State-of-the-art statistical methods in neuroscience have enabled us to fit mathematical models to experimental data and subsequently to infer the dynamics of hidden parameters underlying the observable phenomena. Here, we develop a Bayesian method for inferring the time-varying mean and variance of the synaptic input, along with the dynamics of each ion channel from a single voltage trace of a neuron. An estimation problem may be formulated on the basis of the state-space model with prior distributions that penalize large fluctuations in these parameters. After optimizing the hyperparameters by maximizing the marginal likelihood, the state-space model provides the time-varying parameters of the input signals and the ion channel states. The proposed method is tested not only on the simulated data from the Hodgkin-Huxley type models but also on experimental data obtained from a cortical slice in vitro.

Renewal processes are generalizations of the Poisson process on the real line, whose intervals are drawn i.i.d. from some distribution. Modulated renewal processes allow these distributions to vary with time, allowing the introduction nonstationarity. In this work, we take a nonparametric Bayesian approach, modeling this nonstationarity with a Gaussian process. Our approach is based on the idea of uniformization, allowing us to draw exact samples from an otherwise intractable distribution. We develop a novel and efficient MCMC sampler for posterior inference. In our experiments, we test these on a number of synthetic and real datasets.

A Bayesian approach to partitioning distance matrices is presented. It is inspired by the 'Translation-Invariant Wishart-Dirichlet' process (TIWD) in (Vogt et al., 2010) and shares a number of advantageous properties like the fully probabilistic nature of the inference model, automatic selection of the number of clusters and applicability in semi-supervised settings. In addition, our method (which we call 'fastTIWD') overcomes the main shortcoming of the original TIWD, namely its high computational costs. The fastTIWD reduces the workload in each iteration of a Gibbs sampler from O(n^3) in the TIWD to O(n^2). Our experiments show that this cost reduction does not compromise the quality of the inferred partitions. With this new method it is now possible to 'mine' large relational datasets with a probabilistic model, thereby automatically detecting new and potentially interesting clusters.

In this paper, we derive a method to refine a Bayes network diagnostic model by exploiting constraints implied by expert decisions on test ordering. At each step, the expert executes an evidence gathering test, which suggests the test's relative diagnostic value. We demonstrate that consistency with an expert's test selection leads to non-convex constraints on the model parameters. We incorporate these constraints by augmenting the network with nodes that represent the constraint likelihoods. Gibbs sampling, stochastic hill climbing and greedy search algorithms are proposed to find a MAP estimate that takes into account test ordering constraints and any data available. We demonstrate our approach on diagnostic sessions from a manufacturing scenario.

We consider a general inference setting for discrete probabilistic graphical models where we seek maximum a posteriori (MAP) estimates for a subset of the random variables (max nodes), marginalizing over the rest (sum nodes). We present a hybrid message-passing algorithm to accomplish this. The hybrid algorithm passes a mix of sum and max messages depending on the type of source node (sum or max). We derive our algorithm by showing that it falls out as the solution of a particular relaxation of a variational framework. We further show that the Expectation Maximization algorithm can be seen as an approximation to our algorithm. Experimental results on synthetic and real-world datasets, against several baselines, demonstrate the efficacy of our proposed algorithm.

Variational Message Passing (VMP) is an algorithmic implementation of the Variational Bayes (VB) method which applies only in the special case of conjugate exponential family models. We propose an extension to VMP, which we refer to as Non-conjugate Variational Message Passing (NCVMP) which aims to alleviate this restriction while maintaining modularity, allowing choice in how expectations are calculated, and integrating into an existing message-passing framework: Infer.NET. We demonstrate NCVMP on logistic binary and multinomial regression. In the multinomial case we introduce a novel variational bound for the softmax factor which is tighter than other commonly used bounds whilst maintaining computational tractability.

Variability in single neuron models is typically implemented either by a stochastic Leaky-Integrate-and-Fire model or by a model of the Generalized Linear Model (GLM) family. We use analytical and numerical methods to relate state-of-the-art models from both schools of thought. First we find the analytical expressions relating the subthreshold voltage from the Adaptive Exponential Integrate-and-Fire model (AdEx) to the Spike-Response Model with escape noise (SRM as an example of a GLM). Then we calculate numerically the link-function that provides the firing probability given a deterministic membrane potential. We find a mathematical expression for this link-function and test the ability of the GLM to predict the firing probability of a neuron receiving complex stimulation. Comparing the prediction performance of various link-functions, we find that a GLM with an exponential link-function provides an excellent approximation to the Adaptive Exponential Integrate-and-Fire with colored-noise input. These results help to understand the relationship between the different approaches to stochastic neuron models.

Many applications in computer vision measure the similarity between images or image patches based on some statistics such as oriented gradients. These are often modeled implicitly or explicitly with a Gaussian noise assumption, leading to the use of the Euclidean distance when comparing image descriptors. In this paper, we show that the statistics of gradient based image descriptors often follow a heavy-tailed distribution, which undermines any principled motivation for the use of Euclidean distances. We advocate for the use of a distance measure based on the likelihood ratio test with appropriate probabilistic models that fit the empirical data distribution. We instantiate this similarity measure with the Gamma-compound-Laplace distribution, and show significant improvement over existing distance measures in the application of SIFT feature matching, at relatively low computational cost.

A sizable literature has focused on the problem of estimating a low-dimensional feature space capturing a neuron's stimulus sensitivity. However, comparatively little work has addressed the problem of estimating the nonlinear function from feature space to a neuron's output spike rate. Here, we use a Gaussian process (GP) prior over the infinite-dimensional space of nonlinear functions to obtain Bayesian estimates of the "nonlinearity" in the linear-nonlinear-Poisson (LNP) encoding model. This offers flexibility, robustness, and computational tractability compared to traditional methods (e.g., parametric forms, histograms, cubic splines). Most importantly, we develop a framework for optimal experimental design based on uncertainty sampling. This involves adaptively selecting stimuli to characterize the nonlinearity with as little experimental data as possible, and relies on a method for rapidly updating hyperparameters using the Laplace approximation. We apply these methods to data from color-tuned neurons in macaque V1. We estimate nonlinearities in the 3D space of cone contrasts, which reveal that V1 combines cone inputs in a highly nonlinear manner. With simulated experiments, we show that optimal design substantially reduces the amount of data required to estimate this nonlinear combination rule.

We propose a new sparse Bayesian model for multi-task regression and classification. The model is able to capture correlations between tasks, or more specifically a low-rank approximation of the covariance matrix, while being sparse in the features. We introduce a general family of group sparsity inducing priors based on matrix-variate Gaussian scale mixtures. We show the amount of sparsity can be learnt from the data by combining an approximate inference approach with type II maximum likelihood estimation of the hyperparameters. Empirical evaluations on data sets from biology and vision demonstrate the applicability of the model, where on both regression and classification tasks it achieves competitive predictive performance compared to previously proposed methods.