We present a mixture model whose components are Restricted Boltzmann Machines (RBMs). This possibility has not been considered before because computing the partition function of an RBM is intractable, which appears to make learning a mixture of RBMs intractable as well. Surprisingly, when formulated as a third-order Boltzmann machine, such a mixture model can be learned tractably using contrastive divergence. The energy function of the model captures three-way interactions among visible units, hidden units, and a single hidden multinomial unit that represents the cluster labels. The distinguishing feature of this model is that, unlike other mixture models, the mixing proportions are not explicitly parameterized. Instead, they are defined implicitly via the energy function and depend on all the parameters in the model. We present results for the MNIST and NORB datasets showing that the implicit mixture of RBMs learns clusters that reflect the class structure in the data.

When used to guide decisions, linear regression analysis typically involves estimation of regression coefficients via ordinary least squares and their subsequent use to make decisions. When there are multiple response variables and features do not perfectly capture their relationships, it is beneficial to account for the decision objective when computing regression coefficients. Empirical optimization does so but sacrifices performance when features are well-chosen or training data are insufficient. We propose directed regression, an efficient algorithm that combines merits of ordinary least squares and empirical optimization. We demonstrate through a computational study that directed regression can generate significant performance gains over either alternative. We also develop a theory that motivates the algorithm.

Search engines today present results that are often oblivious to recent shifts in intent. For example, the meaning of the query independence day shifts in early July to a US holiday and to a movie around the time of the box office release. While no studies exactly quantify the magnitude of intent-shifting traffic, studies suggest that news events, seasonal topics, pop culture, etc account for 1/2 the search queries. This paper shows that the signals a search engine receives can be used to both determine that a shift in intent happened, as well as find a result that is now more relevant. We present a meta-algorithm that marries a classifier with a bandit algorithm to achieve regret that depends logarithmically on the number of query impressions, under certain assumptions. We provide strong evidence that this regret is close to the best achievable. Finally, via a series of experiments, we demonstrate that our algorithm outperforms prior approaches, particularly as the amount of intent-shifting traffic increases.

Everyday social interactions are heavily influenced by our snap judgments about others' goals. Even young infants can infer the goals of intentional agents from observing how they interact with objects and other agents in their environment: e.g., that one agent is'helping' or'hindering' another's attempt to get up a hill or open a box. We propose a model for how people can infer these social goals from actions, based on inverse planning in multiagent Markov decision problems (MDPs). The model infers the goal most likely to be driving an agent's behavior byassuming the agent acts approximately rationally given environmental constraints andits model of other agents present.

Recent work on the statistical modeling of neural responses has focused on modulated renewal processes in which the spike rate is a function of the stimulus and recent spiking history. Typically, these models incorporate spike-history dependencies via either: (A) a conditionally-Poisson process with rate dependent on a linear projection of the spike train history (e.g., generalized linear model); or (B) a modulated non-Poisson renewal process (e.g., inhomogeneous gamma process). Here we show that the two approaches can be combined, resulting in a {\it conditional renewal} (CR) model for neural spike trains. This model captures both real and rescaled-time effects, and can be fit by maximum likelihood using a simple application of the time-rescaling theorem [1]. We show that for any modulated renewal process model, the log-likelihood is concave in the linear filter parameters only under certain restrictive conditions on the renewal density (ruling out many popular choices, e.g. gamma with $\kappa \neq1$), suggesting that real-time history effects are easier to estimate than non-Poisson renewal properties. Moreover, we show that goodness-of-fit tests based on the time-rescaling theorem [1] quantify relative-time effects, but do not reliably assess accuracy in spike prediction or stimulus-response modeling. We illustrate the CR model with applications to both real and simulated neural data.

We propose to use Rademacher complexity, originally developed in computational learning theory, as a measure of human learning capacity. Rademacher complexity measuresa learner's ability to fit random labels, and can be used to bound the learner's true error based on the observed training sample error. We first review thedefinition of Rademacher complexity and its generalization bound. We then describe a "learning the noise" procedure to experimentally measure human Rademacher complexities. The results from empirical studies showed that: (i) human Rademacher complexity can be successfully measured, (ii) the complexity dependson the domain and training sample size in intuitive ways, (iii) human learningrespects the generalization bounds, (iv) the bounds can be useful in predicting the danger of overfitting in human learning. Finally, we discuss the potential applications of human Rademacher complexity in cognitive science.

This paper considers a sensitivity analysis in Hidden Markov Models with continuous state and observation spaces. We propose an Infinitesimal Perturbation Analysis (IPA) on the filtering distribution with respect to some parameters of the model. We describe a methodology for using any algorithm that estimates the filtering density, such as Sequential Monte Carlo methods, to design an algorithm that estimates its gradient. The resulting IPA estimator is proven to be asymptotically unbiased, consistent and has computational complexity linear in the number of particles. We consider an application of this analysis to the problem of identifying unknown parameters of the model given a sequence of observations. We derive an IPA estimator for the gradient of the log-likelihood, which may be used in a gradient method for the purpose of likelihood maximization. We illustrate the method with several numerical experiments.

There is a growing body of experimental evidence to suggest that the brain is capable of approximating optimal Bayesian inference in the face of noisy input stimuli. Despite this progress, the neural underpinnings of this computation are still poorly understood. In this paper we focus on the problem of Bayesian filtering of stochastic time series. In particular we introduce a novel neural network, derived from a line attractor architecture, whose dynamics map directly onto those of the Kalman Filter in the limit where the prediction error is small. When the prediction error is large we show that the network responds robustly to change-points in a way that is qualitatively compatible with the optimal Bayesian model. The model suggests ways in which probability distributions are encoded in the brain and makes a number of testable experimental predictions.

In solving complex visual learning tasks, adopting multiple descriptors to more precisely characterize the data has been a feasible way for improving performance. These representations are typically high dimensional and assume diverse forms. Thus finding a way to transform them into a unified space of lower dimension generally facilitates the underlying tasks, such as object recognition or clustering. We describe an approach that incorporates multiple kernel learning with dimensionality reduction (MKL-DR). While the proposed framework is flexible in simultaneously tackling data in various feature representations, the formulation itself is general in that it is established upon graph embedding. It follows that any dimensionality reduction techniques explainable by graph embedding can be generalized by our method to consider data in multiple feature representations.

By adding a spatial regularization kernel to a standard loss function formulation of the boosting problem, we develop a framework for spatially informed boosting. From this regularized loss framework we derive an efficient boosting algorithm that uses additional weights/priors on the base classifiers. We prove that the proposed algorithm exhibits a ``grouping effect, which encourages the selection of all spatially local, discriminative base classifiers. The algorithms primary advantage is in applications where the trained classifier is used to identify the spatial pattern of discriminative information, e.g. the voxel selection problem in fMRI. We demonstrate the algorithms performance on various data sets.