Normalizing flows model a complex target distribution in terms of a bijective transform operating on a simple base distribution. As such, they enable tractable computation of a number of important statistical quantities, particularly likelihoods and samples. Despite these appealing properties, the computation of more complex inference tasks, such as the cumulative distribution function (CDF) over a complex region (e.g., a polytope) remains challenging. Traditional CDF approximations using Monte-Carlo techniques are unbiased but have unbounded variance and low sample efficiency. Instead, we build upon the diffeomorphic properties of normalizing flows and leverage the divergence theorem to estimate the CDF over a closed region in target space in terms of the flux across its \emph{boundary}, as induced by the normalizing flow. We describe both deterministic and stochastic instances of this estimator: while the deterministic variant iteratively improves the estimate by strategically subdividing the boundary, the stochastic variant provides unbiased estimates. Our experiments on popular flow architectures and UCI benchmark datasets show a marked improvement in sample efficiency as compared to traditional estimators.

Bayesian variable selection is a powerful tool for data analysis, as it offers a principled method for variable selection that accounts for prior information and uncertainty. However, wider adoption of Bayesian variable selection has been hampered by computational challenges, especially in difficult regimes with a large number of covariates P or non-conjugate likelihoods. To scale to the large P regime we introduce an efficient MCMC scheme whose cost per iteration is sublinear in P. In addition we show how this scheme can be extended to generalized linear models for count data, which are prevalent in biology, ecology, economics, and beyond. In particular we design efficient algorithms for variable selection in binomial and negative binomial regression, which includes logistic regression as a special case. In experiments we demonstrate the effectiveness of our methods, including on cancer and maize genomic data.

We consider the problem of detecting the presence of a signal in a rank-one spiked Wigner model. For general non-Gaussian noise, assuming that the signal is drawn from the Rademacher prior, we prove that the log likelihood ratio (LR) of the spiked model against the null model converges to a Gaussian when the signal-to-noise ratio is below a certain threshold. The threshold is optimal in the sense that the reliable detection is possible by a transformed principal component analysis (PCA) above it. From the mean and the variance of the limiting Gaussian for the log LR, we compute the limit of the sum of the Type-I error and the Type-II error of the likelihood ratio test. We also prove similar results for a rank-one spiked IID model where the noise is asymmetric but the signal is symmetric.

Particle filtering is a standard Monte-Carlo approach for a wide range of sequential inference tasks. The key component of a particle filter is a set of particles with importance weights that serve as a proxy of the true posterior distribution of some stochastic process. In this work, we propose continuous latent particle filters, an approach that extends particle filtering to the continuous-time domain. We demonstrate how continuous latent particle filters can be used as a generic plug-in replacement for inference techniques relying on a learned variational posterior. Our experiments with different model families based on latent neural stochastic differential equations demonstrate superior performance of continuous-time particle filtering in inference tasks like likelihood estimation and sequential prediction for a variety of stochastic processes.

In this paper, we use the concept of artificial risk fields to predict how human operators control a vehicle in response to upcoming road situations. A risk field assigns a non-negative risk measure to the state of the system in order to model how close that state is to violating a safety property, such as hitting an obstacle or exiting the road. Using risk fields, we construct a stochastic model of the operator that maps from states to likely actions. We demonstrate our approach on a driving task wherein human subjects are asked to drive a car inside a realistic driving simulator while avoiding obstacles placed on the road. We show that the most likely risk field given the driving data is obtained by solving a convex optimization problem. Next, we apply the inferred risk fields to generate distinct driving behaviors while comparing predicted trajectories against ground truth measurements. We observe that the risk fields are excellent at predicting future trajectory distributions with high prediction accuracy for up to twenty seconds prediction horizons. At the same time, we observe some challenges such as the inability to account for how drivers choose to accelerate/decelerate based on the road conditions.

This paper demonstrates our vision for knowledge graphs that assist machines to reason about the cause of signals observed by sensors. We show how the approach allows for constructing smarter surveillance systems that reason about the most likely cause (e.g., an attacker breaking a window) of a signal rather than acting directly on the received signal without consideration for how it was produced.

Prediction of individual's race and ethnicity plays an important role in social science and public health research. Examples include studies of racial disparity in health and voting. Recently, Bayesian Improved Surname Geocoding (BISG), which uses Bayes' rule to combine information from Census surname files with the geocoding of an individual's residence, has emerged as a leading methodology for this prediction task. Unfortunately, BISG suffers from two Census data problems that contribute to unsatisfactory predictive performance for minorities. First, the decennial Census often contains zero counts for minority racial groups in the Census blocks where some members of those groups reside. Second, because the Census surname files only include frequent names, many surnames -- especially those of minorities -- are missing from the list. To address the zero counts problem, we introduce a fully Bayesian Improved Surname Geocoding (fBISG) methodology that accounts for potential measurement error in Census counts by extending the naive Bayesian inference of the BISG methodology to full posterior inference. To address the missing surname problem, we supplement the Census surname data with additional data on last, first, and middle names taken from the voter files of six Southern states where self-reported race is available. Our empirical validation shows that the fBISG methodology and name supplements significantly improve the accuracy of race imputation across all racial groups, and especially for Asians. The proposed methodology, together with additional name data, is available via the open-source software WRU.

This paper introduces Probabilistic Deduction (PD) as an approach to probabilistic structured argumentation. A PD framework is composed of probabilistic rules (p-rules). As rules in classical structured argumentation frameworks, p-rules form deduction systems. In addition, p-rules also represent conditional probabilities that define joint probability distributions. With PD frameworks, one performs probabilistic reasoning by solving Rule-Probabilistic Satisfiability. At the same time, one can obtain an argumentative reading to the probabilistic reasoning with arguments and attacks. In this work, we introduce a probabilistic version of the Closed-World Assumption (P-CWA) and prove that our probabilistic approach coincides with the complete extension in classical argumentation under P-CWA and with maximum entropy reasoning. We present several approaches to compute the joint probability distribution from p-rules for achieving a practical proof theory for PD. PD provides a framework to unify probabilistic reasoning with argumentative reasoning. This is the first work in probabilistic structured argumentation where the joint distribution is not assumed form external sources.

Probabilistic programs provide an expressive representation language for generative models. Given a probabilistic program, we are interested in the task of posterior inference: estimating a latent variable given a set of observed variables. Existing techniques for inference in probabilistic programs often require choosing many hyper-parameters, are computationally expensive, and/or only work for restricted classes of programs. Here we formulate inference as masked language modeling: given a program, we generate a supervised dataset of variables and assignments, and randomly mask a subset of the assignments. We then train a neural network to unmask the random values, defining an approximate posterior distribution. By optimizing a single neural network across a range of programs we amortize the cost of training, yielding a "foundation" posterior able to do zero-shot inference for new programs. The foundation posterior can also be fine-tuned for a particular program and dataset by optimizing a variational inference objective. We show the efficacy of the approach, zero-shot and fine-tuned, on a benchmark of STAN programs.

Road accidents have become the eight leading cause of death all over the world. Lots of these accidents are due to a driver's inattention or lack of focus, due to fatigue. Various factors cause driver's fatigue. This paper considers all the measureable data that manifest driver's fatigue, namely those manifested in the vehicle measureable data while driving as well as the driver's physical and physiological data. Each of the three main factors are further subdivided into smaller details. For example, the vehicle's data is composed of the values obtained from the steering wheel's angle, yaw angle, the position on the lane, and the speed and acceleration of the vehicle while moving. Ontological knowledge and rules for driver fatigue detection are to be integrated into an intelligent system so that on the first sign of dangerous level of fatigue is detected, a warning notification is sent to the driver. This work is intended to contribute to safe road driving.