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.

Dimensionality reduction (DR) algorithms compress high-dimensional data into a lower dimensional representation while preserving important features of the data. DR is a critical step in many analysis pipelines as it enables visualisation, noise reduction and efficient downstream processing of the data. In this work, we introduce the ProbDR variational framework, which interprets a wide range of classical DR algorithms as probabilistic inference algorithms in this framework. ProbDR encompasses PCA, CMDS, LLE, LE, MVU, diffusion maps, kPCA, Isomap, (t-)SNE, and UMAP. In our framework, a low-dimensional latent variable is used to construct a covariance, precision, or a graph Laplacian matrix, which can be used as part of a generative model for the data. Inference is done by optimizing an evidence lower bound. We demonstrate the internal consistency of our framework and show that it enables the use of probabilistic programming languages (PPLs) for DR. Additionally, we illustrate that the framework facilitates reasoning about unseen data and argue that our generative models approximate Gaussian processes (GPs) on manifolds. By providing a unified view of DR, our framework facilitates communication, reasoning about uncertainties, model composition, and extensions, particularly when domain knowledge is present.

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.

We propose a novel non-parametric learning paradigm for the identification of drift and diffusion coefficients of non-linear stochastic differential equations, which relies upon discrete-time observations of the state. The key idea essentially consists of fitting a RKHS-based approximation of the corresponding Fokker-Planck equation to such observations, yielding theoretical estimates of learning rates which, unlike previous works, become increasingly tighter when the regularity of the unknown drift and diffusion coefficients becomes higher. Our method being kernel-based, offline pre-processing may in principle be profitably leveraged to enable efficient numerical implementation.

Masked language models (MLM) do not explicitly define a distribution over language, i.e., they are not language models per se. However, recent work has implicitly treated them as such for the purposes of generation and scoring. This paper studies methods for deriving explicit joint distributions from MLMs, focusing on distributions over two tokens, which makes it possible to calculate exact distributional properties. We find that an approach based on identifying joints whose conditionals are closest to those of the MLM works well and outperforms existing Markov random field-based approaches. We further find that this derived model's conditionals can even occasionally outperform the original MLM's conditionals.

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.

Humans can learn languages from remarkably little experience. Developing computational models that explain this ability has been a major challenge in cognitive science. Bayesian models that build in strong inductive biases - factors that guide generalization - have been successful at explaining how humans might generalize from few examples in controlled settings but are usually too restrictive to be tractably applied to more naturalistic data. By contrast, neural networks have flexible representations that allow them to learn well from naturalistic data but require many more examples than humans receive. We show that learning from limited naturalistic data is possible with an approach that combines the strong inductive biases of a Bayesian model with the flexible representations of a neural network. This approach works by distilling a Bayesian model's biases into a neural network. Like a Bayesian model, the resulting system can learn formal linguistic patterns from a small number of examples. Like a neural network, it can also learn aspects of English syntax from a corpus of natural language - and it outperforms a standard neural network at acquiring the linguistic phenomena of recursion and priming. Bridging the divide between Bayesian models and neural networks makes it possible to handle a broader range of learning scenarios than either approach can handle on its own.

Stein Variational Gradient Descent (SVGD) can transport particles along trajectories that reduce the KL divergence between the target and particle distribution but requires the target score function to compute the update. We introduce a new perspective on SVGD that views it as a local estimator of the reversed KL gradient flow. This perspective inspires us to propose new estimators that use local linear models to achieve the same purpose. The proposed estimators can be computed using only samples from the target and particle distribution without needing the target score function. Our proposed variational gradient estimators utilize local linear models, resulting in computational simplicity while maintaining effectiveness comparable to SVGD in terms of estimation biases. Additionally, we demonstrate that under a mild assumption, the estimation of high-dimensional gradient flow can be translated into a lower-dimensional estimation problem, leading to improved estimation accuracy. We validate our claims with experiments on both simulated and real-world datasets.