Choices made by individuals have widespread impacts--for instance, people choose between political candidates to vote for, between social media posts to share, and between brands to purchase--moreover, data on these choices are increasingly abundant. Discrete choice models are a key tool for learning individual preferences from such data. Additionally, social factors like conformity and contagion influence individual choice. Traditional methods for incorporating these factors into choice models do not account for the entire social network and require hand-crafted features. To overcome these limitations, we use graph learning to study choice in networked contexts. We identify three ways in which graph learning techniques can be used for discrete choice: learning chooser representations, regularizing choice model parameters, and directly constructing predictions from a network. We design methods in each category and test them on real-world choice datasets, including county-level 2016 US election results and Android app installation and usage data. We show that incorporating social network structure can improve the predictions of the standard econometric choice model, the multinomial logit. We provide evidence that app installations are influenced by social context, but we find no such effect on app usage among the same participants, which instead is habit-driven. In the election data, we highlight the additional insights a discrete choice framework provides over classification or regression, the typical approaches. On synthetic data, we demonstrate the sample complexity benefit of using social information in choice models.

Bayesian filtering approximates the true underlying behavior of a time-varying system by inverting an explicit generative model to convert noisy measurements into state estimates. This process typically requires either storage, inversion, and multiplication of large matrices or Monte Carlo estimation, neither of which are practical in high-dimensional state spaces such as the weight spaces of artificial neural networks. Instead of maintaining matrices for the filtering equations or simulating particles, we specify an optimizer that defines the Bayesian filter implicitly. In the linear-Gaussian setting, we show that every Kalman filter has an equivalent formulation using K steps of gradient descent. In the nonlinear setting, our experiments demonstrate that our framework results in filters that are effective, robust, and scalable to high-dimensional systems, comparing well against the standard toolbox of Bayesian filtering solutions. We suggest that it is easier to fine-tune an optimizer than it is to specify the correct filtering equations, making our framework an attractive option for high-dimensional filtering problems. Time-varying systems are ubiquitous in science, engineering, and machine learning. Consider a multielectrode array receiving raw voltage signals from thousands of neurons during a visual perception task. The goal is to infer some underlying neural state that is not directly observable, such that we can draw connections between neural activity and visual perception, but raw voltage signals are a sparse representation of neural activity that is shrouded in noise. To confound the problem further, the underlying neural state changes throughout time in both expected and unexpected ways. This problem, and most time-varying prediction problems, can be formalized as a probablistic state space model where latent variables evolve over time and emit observations (Simon, 2006). One solution to such a problem is to apply a Bayesian filter, a type of probabilistic model that can infer the values of latent variables from observations.

We introduce a new amortized likelihood ratio estimator for likelihood-free simulation-based inference (SBI). Our estimator is simple to train and estimates the likelihood ratio using a single forward pass of the neural estimator. Our approach directly computes the likelihood ratio between two competing parameter sets which is different from the previous approach of comparing two neural network output values. We refer to our model as the direct neural ratio estimator (DNRE). As part of introducing the DNRE, we derive a corresponding Monte Carlo estimate of the posterior. We benchmark our new ratio estimator and compare to previous ratio estimators in the literature. We show that our new ratio estimator often outperforms these previous approaches. As a further contribution, we introduce a new derivative estimator for likelihood ratio estimators that enables us to compare likelihood-free Hamiltonian Monte Carlo (HMC) with random-walk Metropolis-Hastings (MH). We show that HMC is equally competitive, which has not been previously shown. Finally, we include a novel real-world application of SBI by using our neural ratio estimator to design a quadcopter. Code is available at https://github.com/SRI-CSL/dnre.

In this paper, we propose a deep generative time series approach using latent temporal processes for modeling and holistically analyzing complex disease trajectories. We aim to find meaningful temporal latent representations of an underlying generative process that explain the observed disease trajectories in an interpretable and comprehensive way. To enhance the interpretability of these latent temporal processes, we develop a semi-supervised approach for disentangling the latent space using established medical concepts. By combining the generative approach with medical knowledge, we leverage the ability to discover novel aspects of the disease while integrating medical concepts into the model. We show that the learned temporal latent processes can be utilized for further data analysis and clinical hypothesis testing, including finding similar patients and clustering the disease into new sub-types. Moreover, our method enables personalized online monitoring and prediction of multivariate time series including uncertainty quantification. We demonstrate the effectiveness of our approach in modeling systemic sclerosis, showcasing the potential of our machine learning model to capture complex disease trajectories and acquire new medical knowledge.

We present a systematic study of conditional triangular transport maps in function spaces from the perspective of optimal transportation and with a view towards amortized Bayesian inference. More specifically, we develop a theory of constrained optimal transport problems that describe block-triangular Monge maps that characterize conditional measures along with their Kantorovich relaxations. This generalizes the theory of optimal triangular transport to separable infinite-dimensional function spaces with general cost functions. We further tailor our results to the case of Bayesian inference problems and obtain regularity estimates on the conditioning maps from the prior to the posterior. Finally, we present numerical experiments that demonstrate the computational applicability of our theoretical results for amortized and likelihood-free inference of functional parameters.

This article expands the framework of Bayesian inference and provides direct probabilistic methods for approaching inference tasks that are typically handled with information theory. We treat Bayesian probability updating as a random process and uncover intrinsic quantitative features of joint probability distributions called inferential moments. Inferential moments quantify shape information about how a prior distribution is expected to update in response to yet to be obtained information. Further, we quantify the unique probability distribution whose statistical moments are the inferential moments in question. We find a power series expansion of the mutual information in terms of inferential moments, which implies a connection between inferential theoretic logic and elements of information theory. Of particular interest is the inferential deviation, which is the expected variation of the probability of one variable in response to an inferential update of another. We explore two applications that analyze the inferential deviations of a Bayesian network to improve decision-making. We implement simple greedy algorithms for exploring sensor tasking using inferential deviations that generally outperform similar greedy mutual information algorithms in terms of root mean squared error between epistemic probability estimates and the ground truth probabilities they are estimating.

The goal of combining the robustness of neural networks and the expressiveness of symbolic methods has rekindled the interest in Neuro-Symbolic AI. Deep Probabilistic Programming Languages (DPPLs) have been developed for probabilistic logic programming to be carried out via the probability estimations of deep neural networks (DNNs). However, recent SOTA DPPL approaches allow only for limited conditional probabilistic queries and do not offer the power of true joint probability estimation. In our work, we propose an easy integration of tractable probabilistic inference within a DPPL. To this end, we introduce SLASH, a novel DPPL that consists of Neural-Probabilistic Predicates (NPPs) and a logic program, united via answer set programming (ASP). NPPs are a novel design principle allowing for combining all deep model types and combinations thereof to be represented as a single probabilistic predicate. In this context, we introduce a novel +/− notation for answering various types of probabilistic queries by adjusting the atom notations of a predicate. To scale well, we show how to prune the stochastically insignificant parts of the (ground) program, speeding up reasoning without sacrificing the predictive performance. We evaluate SLASH on various tasks, including the benchmark task of MNIST addition and Visual Question Answering (VQA).

Natural disasters such as hurricanes are increasing and causing widespread devastation. People's decisions and actions regarding whether to evacuate or not are critical and have a large impact on emergency planning and response. Our interest lies in computationally modeling complex relationships among various factors influencing evacuation decisions. We conducted a study on the evacuation of Hurricane Irma of the 2017 Atlantic hurricane season. The study was guided by the Protection motivation theory (PMT), a widely-used framework to understand people's responses to potential threats. Graphical models were constructed to represent the complex relationships among the factors involved and the evacuation decision. We evaluated different graphical structures based on conditional independence tests using Irma data. The final model largely aligns with PMT. It shows that both risk perception (threat appraisal) and difficulties in evacuation (coping appraisal) influence evacuation decisions directly and independently. Certain information received from media was found to influence risk perception, and through it influence evacuation behaviors indirectly. In addition, several variables were found to influence both risk perception and evacuation behaviors directly, including family and friends' suggestions, neighbors' evacuation behaviors, and evacuation notices from officials.

Machine learning-aided clinical decision support has the potential to significantly improve patient care. However, existing efforts in this domain for principled quantification of uncertainty have largely been limited to applications of ad-hoc solutions that do not consistently improve reliability. In this work, we consider stochastic neural networks and design a tailor-made multimodal data-driven (M2D2) prior distribution over network parameters. We use simple and scalable Gaussian mean-field variational inference to train a Bayesian neural network using the M2D2 prior. We train and evaluate the proposed approach using clinical time-series data in MIMIC-IV and corresponding chest X-ray images in MIMIC-CXR for the classification of acute care conditions. Our empirical results show that the proposed method produces a more reliable predictive model compared to deterministic and Bayesian neural network baselines.

This paper concerns structure learning or discovery of discrete generative models. It focuses on Bayesian model selection and the assimilation of training data or content, with a special emphasis on the order in which data are ingested. A key move - in the ensuing schemes - is to place priors on the selection of models, based upon expected free energy. In this setting, expected free energy reduces to a constrained mutual information, where the constraints inherit from priors over outcomes (i.e., preferred outcomes). The resulting scheme is first used to perform image classification on the MNIST dataset to illustrate the basic idea, and then tested on a more challenging problem of discovering models with dynamics, using a simple sprite-based visual disentanglement paradigm and the Tower of Hanoi (cf., blocks world) problem. In these examples, generative models are constructed autodidactically to recover (i.e., disentangle) the factorial structure of latent states - and their characteristic paths or dynamics.