Annealed Importance Sampling (AIS) synthesizes weighted samples from an intractable distribution given its unnormalized density function. This algorithm relies on a sequence of interpolating distributions bridging the target to an initial tractable distribution such as the well-known geometric mean path of unnormalized distributions which is assumed to be suboptimal in general. In this paper, we prove that the geometric annealing corresponds to the distribution path that minimizes the KL divergence between the current particle distribution and the desired target when the feasible change in the particle distribution is constrained. Following this observation, we derive the constant rate discretization schedule for this annealing sequence, which adjusts the schedule to the difficulty of moving samples between the initial and the target distributions. We further extend our results to $f$-divergences and present the respective dynamics of annealing sequences based on which we propose the Constant Rate AIS (CR-AIS) algorithm and its efficient implementation for $\alpha$-divergences. We empirically show that CR-AIS performs well on multiple benchmark distributions while avoiding the computationally expensive tuning loop in existing Adaptive AIS.

In this paper, we propose an innovative solution by constructing infinite tree-structured PGMs that correspond exactly to neural networks. Our research reveals that DNNs, during forward propagation, indeed perform approximations of PGM inference that are precise in this alternative PGM structure. Not only does our research complement existing studies that describe neural networks as kernel machines or infinite-sized Gaussian processes, it also elucidates a more direct approximation that DNNs make to exact inference in PGMs. Potential benefits include improved pedagogy and interpretation of DNNs, and algorithms that can merge the strengths of PGMs and DNNs.

Tackling the most pressing problems for humanity, such as the climate crisis and the threat of global pandemics, requires accelerating the pace of scientific discovery. While science has traditionally relied on trial and error and even serendipity to a large extent, the last few decades have seen a surge of data-driven scientific discoveries. However, in order to truly leverage large-scale data sets and high-throughput experimental setups, machine learning methods will need to be further improved and better integrated in the scientific discovery pipeline. A key challenge for current machine learning methods in this context is the efficient exploration of very large search spaces, which requires techniques for estimating reducible (epistemic) uncertainty and generating sets of diverse and informative experiments to perform. This motivated a new probabilistic machine learning framework called GFlowNets, which can be applied in the modeling, hypotheses generation and experimental design stages of the experimental science loop. GFlowNets learn to sample from a distribution given indirectly by a reward function corresponding to an unnormalized probability, which enables sampling diverse, high-reward candidates. GFlowNets can also be used to form efficient and amortized Bayesian posterior estimators for causal models conditioned on the already acquired experimental data. Having such posterior models can then provide estimators of epistemic uncertainty and information gain that can drive an experimental design policy. Altogether, here we will argue that GFlowNets can become a valuable tool for AI-driven scientific discovery, especially in scenarios of very large candidate spaces where we have access to cheap but inaccurate measurements or to expensive but accurate measurements. This is a common setting in the context of drug and material discovery, which we use as examples throughout the paper.

Pre-trained diffusion models have been successfully used as priors in a variety of linear inverse problems, where the goal is to reconstruct a signal from noisy linear measurements. However, existing approaches require knowledge of the linear operator. In this paper, we propose GibbsDDRM, an extension of Denoising Diffusion Restoration Models (DDRM) to a blind setting in which the linear measurement operator is unknown. GibbsDDRM constructs a joint distribution of the data, measurements, and linear operator by using a pre-trained diffusion model for the data prior, and it solves the problem by posterior sampling with an efficient variant of a Gibbs sampler. The proposed method is problem-agnostic, meaning that a pre-trained diffusion model can be applied to various inverse problems without fine-tuning. In experiments, it achieved high performance on both blind image deblurring and vocal dereverberation tasks, despite the use of simple generic priors for the underlying linear operators.

Passive monitoring of acoustic or radio sources has important applications in modern convenience, public safety, and surveillance. A key task in passive monitoring is multiobject tracking (MOT). This paper presents a Bayesian method for multisensor MOT for challenging tracking problems where the object states are high-dimensional, and the measurements follow a nonlinear model. Our method is developed in the framework of factor graphs and the sum-product algorithm (SPA) and implemented using random samples or "particles". The multimodal probability density functions (pdfs) provided by the SPA are effectively represented by a Gaussian mixture model (GMM). To perform the operations of the SPA in high-dimensional spaces, we make use of Particle flow (PFL). Here, particles are migrated towards regions of high likelihood based on the solution of a partial differential equation. This makes it possible to obtain good object detection and tracking performance even in challenging multisensor MOT scenarios with single sensor measurements that have a lower dimension than the object positions. We perform a numerical evaluation in a passive acoustic monitoring scenario where multiple sources are tracked in 3-D from 1-D time-difference-of-arrival (TDOA) measurements provided by pairs of hydrophones. Our numerical results demonstrate favorable detection and estimation accuracy compared to state-of-the-art reference techniques.

Scientists have developed hundreds of techniques to measure the interactions between pairs of processes in complex systems. But these computational methods, from correlation coefficients to causal inference, rely on distinct quantitative theories that remain largely disconnected. Here we introduce a library of 237 statistics of pairwise interactions and assess their behavior on 1053 multivariate time series from a wide range of real-world and model-generated systems. Our analysis highlights new commonalities between different mathematical formulations, providing a unified picture of a rich interdisciplinary literature. Using three real-world case studies, we then show that simultaneously leveraging diverse methods from across science can uncover those most suitable for addressing a given problem, yielding interpretable understanding of the conceptual formulations of pairwise dependence that drive successful performance. Our framework is provided in extendable open software, enabling comprehensive data-driven analysis by integrating decades of methodological advances.

Artificial Intelligence and Machine learning have been widely used in various fields of mathematical computing, physical modeling, computational science, communication science, and stochastic analysis. Approaches based on Deep Artificial Neural Networks (DANN) are very popular in our days. Depending on the learning task, the exact form of DANNs is determined via their multi-layer architecture, activation functions and the so-called loss function. However, for a majority of deep learning approaches based on DANNs, the kernel structure of neural signal processing remains the same, where the node response is encoded as a linear superposition of neural activity, while the non-linearity is triggered by the activation functions. In the current paper, we suggest to analyze the neural signal processing in DANNs from the point of view of homogeneous chaos theory as known from polynomial chaos expansion (PCE). From the PCE perspective, the (linear) response on each node of a DANN could be seen as a $1^{st}$ degree multi-variate polynomial of single neurons from the previous layer, i.e. linear weighted sum of monomials. From this point of view, the conventional DANN structure relies implicitly (but erroneously) on a Gaussian distribution of neural signals. Additionally, this view revels that by design DANNs do not necessarily fulfill any orthogonality or orthonormality condition for a majority of data-driven applications. Therefore, the prevailing handling of neural signals in DANNs could lead to redundant representation as any neural signal could contain some partial information from other neural signals. To tackle that challenge, we suggest to employ the data-driven generalization of PCE theory known as arbitrary polynomial chaos (aPC) to construct a corresponding multi-variate orthonormal representations on each node of a DANN to obtain Deep arbitrary polynomial chaos neural networks.

Machine learning methods for the construction of data-driven reduced order model models are used in an increasing variety of engineering domains, especially as a supplement to expensive computational fluid dynamics for design problems. An important check on the reliability of surrogate models is Uncertainty Quantification (UQ), a self assessed estimate of the model error. Accurate UQ allows for cost savings by reducing both the required size of training data sets and the required safety factors, while poor UQ prevents users from confidently relying on model predictions. We examine several machine learning techniques, including both Gaussian processes and a family UQ-augmented neural networks: Ensemble neural networks (ENN), Bayesian neural networks (BNN), Dropout neural networks (D-NN), and Gaussian neural networks (G-NN). We evaluate UQ accuracy (distinct from model accuracy) using two metrics: the distribution of normalized residuals on validation data, and the distribution of estimated uncertainties. We apply these metrics to two model data sets, representative of complex dynamical systems: an ocean engineering problem in which a ship traverses irregular wave episodes, and a dispersive wave turbulence system with extreme events, the Majda-McLaughlin-Tabak model.

Large transformer models trained on diverse datasets have shown a remarkable ability to learn in-context, achieving high few-shot performance on tasks they were not explicitly trained to solve. In this paper, we study the in-context learning capabilities of transformers in decision-making problems, i.e., reinforcement learning (RL) for bandits and Markov decision processes. To do so, we introduce and study Decision-Pretrained Transformer (DPT), a supervised pretraining method where the transformer predicts an optimal action given a query state and an in-context dataset of interactions, across a diverse set of tasks. This procedure, while simple, produces a model with several surprising capabilities. We find that the pretrained transformer can be used to solve a range of RL problems in-context, exhibiting both exploration online and conservatism offline, despite not being explicitly trained to do so. The model also generalizes beyond the pretraining distribution to new tasks and automatically adapts its decision-making strategies to unknown structure. Theoretically, we show DPT can be viewed as an efficient implementation of Bayesian posterior sampling, a provably sample-efficient RL algorithm. We further leverage this connection to provide guarantees on the regret of the in-context algorithm yielded by DPT, and prove that it can learn faster than algorithms used to generate the pretraining data. These results suggest a promising yet simple path towards instilling strong in-context decision-making abilities in transformers.

Avatars, as promising digital assistants in Vehicular Metaverses, can enable drivers and passengers to immerse in 3D virtual spaces, serving as a practical emerging example of Artificial Intelligence of Things (AIoT) in intelligent vehicular environments. The immersive experience is achieved through seamless human-avatar interaction, e.g., augmented reality navigation, which requires intensive resources that are inefficient and impractical to process on intelligent vehicles locally. Fortunately, offloading avatar tasks to RoadSide Units (RSUs) or cloud servers for remote execution can effectively reduce resource consumption. However, the high mobility of vehicles, the dynamic workload of RSUs, and the heterogeneity of RSUs pose novel challenges to making avatar migration decisions. To address these challenges, in this paper, we propose a dynamic migration framework for avatar tasks based on real-time trajectory prediction and Multi-Agent Deep Reinforcement Learning (MADRL). Specifically, we propose a model to predict the future trajectories of intelligent vehicles based on their historical data, indicating the future workloads of RSUs.Based on the expected workloads of RSUs, we formulate the avatar task migration problem as a long-term mixed integer programming problem. To tackle this problem efficiently, the problem is transformed into a Partially Observable Markov Decision Process (POMDP) and solved by multiple DRL agents with hybrid continuous and discrete actions in decentralized. Numerical results demonstrate that our proposed algorithm can effectively reduce the latency of executing avatar tasks by around 25% without prediction and 30% with prediction and enhance user immersive experiences in the AIoT-enabled Vehicular Metaverse (AeVeM).