Bayesian inference remains one of the most important tool-kits for any scientist, but increasingly expensive likelihood functions are required for ever-more complex experiments, raising the cost of generating a Monte Carlo sample of the posterior. Recent attention has been directed towards the use of emulators of the posterior based on Gaussian Process (GP) regression combined with active sampling to achieve comparable precision with far fewer costly likelihood evaluations. Key to this approach is the batched acquisition of proposals, so that the true posterior can be evaluated in parallel. This is usually achieved via sequential maximization of the highly multimodal acquisition function. Unfortunately, this approach parallelizes poorly and is prone to getting stuck in local maxima. Our approach addresses this issue by generating nearly-optimal batches of candidates using an almost-embarrassingly parallel Nested Sampler on the mean prediction of the GP. The resulting nearly-sorted Monte Carlo sample is used to generate a batch of candidates ranked according to their sequentially conditioned acquisition function values at little cost. The final sample can also be used for inferring marginal quantities. Our proposed implementation (NORA) demonstrates comparable accuracy to sequential conditioned acquisition optimization and efficient parallelization in various synthetic and cosmological inference problems.

Probabilistic modeling of multidimensional spatiotemporal data is critical to many real-world applications. As real-world spatiotemporal data often exhibits complex dependencies that are nonstationary and nonseparable, developing effective and computationally efficient statistical models to accommodate nonstationary/nonseparable processes containing both long-range and short-scale variations becomes a challenging task, in particular for large-scale datasets with various corruption/missing structures. In this paper, we propose a new statistical framework -- Bayesian Complementary Kernelized Learning (BCKL) -- to achieve scalable probabilistic modeling for multidimensional spatiotemporal data. To effectively characterize complex dependencies, BCKL integrates two complementary approaches -- kernelized low-rank tensor factorization and short-range spatiotemporal Gaussian Processes. Specifically, we use a multi-linear low-rank factorization component to capture the global/long-range correlations in the data and introduce an additive short-scale GP based on compactly supported kernel functions to characterize the remaining local variabilities. We develop an efficient Markov chain Monte Carlo (MCMC) algorithm for model inference and evaluate the proposed BCKL framework on both synthetic and real-world spatiotemporal datasets. Our experiment results show that BCKL offers superior performance in providing accurate posterior mean and high-quality uncertainty estimates, confirming the importance of both global and local components in modeling spatiotemporal data.

Bayesian Decision Trees (DTs) are generally considered a more advanced and accurate model than a regular Decision Tree (DT) because they can handle complex and uncertain data. Existing work on Bayesian DTs uses Markov Chain Monte Carlo (MCMC) with an accept-reject mechanism and sample using naive proposals to proceed to the next iteration, which can be slow because of the burn-in time needed. We can reduce the burn-in period by proposing a more sophisticated way of sampling or by designing a different numerical Bayesian approach. In this paper, we propose a replacement of the MCMC with an inherently parallel algorithm, the Sequential Monte Carlo (SMC), and a more effective sampling strategy inspired by the Evolutionary Algorithms (EA). Experiments show that SMC combined with the EA can produce more accurate results compared to MCMC in 100 times fewer iterations.

This paper is concerned with the problem of policy evaluation with linear function approximation in discounted infinite horizon Markov decision processes. We investigate the sample complexities required to guarantee a predefined estimation error of the best linear coefficients for two widely-used policy evaluation algorithms: the temporal difference (TD) learning algorithm and the two-timescale linear TD with gradient correction (TDC) algorithm. In both the on-policy setting, where observations are generated from the target policy, and the off-policy setting, where samples are drawn from a behavior policy potentially different from the target policy, we establish the first sample complexity bound with high-probability convergence guarantee that attains the optimal dependence on the tolerance level. We also exhihit an explicit dependence on problem-related quantities, and show in the on-policy setting that our upper bound matches the minimax lower bound on crucial problem parameters, including the choice of the feature maps and the problem dimension.

Actor-critic algorithms address the dual goals of reinforcement learning (RL), policy evaluation and improvement, via two separate function approximators. The practicality of this approach comes at the expense of training instability, caused mainly by the destructive effect of the approximation errors of the critic on the actor. We tackle this bottleneck by employing an existing Probably Approximately Correct (PAC) Bayesian bound for the first time as the critic training objective of the Soft Actor-Critic (SAC) algorithm. We further demonstrate that online learning performance improves significantly when a stochastic actor explores multiple futures by critic-guided random search. We observe our resulting algorithm to compare favorably to the state of the art on multiple classical control and locomotion tasks in terms of both sample efficiency and regret minimization.

PAC-Bayes learning is an established framework to both assess the generalisation ability of learning algorithms, and design new learning algorithm by exploiting generalisation bounds as training objectives. Most of the exisiting bounds involve a \emph{Kullback-Leibler} (KL) divergence, which fails to capture the geometric properties of the loss function which are often useful in optimisation. We address this by extending the emerging \emph{Wasserstein PAC-Bayes} theory. We develop new PAC-Bayes bounds with Wasserstein distances replacing the usual KL, and demonstrate that sound optimisation guarantees translate to good generalisation abilities. In particular we provide generalisation bounds for the \emph{Bures-Wasserstein SGD} by exploiting its optimisation properties.

We demonstrate unprecedented accuracy for rapid gravitational-wave parameter estimation with deep learning. Using neural networks as surrogates for Bayesian posterior distributions, we analyze eight gravitational-wave events from the first LIGO-Virgo Gravitational-Wave Transient Catalog and find very close quantitative agreement with standard inference codes, but with inference times reduced from O(day) to a minute per event. Our networks are trained using simulated data, including an estimate of the detector-noise characteristics near the event. This encodes the signal and noise models within millions of neural-network parameters, and enables inference for any observed data consistent with the training distribution, accounting for noise nonstationarity from event to event. Our algorithm -- called "DINGO" -- sets a new standard in fast-and-accurate inference of physical parameters of detected gravitational-wave events, which should enable real-time data analysis without sacrificing accuracy.

Counterfactual reasoning -- envisioning hypothetical scenarios, or possible worlds, where some circumstances are different from what (f)actually occurred (counter-to-fact) -- is ubiquitous in human cognition. Conventionally, counterfactually-altered circumstances have been treated as "small miracles" that locally violate the laws of nature while sharing the same initial conditions. In Pearl's structural causal model (SCM) framework this is made mathematically rigorous via interventions that modify the causal laws while the values of exogenous variables are shared. In recent years, however, this purely interventionist account of counterfactuals has increasingly come under scrutiny from both philosophers and psychologists. Instead, they suggest a backtracking account of counterfactuals, according to which the causal laws remain unchanged in the counterfactual world; differences to the factual world are instead "backtracked" to altered initial conditions (exogenous variables). In the present work, we explore and formalise this alternative mode of counterfactual reasoning within the SCM framework. Despite ample evidence that humans backtrack, the present work constitutes, to the best of our knowledge, the first general account and algorithmisation of backtracking counterfactuals. We discuss our backtracking semantics in the context of related literature and draw connections to recent developments in explainable artificial intelligence (XAI).

In light of the growing popularity of Exploratory Data Analysis (EDA), understanding the underlying causes of the knowledge acquired by EDA is crucial. However, it remains under-researched. This study promotes a transparent and explicable perspective on data analysis, called eXplainable Data Analysis (XDA). For this reason, we present XInsight, a general framework for XDA. XInsight provides data analysis with qualitative and quantitative explanations of causal and non-causal semantics. This way, it will significantly improve human understanding and confidence in the outcomes of data analysis, facilitating accurate data interpretation and decision making in the real world. XInsight is a three-module, end-to-end pipeline designed to extract causal graphs, translate causal primitives into XDA semantics, and quantify the quantitative contribution of each explanation to a data fact. XInsight uses a set of design concepts and optimizations to address the inherent difficulties associated with integrating causality into XDA. Experiments on synthetic and real-world datasets as well as a user study demonstrate the highly promising capabilities of XInsight.

With the rapid development of social media such as Twitter and Weibo, detecting keywords from a huge volume of text data streams in real-time has become a critical problem. The keyword detection problem aims at searching important information from massive text data to reflect the most important events or topics. However, social media data usually has unique features: the documents are usually short, the language is colloquial, and the data is likely to have significant temporal patterns. Therefore, it could be challenging to discover critical information from these text streams. In this paper, we propose a novel method to address the keyword detection problem in social media. Our model combines the Inverse Document Frequency (IDF) and Latent Dirichlet Allocation (LDA) models to better cope with the distinct attributes of social media data, such as the number of likes, comments, and retweets. By weighting the importance of each document based on these attributes, our method can effectively detect more representative keywords over time. Comprehensive experiments conducted under various conditions on Weibo data illustrate that our approach outperforms the baselines in various evaluation metrics, including precision and recall for multiple problem settings.