The highly variable dynamics of neocortical circuits observed in vivo have been hypothesized to represent a signature of ongoing stochastic inference but stand in apparent contrast to the deterministic response of neurons measured in vitro. Based on a propagation of the membrane autocorrelation across spike bursts, we provide an analytical derivation of the neural activation function that holds for a large parameter space, including the high-conductance state. On this basis, we show how an ensemble of leaky integrate-and-fire neurons with conductance-based synapses embedded in a spiking environment can attain the correct firing statistics for sampling from a well-defined target distribution. For recurrent networks, we examine convergence toward stationarity in computer simulations and demonstrate sample-based Bayesian inference in a mixed graphical model. This points to a new computational role of high-conductance states and establishes a rigorous link between deterministic neuron models and functional stochastic dynamics on the network level.

Decision makers, such as doctors and judges, make crucial decisions such as recommending treatments to patients, and granting bails to defendants on a daily basis. Such decisions typically involve weighting the potential benefits of taking an action against the costs involved. In this work, we aim to automate this task of learning \emph{cost-effective, interpretable and actionable treatment regimes}. We formulate this as a problem of learning a decision list -- a sequence of if-then-else rules -- which maps characteristics of subjects (eg., diagnostic test results of patients) to treatments. We propose a novel objective to construct a decision list which maximizes outcomes for the population, and minimizes overall costs. We model the problem of learning such a list as a Markov Decision Process (MDP) and employ a variant of the Upper Confidence Bound for Trees (UCT) strategy which leverages customized checks for pruning the search space effectively. Experimental results on real world observational data capturing judicial bail decisions and treatment recommendations for asthma patients demonstrate the effectiveness of our approach.

We present a sparse estimation and dictionary learning framework for compressed fiber sensing based on a probabilistic hierarchical sparse model. To handle severe dictionary coherence, selective shrinkage is achieved using a Weibull prior, which can be related to non-convex optimization with $p$-norm constraints for $0 < p < 1$. In addition, we leverage the specific dictionary structure to promote collective shrinkage based on a local similarity model. This is incorporated in form of a kernel function in the joint prior density of the sparse coefficients, thereby establishing a Markov random field-relation. Approximate inference is accomplished using a hybrid technique that combines Hamilton Monte Carlo and Gibbs sampling. To estimate the dictionary parameter, we pursue two strategies, relying on either a deterministic or a probabilistic model for the dictionary parameter. In the first strategy, the parameter is estimated based on alternating estimation. In the second strategy, it is jointly estimated along with the sparse coefficients. The performance is evaluated in comparison to an existing method in various scenarios using simulations and experimental data.

Large margin classifiers, such as the support vector machine (SVM) [1] and the maximum entropy discrimination (MED) classifier [2], have enjoyed great popularity in the signal processing and machine learning communities due to their broad applicability, robust performance, and the availability of fast software implementations. When the training data is representative of the test data, the performance of MED/SVM has theoretical guarantees that have been validated in practice [1], [3], [4]. Moreover, since the decision boundary of the MED/SVM is solely defined by a few support vectors, the algorithm can tolerate random feature distortions and perturbations. However, in many real applications, anomalous measurements are inherent to the data set due to strong environmental noise or possible sensor failures. Such anomalies arise in industrial process monitoring, video surveillance, tactical multimodal sensing, robust spectrum sensing [5], [6], and, more generally, any application that involves unattended sensors in difficult environments (Figure 1).

Recent advances in Bayesian learning with large-scale data have witnessed emergence of stochastic gradient MCMC algorithms (SG-MCMC), such as stochastic gradient Langevin dynamics (SGLD), stochastic gradient Hamiltonian MCMC (SGHMC), and the stochastic gradient thermostat. While finite-time convergence properties of the SGLD with a 1st-order Euler integrator have recently been studied, corresponding theory for general SG-MCMCs has not been explored. In this paper we consider general SG-MCMCs with high-order integrators, and develop theory to analyze finite-time convergence properties and their asymptotic invariant measures. Our theoretical results show faster convergence rates and more accurate invariant measures for SG-MCMCs with higher-order integrators. For example, with the proposed efficient 2nd-order symmetric splitting integrator, the {\em mean square error} (MSE) of the posterior average for the SGHMC achieves an optimal convergence rate of $L^{-4/5}$ at $L$ iterations, compared to $L^{-2/3}$ for the SGHMC and SGLD with 1st-order Euler integrators. Furthermore, convergence results of decreasing-step-size SG-MCMCs are also developed, with the same convergence rates as their fixed-step-size counterparts for a specific decreasing sequence. Experiments on both synthetic and real datasets verify our theory, and show advantages of the proposed method in two large-scale real applications.

We consider the problem of robust compressed sensing whose objective is to recover a high-dimensional sparse signal from compressed measurements corrupted by outliers. A new sparse Bayesian learning method is developed for robust compressed sensing. The basic idea of the proposed method is to identify and remove the outliers from sparse signal recovery. To automatically identify the outliers, we employ a set of binary indicator hyperparameters to indicate which observations are outliers. These indicator hyperparameters are treated as random variables and assigned a beta process prior such that their values are confined to be binary. In addition, a Gaussian-inverse Gamma prior is imposed on the sparse signal to promote sparsity. Based on this hierarchical prior model, we develop a variational Bayesian method to estimate the indicator hyperparameters as well as the sparse signal. Simulation results show that the proposed method achieves a substantial performance improvement over existing robust compressed sensing techniques.

Body-worn video (BWV) cameras are increasingly utilized by police departments to provide a record of police-public interactions. However, large-scale BWV deployment produces terabytes of data per week, necessitating the development of effective computational methods to identify salient changes in video. In work carried out at the 2016 RIPS program at IPAM, UCLA, we present a novel two-stage framework for video change-point detection. First, we employ state-of-the-art machine learning methods including convolutional neural networks and support vector machines for scene classification. We then develop and compare change-point detection algorithms utilizing mean squared-error minimization, forecasting methods, hidden Markov models, and maximum likelihood estimation to identify noteworthy changes. We test our framework on detection of vehicle exits and entrances in a BWV data set provided by the Los Angeles Police Department and achieve over 90% recall and nearly 70% precision -- demonstrating robustness to rapid scene changes, extreme luminance differences, and frequent camera occlusions.

During the last decades more and more textual data have become available, creating a growing need to statistically analyze large amounts of textual data. The hugely popular Latent Dirichlet Allocation (LDA) model introduced by Blei et al. (2003) is a generative probability model where each document is summarized by a set of latent semantic themes, often called topics; formally, a topic is a probability distribution over the vocabulary. An estimated LDA model is therefore a compressed latent representation of the documents. LDA is a mixed membership model where each document is a mixture of topics, where each word (token) in a document belongs to a single topic. The basic LDA model is unsupervised, i.e. the topics are learned solely from the words in the documents without access to document labels. In many situations there are also other information we would like to incorporate in modeling a corpus of documents. A common example is when we have labeled documents, such as ratings of movies together with a movie description, illness category in medical journals or the location of the identified bug together with bug reports. In these situation, one can use a so called supervised topic model to find the semantic structure in the documents that are related to the class of interest. One of the first approaches to supervised topic models was proposed by Mcauliffe and Blei (2008).

We develop a class of rules spanning the range between quadratic discriminant analysis and naive Bayes, through a path of sparse graphical models. A group lasso penalty is used to introduce shrinkage and encourage a similar pattern of sparsity across precision matrices. It gives sparse estimates of interactions and produces interpretable models. Inspired by the connected-components structure of the estimated precision matrices, we propose the community Bayes model, which partitions features into several conditional independent communities and splits the classification problem into separate smaller ones. The community Bayes idea is quite general and can be applied to non-Gaussian data and likelihood-based classifiers.

Probabilistic programming languages (PPLs) are a powerful modeling tool, able to represent any computable probability distribution. Unfortunately, probabilistic program inference is often intractable, and existing PPLs mostly rely on expensive, approximate sampling-based methods. To alleviate this problem, one could try to learn from past inferences, so that future inferences run faster. This strategy is known as amortized inference; it has recently been applied to Bayesian networks and deep generative models. This paper proposes a system for amortized inference in PPLs. In our system, amortization comes in the form of a parameterized guide program. Guide programs have similar structure to the original program, but can have richer data flow, including neural network components. These networks can be optimized so that the guide approximately samples from the posterior distribution defined by the original program. We present a flexible interface for defining guide programs and a stochastic gradient-based scheme for optimizing guide parameters, as well as some preliminary results on automatically deriving guide programs. We explore in detail the common machine learning pattern in which a 'local' model is specified by 'global' random values and used to generate independent observed data points; this gives rise to amortized local inference supporting global model learning.