Recent work has examined the estimation of models of stimulus-driven neural activity in which some linear filtering process is followed by a nonlinear, probabilistic spiking stage. We analyze the estimation of one such model for which this nonlinear step is implemented by a noisy, leaky, integrate-and-fire mechanism with a spike-dependent aftercurrent. This model is a biophysically plausible alternative to models with Poisson (memory-less) spiking, and has been shown to effectively reproduce various spiking statistics of neurons in vivo. However, the problem of estimating the model from extracellular spike train data has not been examined in depth. We formulate the problem in terms of maximum likelihood estimation, and show that the computational problem of maximizing the likelihood is tractable.

We present a Bayesian approach to color constancy which utilizes a non-Gaussian probabilistic model of the image formation process. The parameters of this model are estimated directly from an uncalibrated image set and a small number of additional algorithmic parameters are chosen using cross validation. The algorithm is empirically shown to exhibit RMS error lower than other color constancy algorithms based on the Lambertian surface reflectance model when estimating the illuminants of a set of test images. This is demonstrated via a direct performance comparison utilizing a publicly available set of real world test images and code base.

Recent multi-agent extensions of Q-Learning require knowledge of other agents' payoffs and Q-functions, and assume game-theoretic play at all times by all other agents. This paper proposes a fundamentally different approach, dubbed "Hyper-Q" Learning, in which values of mixed strategies rather than base actions are learned, and in which other agents' strategies are estimated from observed actions via Bayesian inference. Hyper-Q may be effective against many different types of adaptive agents, even if they are persistently dynamic. Against certain broad categories of adaptation, it is argued that Hyper-Q may converge to exact optimal time-varying policies. In tests using Rock-Paper-Scissors, Hyper-Q learns to significantly exploit an Infinitesimal Gradient Ascent (IGA) player, as well as a Policy Hill Climber (PHC) player. Preliminary analysis of Hyper-Q against itself is also presented.

We introduce a class of nonstationary covariance functions for Gaussian process (GP) regression. Nonstationary covariance functions allow the model to adapt to functions whose smoothness varies with the inputs. The class includes a nonstationary version of the Matérn stationary covariance, in which the differentiability of the regression function is controlled by a parameter, freeing one from fixing the differentiability in advance. In experiments, the nonstationary GP regression model performs well when the input space is two or three dimensions, outperforming a neural network model and Bayesian free-knot spline models, and competitive with a Bayesian neural network, but is outperformed in one dimension by a state-of-the-art Bayesian free-knot spline model.

The bootstrap has become a popular method for exploring model (structure) uncertainty. Our experiments with artificial and realworld data demonstrate that the graphs learned from bootstrap samples can be severely biased towards too complex graphical models. Accounting for this bias is hence essential, e.g., when exploring model uncertainty. We find that this bias is intimately tied to (well-known) spurious dependences induced by the bootstrap. The leading-order bias-correction equals one half of Akaike's penalty for model complexity. We demonstrate the effect of this simple bias-correction in our experiments. We also relate this bias to the bias of the plugin estimator for entropy, as well as to the difference between the expected test and training errors of a graphical model, which asymptotically equals Akaike's penalty (rather than one half).

This paper compares the ability of human observers to detect target image curves with that of an ideal observer. The target curves are sampled from a generative model which specifies (probabilistically) the geometry and local intensity properties of the curve. The ideal observer performs Bayesian inference on the generative model using MAP estimation. Varying the probability model for the curve geometry enables us investigate whether human performance is best for target curves that obey specific shape statistics, in particular those observed on natural shapes. Experiments are performed with data on both rectangular and hexagonal lattices. Our results show that human observers' performance approaches that of the ideal observer and are, in general, closest to the ideal for conditions where the target curve tends to be straight or similar to natural statistics on curves. This suggests a bias of human observers towards straight curves and natural statistics.

In this paper we present Discriminative Random Fields (DRF), a discriminative framework for the classification of natural image regions by incorporating neighborhood spatial dependencies in the labels as well as the observed data. The proposed model exploits local discriminative models and allows to relax the assumption of conditional independence of the observed data given the labels, commonly used in the Markov Random Field (MRF) framework. The parameters of the DRF model are learned using penalized maximum pseudo-likelihood method. Furthermore, the form of the DRF model allows the MAP inference for binary classification problems using the graph min-cut algorithms. The performance of the model was verified on the synthetic as well as the real-world images. The DRF model outperforms the MRF model in the experiments.

A general linear response method for deriving improved estimates of correlations in the variational Bayes framework is presented. Three applications are given and it is discussed how to use linear response as a general principle for improving mean field approximations.

Existing source location and recovery algorithms used in magnetoencephalographic imaging generally assume that the source activity at different brain locations is independent or that the correlation structure is known. However, electrophysiological recordings of local field potentials show strong correlations in aggregate activity over significant distances. Indeed, it seems very likely that stimulus-evoked activity would follow strongly correlated time-courses in different brain areas. Here, we present, and validate through simulations, a new approach to source reconstruction in which the correlation between sources is modelled and estimated explicitly by variational Bayesian methods, facilitating accurate recovery of source locations and the time-courses of their activation.

In the problem of probability forecasting the learner's goal is to output, given a training set and a new object, a suitable probability measure on the possible values of the new object's label. An online algorithm for probability forecasting is said to be well-calibrated if the probabilities it outputs agree with the observed frequencies. We give a natural nonasymptotic formalization of the notion of well-calibratedness, which we then study under the assumption of randomness (the object/label pairs are independent and identically distributed). It turns out that, although no probability forecasting algorithm is automatically well-calibrated in our sense, there exists a wide class of algorithms for "multiprobability forecasting" (such algorithms are allowed to output a set, ideally very narrow, of probability measures) which satisfy this property; we call the algorithms in this class "Venn probability machines". Our experimental results demonstrate that a 1-Nearest Neighbor Venn probability machine performs reasonably well on a standard benchmark data set, and one of our theoretical results asserts that a simple Venn probability machine asymptotically approaches the true conditional probabilities regardless, and without knowledge, of the true probability measure generating the examples.