High-energy physics requires the generation of large numbers of simulated data samples from complex but analytically tractable distributions called matrix elements. Surrogate models, such as normalizing flows, are gaining popularity for this task due to their computational efficiency. We adopt an approach based on Flow Annealed importance sampling Bootstrap (FAB) that evaluates the differentiable target density during training and helps avoid the costly generation of training data in advance. We show that FAB reaches higher sampling efficiency with fewer target evaluations in high dimensions in comparison to other methods.

Conformal Prediction offers a powerful framework for quantifying uncertainty in machine learning models, enabling the construction of prediction sets with finite-sample validity guarantees. While easily adaptable to non-probabilistic models, applying conformal prediction to probabilistic generative models, such as Normalising Flows is not straightforward. This work proposes a novel method to conformalise conditional normalising flows, specifically addressing the problem of obtaining prediction regions for multi-step time series forecasting. Our approach leverages the flexibility of normalising flows to generate potentially disjoint prediction regions, leading to improved predictive efficiency in the presence of potential multimodal predictive distributions.

Deep learning has seen substantial achievements, with numerical and theoretical evidence suggesting that singularities of statistical models are considered a contributing factor to its performance. From this remarkable success of classical statistical models, it is naturally expected that quantum singular models will play a vital role in many quantum statistical tasks. However, while the theory of quantum statistical models in regular cases has been established, theoretical understanding of quantum singular models is still limited. To investigate the statistical properties of quantum singular models, we focus on two prominent tasks in quantum statistical inference: quantum state estimation and model selection. In particular, we base our study on classical singular learning theory and seek to extend it within the framework of Bayesian quantum state estimation. To this end, we define quantum generalization and training loss functions and give their asymptotic expansions through algebraic geometrical methods. The key idea of the proof is the introduction of a quantum analog of the likelihood function using classical shadows. Consequently, we construct an asymptotically unbiased estimator of the quantum generalization loss, the quantum widely applicable information criterion (QWAIC), as a computable model selection metric from given measurement outcomes.

It has long been posited that there is a connection between the dynamical equations describing evolutionary processes in biology and sequential Bayesian learning methods. This manuscript describes new research in which this precise connection is rigorously established in the continuous time setting. Here we focus on a partial differential equation known as the Kushner-Stratonovich equation describing the evolution of the posterior density in time. Of particular importance is a piecewise smooth approximation of the observation path from which the discrete time filtering equations, which are shown to converge to a Stratonovich interpretation of the Kushner-Stratonovich equation. This smooth formulation will then be used to draw precise connections between nonlinear stochastic filtering and replicator-mutator dynamics. Additionally, gradient flow formulations will be investigated as well as a form of replicator-mutator dynamics which is shown to be beneficial for the misspecified model filtering problem. It is hoped this work will spur further research into exchanges between sequential learning and evolutionary biology and to inspire new algorithms in filtering and sampling.

Estimating causal effects from nonexperimental data is a fundamental problem in many fields of science. A key component of this task is selecting an appropriate set of covariates for confounding adjustment to avoid bias. Most existing methods for covariate selection often assume the absence of latent variables and rely on learning the global network structure among variables. However, identifying the global structure can be unnecessary and inefficient, especially when our primary interest lies in estimating the effect of a treatment variable on an outcome variable. To address this limitation, we propose a novel local learning approach for covariate selection in nonparametric causal effect estimation, which accounts for the presence of latent variables. Our approach leverages testable independence and dependence relationships among observed variables to identify a valid adjustment set for a target causal relationship, ensuring both soundness and completeness under standard assumptions. We validate the effectiveness of our algorithm through extensive experiments on both synthetic and real-world data.

The multimedia content and streaming are a major means of information exchange in the modern era and there is an increasing demand for such services. This coupled with the advancement of future wireless networks B5G/6G and the proliferation of intelligent handheld mobile devices, has facilitated the availability of multimedia content to heterogeneous mobile users. Apart from the conventional video, the 360$^o$ videos have gained popularity with the emerging virtual reality applications. All formats of videos (conventional and 360$^o$) undergo processing, compression, and transmission across dynamic wireless channels with restricted bandwidth to facilitate the streaming services. This causes video impairments, leading to quality degradation and poses challenges in delivering good Quality-of-Experience (QoE) to the viewers. The QoE is a prominent subjective quality measure to assess multimedia services. This requires end-to-end QoE evaluation. Efficient multimedia streaming techniques can improve the service quality while dealing with dynamic network and end-user challenges. A paradigm shift in user-centric multimedia services is envisioned with a focus on Machine Learning (ML) based QoE modeling and streaming strategies. This survey paper presents a comprehensive overview of the overall and continuous, time varying QoE modeling for the purpose of QoE management in multimedia services. It also examines the recent research on intelligent and adaptive multimedia streaming strategies, with a special emphasis on ML based techniques for video (conventional and 360$^o$) streaming. This paper discusses the overall and continuous QoE modeling to optimize the end-user viewing experience, efficient video streaming with a focus on user-centric strategies, associated datasets for modeling and streaming, along with existing shortcoming and open challenges.

Understanding the inner mechanisms of black-box foundation models (FMs) is essential yet challenging in artificial intelligence and its applications. Over the last decade, the long-running focus has been on their explainability, leading to the development of post-hoc explainable methods to rationalize the specific decisions already made by black-box FMs. However, these explainable methods have certain limitations in terms of faithfulness and resource requirement. Consequently, a new class of interpretable methods should be considered to unveil the underlying mechanisms of FMs in an accurate, comprehensive, heuristic, and resource-light way. This survey aims to review those interpretable methods that comply with the aforementioned principles and have been successfully applied to FMs. These methods are deeply rooted in machine learning theory, covering the analysis of generalization performance, expressive capability, and dynamic behavior. They provide a thorough interpretation of the entire workflow of FMs, ranging from the inference capability and training dynamics to their ethical implications. Ultimately, drawing upon these interpretations, this review identifies the next frontier research directions for FMs.

In the big data era, integrating information from multiple heterogeneous sources has become increasingly crucial for achieving larger sample sizes and more diverse study populations. The applications of data integration are in a variety of fields, including but not limited to, causal inference on heterogeneous populations (Shi et al., 2023), survey sampling (Yang et al., 2020), health policy (Paddock et al., 2024), retrospective psychometrics (Howe and Brown, 2023), and multi-omics biological science (Du et al., 2022). Data integration methods have been proposed to mitigate the unwanted effects of heterogeneous datasets and unmeasured covariates, recovering the common variation across datasets. However, a critical and often overlooked question is whether reliable statistical inference can be made from integrated data. Directly performing statistical inference on integrated outcomes and covariates of interests fails to account for the complex correlation structures introduced by the data integration process, often leading to improper analyses that incorrectly assume the corrected data points are independent (Li et al., 2023). While data integration is broadly utilized in various fields, our paper focuses on a challenging scenario with the presence of high-dimensional outcomes.

For several decades now, Bayesian inference techniques have been applied to theories of particle physics, cosmology and astrophysics to obtain the probability density functions of their free parameters. In this study, we review and compare a wide range of Markov Chain Monte Carlo (MCMC) and nested sampling techniques to determine their relative efficacy on functions that resemble those encountered most frequently in the particle astrophysics literature. Our first series of tests explores a series of high-dimensional analytic test functions that exemplify particular challenges, for example highly multimodal posteriors or posteriors with curving degeneracies. We then investigate two real physics examples, the first being a global fit of the $\Lambda$CDM model using cosmic microwave background data from the Planck experiment, and the second being a global fit of the Minimal Supersymmetric Standard Model using a wide variety of collider and astrophysics data. We show that several examples widely thought to be most easily solved using nested sampling approaches can in fact be more efficiently solved using modern MCMC algorithms, but the details of the implementation matter. Furthermore, we also provide a series of useful insights for practitioners of particle astrophysics and cosmology.

The Bayesian paradigm offers the possibility to incorporate prior knowledge into a statistical model through the specification of prior distributions. This possibility is a central advantage of the Bayesian paradigm (Mikkola et al 2023), yet it also presents one of its most challenging aspects (Simpson et al 2017; lgorzata Roos et al 2015; Van Dongen 2006). In the following, we define prior knowledge as the expertise provided by a domain expert -- an individual with extensive knowledge of a specific subject matter (Falconer et al 2022). This knowledge can be represented in various forms, but to integrate it into a Bayesian model, we need to translate it into a formal mathematical language that can be expressed as a prior distribution over the model parameters (Perepolkin et al 2023; O'Hagan 2019; Martin et al 2012; Garthwaite et al 2005). A whole field of research, commonly referred to as (expert) prior elicitation, has emerged around the question of how to gather expert knowledge and translate it into appropriate prior distributions (Stefan et al 2022; Mikkola et al 2023; Falconer et al 2022).