The task of drawing samples efficiently from high-dimensional complex probability distributions enables us to perform inference using complex statistical models from large amounts of data, where uncertainty quantification is of paramount importance to understand the intrinsic risk associated with every decision made with models learned from data. The ability to quantify uncertainty when comparing a theoretical or computational model to observations is critical to conducting a sound scientific investigation, particularly in machine-learned models and in the physical sciences like physics [92]. More specifically, Bayesian inference [96, 184] is a prominent method for linking models and observations and estimating uncertainties, in which sampling techniques are widely adopted, which also finds applications to various areas such as imaging processing and inverse problems (see e.g., [87]), and Bayesian neural networks and deep learning [134], etc. While Markov chain Monte Carlo (MCMC) methods [164] have been the major workhorse of such sampling tasks, most traditional MCMC algorithms were regarded as unscalable to high dimensions. In particular, in modern large-scale applications such as Bayesian deep learning in the overparameterized regime in which we want to make posterior inference on the neural network weights, traditional MCMC algorithms become computationally prohibitive in such high dimensions and alternative approaches such as variational inference (VI; see e.g., [21]) have been widely adopted.

Generative flow networks (GFlowNets) are amortized variational inference algorithms that are trained to sample from unnormalized target distributions over compositional objects. A key limitation of GFlowNets until this time has been that they are restricted to discrete spaces. We present a theory for generalized GFlowNets, which encompasses both existing discrete GFlowNets and ones with continuous or hybrid state spaces, and perform experiments with two goals in mind. First, we illustrate critical points of the theory and the importance of various assumptions. Second, we empirically demonstrate how observations about discrete GFlowNets transfer to the continuous case and show strong results compared to non-GFlowNet baselines on several previously studied tasks. This work greatly widens the perspectives for the application of GFlowNets in probabilistic inference and various modeling settings.

In high-dimensional Bayesian statistics, several methods have been developed, including many prior distributions that lead to the sparsity of estimated parameters. However, such priors have limitations in handling the spectral eigenvector structure of data, and as a result, they are ill-suited for analyzing over-parameterized models (high-dimensional linear models that do not assume sparsity) that have been developed in recent years. This paper introduces a Bayesian approach that uses a prior dependent on the eigenvectors of data covariance matrices, but does not induce the sparsity of parameters. We also provide contraction rates of derived posterior distributions and develop a truncated Gaussian approximation of the posterior distribution. The former demonstrates the efficiency of posterior estimation, while the latter enables quantification of parameter uncertainty using a Bernstein-von Mises-type approach. These results indicate that any Bayesian method that can handle the spectrum of data and estimate non-sparse high dimensions would be possible.

Laser-plasma physics has developed rapidly over the past few decades as high-power lasers have become both increasingly powerful and more widely available. Early experimental and numerical research in this field was restricted to single-shot experiments with limited parameter exploration. However, recent technological improvements make it possible to gather an increasing amount of data, both in experiments and simulations. This has sparked interest in using advanced techniques from mathematics, statistics and computer science to deal with, and benefit from, big data. At the same time, sophisticated modeling techniques also provide new ways for researchers to effectively deal with situations in which still only sparse amounts of data are available. This paper aims to present an overview of relevant machine learning methods with focus on applicability to laser-plasma physics, including its important sub-fields of laser-plasma acceleration and inertial confinement fusion.

Discovering causal relations from observational data is important. The existence of unobserved variables, such as latent confounders or mediators, can mislead the causal identification. To address this issue, proximal causal discovery methods proposed to adjust for the bias with the proxy of the unobserved variable. However, these methods presumed the data is discrete, which limits their real-world application. In this paper, we propose a proximal causal discovery method that can well handle the continuous variables. Our observation is that discretizing continuous variables can can lead to serious errors and comprise the power of the proxy. Therefore, to use proxy variables in the continuous case, the critical point is to control the discretization error. To this end, we identify mild regularity conditions on the conditional distributions, enabling us to control the discretization error to an infinitesimal level, as long as the proxy is discretized with sufficiently fine, finite bins. Based on this, we design a proxy-based hypothesis test for identifying causal relationships when unobserved variables are present. Our test is consistent, meaning it has ideal power when large samples are available. We demonstrate the effectiveness of our method using synthetic and real-world data.

Efficient traffic management is crucial for maintaining urban mobility, especially in densely populated areas where congestion, accidents, and delays can lead to frustrating and expensive commutes. However, existing prediction methods face challenges in terms of optimizing a single objective and understanding the complex composition of the transportation system. Moreover, they lack the ability to understand the macroscopic system and cannot efficiently utilize big data. In this paper, we propose a novel approach, Transportation Foundation Model (TFM), which integrates the principles of traffic simulation into traffic prediction. TFM uses graph structures and dynamic graph generation algorithms to capture the participatory behavior and interaction of transportation system actors. This data-driven and model-free simulation method addresses the challenges faced by traditional systems in terms of structural complexity and model accuracy and provides a foundation for solving complex transportation problems with real data. The proposed approach shows promising results in accurately predicting traffic outcomes in an urban transportation setting.

Agent-based modelling (ABMing) is a powerful and intuitive approach to modelling complex systems; however, the intractability of ABMs' likelihood functions and the non-differentiability of the mathematical operations comprising these models present a challenge to their use in the real world. These difficulties have in turn generated research on approximate Bayesian inference methods for ABMs and on constructing differentiable approximations to arbitrary ABMs, but little work has been directed towards designing approximate Bayesian inference techniques for the specific case of differentiable ABMs. In this work, we aim to address this gap and discuss how generalised variational inference procedures may be employed to provide misspecification-robust Bayesian parameter inferences for differentiable ABMs. We demonstrate with experiments on a differentiable ABM of the COVID-19 pandemic that our approach can result in accurate inferences, and discuss avenues for future work.

Flexible district heating grids form an important part of future, low-carbon energy systems. We examine probabilistic state estimation in such grids, i.e., we aim to estimate the posterior probability distribution over all grid state variables such as pressures, temperatures, and mass flows conditional on measurements of a subset of these states. Since the posterior state distribution does not belong to a standard class of probability distributions, we use Markov Chain Monte Carlo (MCMC) sampling in the space of network heat exchanges and evaluate the samples in the grid state space to estimate the posterior. Converting the heat exchange samples into grid states by solving the non-linear grid equations makes this approach computationally burdensome. However, we propose to speed it up by employing a deep neural network that is trained to approximate the solution of the exact but slow non-linear solver. This novel approach is shown to deliver highly accurate posterior distributions both for classic tree-shaped as well as meshed heating grids, at significantly reduced computational costs that are acceptable for online control. Our state estimation approach thus enables tightening the safety margins for temperature and pressure control and thereby a more efficient grid operation.

Recently, diffusion models have been successfully applied to improving adversarial robustness of image classifiers by purifying the adversarial noises or generating realistic data for adversarial training. However, the diffusion-based purification can be evaded by stronger adaptive attacks while adversarial training does not perform well under unseen threats, exhibiting inevitable limitations of these methods. To better harness the expressive power of diffusion models, in this paper we propose Robust Diffusion Classifier (RDC), a generative classifier that is constructed from a pre-trained diffusion model to be adversarially robust. Our method first maximizes the data likelihood of a given input and then predicts the class probabilities of the optimized input using the conditional likelihood of the diffusion model through Bayes' theorem. Since our method does not require training on particular adversarial attacks, we demonstrate that it is more generalizable to defend against multiple unseen threats. In particular, RDC achieves $73.24\%$ robust accuracy against $\ell_\infty$ norm-bounded perturbations with $\epsilon_\infty=8/255$ on CIFAR-10, surpassing the previous state-of-the-art adversarial training models by $+2.34\%$. The findings highlight the potential of generative classifiers by employing diffusion models for adversarial robustness compared with the commonly studied discriminative classifiers.

Fake currency, unauthorized imitation money lacking government approval, constitutes a form of fraud. Particularly in Afghanistan, the prevalence of fake currency poses significant challenges and detrimentally impacts the economy. While banks and commercial establishments employ authentication machines, the public lacks access to such systems, necessitating a program that can detect counterfeit banknotes accessible to all. This paper introduces a method using image processing to identify counterfeit Afghan banknotes by analyzing specific security features. Extracting first and second order statistical features from input images, the WEKA machine learning tool was employed to construct models and perform classification with Random Forest, PART, and Na\"ive Bayes algorithms. The Random Forest algorithm achieved exceptional accuracy of 99% in detecting fake Afghan banknotes, indicating the efficacy of the proposed method as a solution for identifying counterfeit currency.