We present an exact Bayesian inference method for discrete statistical models, which can find exact solutions to a large class of discrete inference problems, even with infinite support and continuous priors. To express such models, we introduce a probabilistic programming language that supports discrete and continuous sampling, discrete observations, affine functions, (stochastic) branching, and conditioning on discrete events. Our key tool is probability generating functions: they provide a compact closed-form representation of distributions that are definable by programs, thus enabling the exact computation of posterior probabilities, expectation, variance, and higher moments. Our inference method is provably correct and fully automated in a tool called Genfer, which uses automatic differentiation (specifically, Taylor polynomials), but does not require computer algebra. Our experiments show that Genfer is often faster than the existing exact inference tools PSI, Dice, and Prodigy. On a range of real-world inference problems that none of these exact tools can solve, Genfer's performance is competitive with approximate Monte Carlo methods, while avoiding approximation errors.

Evaluating and optimizing policies in the presence of unobserved confounders is a problem of growing interest in offline reinforcement learning. Using conventional methods for offline RL in the presence of confounding can not only lead to poor decisions and poor policies, but also have disastrous effects in critical applications such as healthcare and education. We map out the landscape of offline policy evaluation for confounded MDPs, distinguishing assumptions on confounding based on whether they are memoryless and on their effect on the data-collection policies. We characterize settings where consistent value estimates are provably not achievable, and provide algorithms with guarantees to instead estimate lower bounds on the value. When consistent estimates are achievable, we provide algorithms for value estimation with sample complexity guarantees. We also present new algorithms for offline policy improvement and prove local convergence guarantees. Finally, we experimentally evaluate our algorithms on both a gridworld environment and a simulated healthcare setting of managing sepsis patients. In gridworld, our model-based method provides tighter lower bounds than existing methods, while in the sepsis simulator, our methods significantly outperform confounder-oblivious benchmarks.

Conditional Neural Processes (CNPs) are a class of metalearning models popular for combining the runtime efficiency of amortized inference with reliable uncertainty quantification. Many relevant machine learning tasks, such as in spatio-temporal modeling, Bayesian Optimization and continuous control, inherently contain equivariances -- for example to translation -- which the model can exploit for maximal performance. However, prior attempts to include equivariances in CNPs do not scale effectively beyond two input dimensions. In this work, we propose Relational Conditional Neural Processes (RCNPs), an effective approach to incorporate equivariances into any neural process model. Our proposed method extends the applicability and impact of equivariant neural processes to higher dimensions. We empirically demonstrate the competitive performance of RCNPs on a large array of tasks naturally containing equivariances.

Humans and animals exhibit a range of interesting behaviors in dynamic environments, and it is unclear how our brains actively reformat this dense sensory information to enable these behaviors. Experimental neuroscience is undergoing a revolution in its ability to record and manipulate hundreds to thousands of neurons while an animal is performing a complex behavior. As these paradigms enable unprecedented access to the brain, a natural question that arises is how to distill these data into interpretable insights about how neural circuits give rise to intelligent behaviors. The classical approach in systems neuroscience has been to ascribe well-defined operations to individual neurons and provide a description of how these operations combine to produce a circuit-level theory of neural computations. While this approach has had some success for small-scale recordings with simple stimuli, designed to probe a particular circuit computation, often times these ultimately lead to disparate descriptions of the same system across stimuli. Perhaps more strikingly, many response profiles of neurons are difficult to succinctly describe in words, suggesting that new approaches are needed in light of these experimental observations. In this thesis, we offer a different definition of interpretability that we show has promise in yielding unified structural and functional models of neural circuits, and describes the evolutionary constraints that give rise to the response properties of the neural population, including those that have previously been difficult to describe individually. We demonstrate the utility of this framework across multiple brain areas and species to study the roles of recurrent processing in the primate ventral visual pathway; mouse visual processing; heterogeneity in rodent medial entorhinal cortex; and facilitating biological learning.

Reconstructing a continuous surface from an unoritented 3D point cloud is a fundamental task in 3D shape processing. In recent years, several methods have been proposed to address this problem using implicit neural representations (INRs). In this study, we propose a method to optimize INRs using energy-based models (EBMs). By employing the absolute value of the coordinate-based neural networks as the energy function, the INR can be optimized through the estimation of the point cloud distribution by the EBM. In addition, appropriate parameter settings of the EBM enable the model to consider the magnitude of point cloud noise. Our experiments confirmed that the proposed method is more robust against point cloud noise than conventional surface reconstruction methods.

We propose a straightforward solution for detecting scarce topics in unbalanced short-text datasets. Our approach, named CWUTM (Topic model based on co-occurrence word networks for unbalanced short text datasets), Our approach addresses the challenge of sparse and unbalanced short text topics by mitigating the effects of incidental word co-occurrence. This allows our model to prioritize the identification of scarce topics (Low-frequency topics). Unlike previous methods, CWUTM leverages co-occurrence word networks to capture the topic distribution of each word, and we enhanced the sensitivity in identifying scarce topics by redefining the calculation of node activity and normalizing the representation of both scarce and abundant topics to some extent. Moreover, CWUTM adopts Gibbs sampling, similar to LDA, making it easily adaptable to various application scenarios. Our extensive experimental validation on unbalanced short-text datasets demonstrates the superiority of CWUTM compared to baseline approaches in discovering scarce topics. According to the experimental results the proposed model is effective in early and accurate detection of emerging topics or unexpected events on social platforms.

We approach the fundamental problem of obstacle avoidance for robotic systems via the lens of online learning. In contrast to prior work that either assumes worst-case realizations of uncertainty in the environment or a stationary stochastic model of uncertainty, we propose a method that is efficient to implement and provably grants instance-optimality with respect to perturbations of trajectories generated from an open-loop planner (in the sense of minimizing worst-case regret). The resulting policy adapts online to realizations of uncertainty and provably compares well with the best obstacle avoidance policy in hindsight from a rich class of policies. The method is validated in simulation on a dynamical system environment and compared to baseline open-loop planning and robust Hamilton- Jacobi reachability techniques. Further, it is implemented on a hardware example where a quadruped robot traverses a dense obstacle field and encounters input disturbances due to time delays, model uncertainty, and dynamics nonlinearities.

Electrical load forecasting plays a crucial role in decision-making for power systems, including unit commitment and economic dispatch. The integration of renewable energy sources and the occurrence of external events, such as the COVID-19 pandemic, have rapidly increased uncertainties in load forecasting. The uncertainties in load forecasting can be divided into two types: epistemic uncertainty and aleatoric uncertainty. Separating these types of uncertainties can help decision-makers better understand where and to what extent the uncertainty is, thereby enhancing their confidence in the following decision-making. This paper proposes a diffusion-based Seq2Seq structure to estimate epistemic uncertainty and employs the robust additive Cauchy distribution to estimate aleatoric uncertainty. Our method not only ensures the accuracy of load forecasting but also demonstrates the ability to separate the two types of uncertainties and be applicable to different levels of loads. The relevant code can be found at \url{https://anonymous.4open.science/r/DiffLoad-4714/}.

Test log-likelihood, also known as predictive log-likelihood or test log-predictive, is computed as the log-predictive density averaged over a set of held-out data. It is often used to compare different models of the same data or to compare different algorithms used to fit the same probabilistic model. Although there are compelling reasons for this practice (Section 2.1), we provide examples that falsify the following, usually implicit, claims: Claim: The higher the test log-likelihood, the more accurately an approximate inference algorithm recovers the Bayesian posterior distribution of latent model parameters (Section 3). Claim: The higher the test log-likelihood, the better the predictive performance on held-out data according to other measurements, like root mean squared error (Section 4). Our examples demonstrate that test log-likelihood is not always a good proxy for posterior approximation error. They further demonstrate that forecast evaluations based on test log-likelihood may not agree with forecast evaluations based on root mean squared error. We are not the first to highlight discrepancies between test log-likelihood and other analysis objectives. For instance, Quiñonero-Candela et al. (2005) and Kohonen and Suomela (2005) showed that when predicting discrete data with continuous distributions, test log-likelihood can be made arbitrarily large by concentrating probability into vanishingly small intervals. Chang et al. (2009) observed

Defining and measuring trust in dynamic, multiagent teams is important in a range of contexts, particularly in defense and security domains. Team members should be trusted to work towards agreed goals and in accordance with shared values. In this paper, our concern is with the definition of goals and values such that it is possible to define 'trust' in a way that is interpretable, and hence usable, by both humans and robots. We argue that the outcome of team activity can be considered in terms of 'goal', 'individual/team values', and 'legal principles'. We question whether alignment is possible at the level of 'individual/team values', or only at the 'goal' and 'legal principles' levels. We argue for a set of metrics to define trust in human-robot teams that are interpretable by human or robot team members, and consider an experiment that could demonstrate the notion of 'satisficing trust' over the course of a simulated mission.