Reconstructing astrophysical and cosmological fields from observations is challenging. It requires accounting for non-linear transformations, mixing of spatial structure, and noise. In contrast, forward simulators that map fields to observations are readily available for many applications. We present a versatile Bayesian field reconstruction algorithm rooted in simulation-based inference and enhanced by autoregressive modeling. The proposed technique is applicable to generic (non-differentiable) forward simulators and allows sampling from the posterior for the underlying field. We show first promising results on a proof-of-concept application: the recovery of cosmological initial conditions from late-time density fields.

Sentiment analysis (SA) is commonly applied to digital textual data, revealing insight into opinions and feelings. Many systematic reviews have summarized existing work, but often overlook discussions of validity and scientific practices. Here, we present an overview of reviews, synthesizing 38 systematic reviews, containing 2,275 primary studies. We devise a bespoke quality assessment framework designed to assess the rigor and quality of systematic review methodologies and reporting standards. Our findings show diverse applications and methods, limited reporting rigor, and challenges over time. We discuss how future research and practitioners can address these issues and highlight their importance across numerous applications.

While most machine learning models can provide confidence in their predictions, confidence is insufficient to understand a prediction's reliability. For instance, the model may have a low confidence prediction if the input is not well-represented in the training dataset or if the input is inherently ambiguous. In this work, we investigate the relationship between how atypical (rare) a sample or a class is and the reliability of a model's predictions. We first demonstrate that atypicality is strongly related to miscalibration and accuracy. In particular, we empirically show that predictions for atypical inputs or atypical classes are more overconfident and have lower accuracy. Using these insights, we show incorporating atypicality improves uncertainty quantification and model performance for discriminative neural networks and large language models. In a case study, we show that using atypicality improves the performance of a skin lesion classifier across different skin tone groups without having access to the group attributes. Overall, we propose that models should use not only confidence but also atypicality to improve uncertainty quantification and performance. Our results demonstrate that simple post-hoc atypicality estimators can provide significant value.

A single panel of a comic book can say a lot: it can depict not only where the characters currently are, but also their motions, their motivations, their emotions, and what they might do next. More generally, humans routinely infer complex sequences of past and future events from a *static snapshot* of a *dynamic scene*, even in situations they have never seen before. In this paper, we model how humans make such rapid and flexible inferences. Building on a long line of work in cognitive science, we offer a Monte Carlo algorithm whose inferences correlate well with human intuitions in a wide variety of domains, while only using a small, cognitively-plausible number of samples. Our key technical insight is a surprising connection between our inference problem and Monte Carlo path tracing, which allows us to apply decades of ideas from the computer graphics community to this seemingly-unrelated theory of mind task.

We introduce a two-stage probabilistic framework for statistical downscaling using unpaired data. Statistical downscaling seeks a probabilistic map to transform low-resolution data from a biased coarse-grained numerical scheme to high-resolution data that is consistent with a high-fidelity scheme. Our framework tackles the problem by composing two transformations: (i) a debiasing step via an optimal transport map, and (ii) an upsampling step achieved by a probabilistic diffusion model with a posteriori conditional sampling. This approach characterizes a conditional distribution without needing paired data, and faithfully recovers relevant physical statistics from biased samples. We demonstrate the utility of the proposed approach on one- and two-dimensional fluid flow problems, which are representative of the core difficulties present in numerical simulations of weather and climate. Our method produces realistic high-resolution outputs from low-resolution inputs, by upsampling resolutions of 8x and 16x. Moreover, our procedure correctly matches the statistics of physical quantities, even when the low-frequency content of the inputs and outputs do not match, a crucial but difficult-to-satisfy assumption needed by current state-of-the-art alternatives. Code for this work is available at: https://github.com/google-research/swirl-dynamics/tree/main/swirl_dynamics/projects/probabilistic_diffusion.

Actor-critic (AC) methods are widely used in reinforcement learning (RL) and benefit from the flexibility of using any policy gradient method as the actor and value-based method as the critic. The critic is usually trained by minimizing the TD error, an objective that is potentially decorrelated with the true goal of achieving a high reward with the actor. We address this mismatch by designing a joint objective for training the actor and critic in a decision-aware fashion. We use the proposed objective to design a generic, AC algorithm that can easily handle any function approximation. We explicitly characterize the conditions under which the resulting algorithm guarantees monotonic policy improvement, regardless of the choice of the policy and critic parameterization. Instantiating the generic algorithm results in an actor that involves maximizing a sequence of surrogate functions (similar to TRPO, PPO) and a critic that involves minimizing a closely connected objective. Using simple bandit examples, we provably establish the benefit of the proposed critic objective over the standard squared error. Finally, we empirically demonstrate the benefit of our decision-aware actor-critic framework on simple RL problems.

Neural networks are emerging as a tool for scalable data-driven simulation of high-dimensional dynamical systems, especially in settings where numerical methods are infeasible or computationally expensive. Notably, it has been shown that incorporating domain symmetries in deterministic neural simulators can substantially improve their accuracy, sample efficiency, and parameter efficiency. However, to incorporate symmetries in probabilistic neural simulators that can simulate stochastic phenomena, we need a model that produces equivariant distributions over trajectories, rather than equivariant function approximations. In this paper, we propose Equivariant Probabilistic Neural Simulation (EPNS), a framework for autoregressive probabilistic modeling of equivariant distributions over system evolutions. We use EPNS to design models for a stochastic n-body system and stochastic cellular dynamics. Our results show that EPNS considerably outperforms existing neural network-based methods for probabilistic simulation. More specifically, we demonstrate that incorporating equivariance in EPNS improves simulation quality, data efficiency, rollout stability, and uncertainty quantification. We conclude that EPNS is a promising method for efficient and effective data-driven probabilistic simulation in a diverse range of domains.

Learning causal structures from interventional data is a fundamental problem with broad applications across various fields. While many previous works have focused on recovering the entire causal graph, in practice, there are scenarios where learning only part of the causal graph suffices. This is called $targeted$ causal discovery. In our work, we focus on two such well-motivated problems: subset search and causal matching. We aim to minimize the number of interventions in both cases. Towards this, we introduce the $Meek~separator$, which is a subset of vertices that, when intervened, decomposes the remaining unoriented edges into smaller connected components. We then present an efficient algorithm to find Meek separators that are of small sizes. Such a procedure is helpful in designing various divide-and-conquer-based approaches. In particular, we propose two randomized algorithms that achieve logarithmic approximation for subset search and causal matching, respectively. Our results provide the first known average-case provable guarantees for both problems. We believe that this opens up possibilities to design near-optimal methods for many other targeted causal structure learning problems arising from various applications.

This paper investigates posterior sampling algorithms for competitive reinforcement learning (RL) in the context of general function approximations. Focusing on zero-sum Markov games (MGs) under two critical settings, namely self-play and adversarial learning, we first propose the self-play and adversarial generalized eluder coefficient (GEC) as complexity measures for function approximation, capturing the exploration-exploitation trade-off in MGs. Based on self-play GEC, we propose a model-based self-play posterior sampling method to control both players to learn Nash equilibrium, which can successfully handle the partial observability of states. Furthermore, we identify a set of partially observable MG models fitting MG learning with the adversarial policies of the opponent. Incorporating the adversarial GEC, we propose a model-based posterior sampling method for learning adversarial MG with potential partial observability. We further provide low regret bounds for proposed algorithms that can scale sublinearly with the proposed GEC and the number of episodes $T$. To the best of our knowledge, we for the first time develop generic model-based posterior sampling algorithms for competitive RL that can be applied to a majority of tractable zero-sum MG classes in both fully observable and partially observable MGs with self-play and adversarial learning.

Support vector machine (SVM) is one of the most studied paradigms in the realm of machine learning for classification and regression problems. It relies on vectorized input data. However, a significant portion of the real-world data exists in matrix format, which is given as input to SVM by reshaping the matrices into vectors. The process of reshaping disrupts the spatial correlations inherent in the matrix data. Also, converting matrices into vectors results in input data with a high dimensionality, which introduces significant computational complexity. To overcome these issues in classifying matrix input data, support matrix machine (SMM) is proposed. It represents one of the emerging methodologies tailored for handling matrix input data. The SMM method preserves the structural information of the matrix data by using the spectral elastic net property which is a combination of the nuclear norm and Frobenius norm. This article provides the first in-depth analysis of the development of the SMM model, which can be used as a thorough summary by both novices and experts. We discuss numerous SMM variants, such as robust, sparse, class imbalance, and multi-class classification models. We also analyze the applications of the SMM model and conclude the article by outlining potential future research avenues and possibilities that may motivate academics to advance the SMM algorithm.