We introduce the Piecewise-Constant Conditional Intensity Model, a model for learning temporal dependencies in event streams. We describe a closed-form Bayesian approach to learning these models, and describe an importance sampling algorithm for forecasting future events using these models, using a proposal distribution based on Poisson superposition. We then use synthetic data, supercomputer event logs, and web search query logs to illustrate that our learning algorithm can efficiently learn nonlinear temporal dependencies, and that our importance sampling algorithm can effectively forecast future events.

We consider the problem of Bayesian inference for continuous time multi-stable stochastic systems which can change both their diffusion and drift parameters at discrete times. We propose exact inference and sampling methodologies for two specific cases where the discontinuous dynamics is given by a Poisson process and a two-state Markovian switch. We test the methodology on simulated data, and apply it to two real data sets in finance and systems biology. Our experimental results show that the approach leads to valid inferences and non-trivial insights.

Latent tree graphical models are natural tools for expressing long range and hierarchical dependencies among many variables which are common in computer vision, bioinformatics and natural language processing problems. However, existing models are largely restricted to discrete and Gaussian variables due to computational constraints; furthermore, algorithms for estimating the latent tree structure and learning the model parameters are largely restricted to heuristic local search. We present a method based on kernel embeddings of distributions for latent tree graphical models with continuous and non-Gaussian variables. Our method can recover the latent tree structures with provable guarantees and perform local-minimum free parameter learning and efficient inference. Experiments on simulated and real data show the advantage of our proposed approach.

For many real-world applications, we often need to select correlated variables---such as genetic variations and imaging features associated with Alzheimer's disease---in a high dimensional space. The correlation between variables presents a challenge to classical variable selection methods. To address this challenge, the elastic net has been developed and successfully applied to many applications. Despite its great success, the elastic net does not exploit the correlation information embedded in the data to select correlated variables. To overcome this limitation, we present a novel hybrid model, EigenNet, that uses the eigenstructures of data to guide variable selection. Specifically, it integrates a sparse conditional classification model with a generative model capturing variable correlations in a principled Bayesian framework. We develop an efficient active-set algorithm to estimate the model via evidence maximization. Experiments on synthetic data and imaging genetics data demonstrated the superior predictive performance of the EigenNet over the lasso, the elastic net, and the automatic relevance determination.

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.

Synaptic plasticity underlies learning and is thus central for development, memory, and recovery from injury. However, it is often difficult to detect changes in synaptic strength in vivo, since intracellular recordings are experimentally challenging. Here we present two methods aimed at inferring changes in the coupling between pairs of neurons from extracellularly recorded spike trains. First, using a generalized bilinear model with Poisson output we estimate time-varying coupling assuming that all changes are spike-timing-dependent. This approach allows model-based estimation of STDP modification functions from pairs of spike trains. Then, using recursive point-process adaptive filtering methods we estimate more general variation in coupling strength over time. Using simulations of neurons undergoing spike-timing dependent modification, we show that the true modification function can be recovered. Using multi-electrode data from motor cortex we then illustrate the use of this technique on in vivo data.

Many functional descriptions of spiking neurons assume a cascade structure where inputs are passed through an initial linear filtering stage that produces a low-dimensional signal that drives subsequent nonlinear stages. This paper presents a novel and systematic parameter estimation procedure for such models and applies the method to two neural estimation problems: (i) compressed-sensing based neural mapping from multi-neuron excitation, and (ii) estimation of neural receptive yields in sensory neurons. The proposed estimation algorithm models the neurons via a graphical model and then estimates the parameters in the model using a recently-developed generalized approximate message passing (GAMP) method. The GAMP method is based on Gaussian approximations of loopy belief propagation. In the neural connectivity problem, the GAMP-based method is shown to be computational efficient, provides a more exact modeling of the sparsity, can incorporate nonlinearities in the output and significantly outperforms previous compressed-sensing methods. For the receptive field estimation, the GAMP method can also exploit inherent structured sparsity in the linear weights. The method is validated on estimation of linear nonlinear Poisson (LNP) cascade models for receptive fields of salamander retinal ganglion cells.

Markov Random Fields (MRFs) have proven very powerful both as density estimators and feature extractors for classification. However, their use is often limited by an inability to estimate the partition function $Z$. In this paper, we exploit the gradient descent training procedure of restricted Boltzmann machines (a type of MRF) to {\bf track} the log partition function during learning. Our method relies on two distinct sources of information: (1) estimating the change $\Delta Z$ incurred by each gradient update, (2) estimating the difference in $Z$ over a small set of tempered distributions using bridge sampling. The two sources of information are then combined using an inference procedure similar to Kalman filtering. Learning MRFs through Tempered Stochastic Maximum Likelihood, we can estimate $Z$ using no more temperatures than are required for learning. Comparing to both exact values and estimates using annealed importance sampling (AIS), we show on several datasets that our method is able to accurately track the log partition function. In contrast to AIS, our method provides this estimate at each time-step, at a computational cost similar to that required for training alone.

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.

We show that the lambda-return target used in the TD(lambda) family of algorithms is the maximum likelihood estimator for a specific model of how the variance of an n-step return estimate increases with n. We introduce the gamma-return estimator, an alternative target based on a more accurate model of variance, which defines the TD_gamma family of complex-backup temporal difference learning algorithms. We derive TD_gamma, the gamma-return equivalent of the original TD(lambda) algorithm, which eliminates the lambda parameter but can only perform updates at the end of an episode and requires time and space proportional to the episode length. We then derive a second algorithm, TD_gamma(C), with a capacity parameter C. TD_gamma(C) requires C times more time and memory than TD(lambda) and is incremental and online. We show that TD_gamma outperforms TD(lambda) for any setting of lambda on 4 out of 5 benchmark domains, and that TD_gamma(C) performs as well as or better than TD_gamma for intermediate settings of C.