the outcomes of other auctions, and bidders have limited information about factors that drive outcomes, such as other bidders' preferences and past actions. In this work, we formulate the bidder's problem as one of price prediction (i.e., learning) and optimization. We define the concept of stable price predictions and show that (approximate) equilibrium in sequential auctions can be characterized as a profile of strategies that (approximately) optimize with respect to such (approximately) stable price predictions. We show how equilibria found with our formulation compare to known theoretical equilibria for simpler auction domains, and we find new approximate equilibria for a more complex auction domain where analytical solutions were heretofore unknown.

In many applications, one has information, e.g., labels that are provided in a semi-supervised manner, about a specific target region of a large data set, and one wants to perform machine learning and data analysis tasks nearby that pre-specified target region. Locally-biased problems of this sort are particularly challenging for popular eigenvector-based machine learning and data analysis tools. At root, the reason is that eigenvectors are inherently global quantities. In this paper, we address this issue by providing a methodology to construct semi-supervised eigenvectors of a graph Laplacian, and we illustrate how these locally-biased eigenvectors can be used to perform locally-biased machine learning. These semi-supervised eigenvectors capture successively-orthogonalized directions of maximum variance, conditioned on being well-correlated with an input seed set of nodes that is assumed to be provided in a semi-supervised manner. We also provide several empirical examples demonstrating how these semi-supervised eigenvectors can be used to perform locally-biased learning.

We uncover relations between robust MDPs and risk-sensitive MDPs. The objective of a robust MDP is to minimize a function, such as the expectation of cumulative cost, for the worst case when the parameters have uncertainties. The objective of a risk-sensitive MDP is to minimize a risk measure of the cumulative cost when the parameters are known. We show that a risk-sensitive MDP of minimizing the expected exponential utility is equivalent to a robust MDP of minimizing the worst-case expectation with a penalty for the deviation of the uncertain parameters from their nominal values, which is measured with the Kullback-Leibler divergence. We also show that a risk-sensitive MDP of minimizing an iterated risk measure that is composed of certain coherent risk measures is equivalent to a robust MDP of minimizing the worst-case expectation when the possible deviations of uncertain parameters from their nominal values are characterized with a concave function.