We propose a new approach to temporal inference, inspired by the Pearlian causal inference paradigm - though quite different from Pearl's approach formally. Rather than using directed acyclic graphs, we make use of factored sets, which are sets expressed as Cartesian products. We show that finite factored sets are powerful tools for inferring temporal relations. We introduce an analog of d-separation for factored sets, conditional orthogonality, and we demonstrate that this notion is equivalent to conditional independence in all probability distributions on a finite factored set.

Bayesian Networks (BNs) have become increasingly popular over the last few decades as a tool for reasoning under uncertainty in fields as diverse as medicine, biology, epidemiology, economics and the social sciences. This is especially true in real-world areas where we seek to answer complex questions based on hypothetical evidence to determine actions for intervention. However, determining the graphical structure of a BN remains a major challenge, especially when modelling a problem under causal assumptions. Solutions to this problem include the automated discovery of BN graphs from data, constructing them based on expert knowledge, or a combination of the two. This paper provides a comprehensive review of combinatoric algorithms proposed for learning BN structure from data, describing 61 algorithms including prototypical, well-established and state-of-the-art approaches. The basic approach of each algorithm is described in consistent terms, and the similarities and differences between them highlighted. Methods of evaluating algorithms and their comparative performance are discussed including the consistency of claims made in the literature. Approaches for dealing with data noise in real-world datasets and incorporating expert knowledge into the learning process are also covered.

Recent \emph{Weak Supervision (WS)} approaches have had widespread success in easing the bottleneck of labeling training data for machine learning by synthesizing labels from multiple potentially noisy supervision sources. However, proper measurement and analysis of these approaches remain a challenge. First, datasets used in existing works are often private and/or custom, limiting standardization. Second, WS datasets with the same name and base data often vary in terms of the labels and weak supervision sources used, a significant "hidden" source of evaluation variance. Finally, WS studies often diverge in terms of the evaluation protocol and ablations used. To address these problems, we introduce a benchmark platform, \benchmark, for a thorough and standardized evaluation of WS approaches. It consists of 22 varied real-world datasets for classification and sequence tagging; a range of real, synthetic, and procedurally-generated weak supervision sources; and a modular, extensible framework for WS evaluation, including implementations for popular WS methods. We use \benchmark to conduct extensive comparisons over more than 100 method variants to demonstrate its efficacy as a benchmark platform. The code is available at \url{https://github.com/JieyuZ2/wrench}.

Pool-based active learning (AL) aims to optimize the annotation process (i.e., labeling) as the acquisition of annotations is often time-consuming and therefore expensive. For this purpose, an AL strategy queries annotations intelligently from annotators to train a high-performance classification model at a low annotation cost. Traditional AL strategies operate in an idealized framework. They assume a single, omniscient annotator who never gets tired and charges uniformly regardless of query difficulty. However, in real-world applications, we often face human annotators, e.g., crowd or in-house workers, who make annotation mistakes and can be reluctant to respond if tired or faced with complex queries. Recently, a wide range of novel AL strategies has been proposed to address these issues. They differ in at least one of the following three central aspects from traditional AL: (1) They explicitly consider (multiple) human annotators whose performances can be affected by various factors, such as missing expertise. (2) They generalize the interaction with human annotators by considering different query and annotation types, such as asking an annotator for feedback on an inferred classification rule. (3) They take more complex cost schemes regarding annotations and misclassifications into account. This survey provides an overview of these AL strategies and refers to them as real-world AL. Therefore, we introduce a general real-world AL strategy as part of a learning cycle and use its elements, e.g., the query and annotator selection algorithm, to categorize about 60 real-world AL strategies. Finally, we outline possible directions for future research in the field of AL.

This article considers the popular MCMC method of unadjusted Langevin Monte Carlo (LMC) and provides a non-asymptotic analysis of its sampling error in 2-Wasserstein distance. The proof is based on a mean-square analysis framework refined from Li et al. (2019), which works for a large class of sampling algorithms based on discretizations of contractive SDEs. We establish an $\tilde{O}(\sqrt{d}/\epsilon)$ mixing time bound for LMC, without warm start, under the common log-smooth and log-strongly-convex conditions, plus a growth condition on the 3rd-order derivative of the potential of target measures. This bound improves the best previously known $\tilde{O}(d/\epsilon)$ result and is optimal (in terms of order) in both dimension $d$ and accuracy tolerance $\epsilon$ for target measures satisfying the aforementioned assumptions. Our theoretical analysis is further validated by numerical experiments.

In particular, time series data have become ubiquitous in our days, arising frequently in a broad variety of fields including medicine, computer science, finance, environmental sciences, machine learning, marketing and neuroscience, among many others. Typically, time series involve a huge number of records, present dynamic behavior patterns which might change over time, and one frequently has to deal with realizations of different length. Due to this complex nature, standard techniques to perform data mining tasks as classification, clustering or anomaly detection often produce unsatisfactory results. Complexity is still greater by treating with high dimensional time series, where the interdependence structure and large dimensionality are serious obstacles to develop efficient procedures. Univariate time series (UTS) were the main focus of intensive research until recently, but multivariate time series (MTS) have received lately a great deal of attention due to the advance of technology and storage capabilities of everyday devices. Well-known examples of MTS are multi-lead ECG signals of patients or records containing several economic indicators of a given country over time, but many other examples can be easily obtained from different fields. Among time series data mining tasks, clustering is a central problem. In fact, identifying groups of similar series is basic for many applications in order to detect a few representative patterns, forecast future performances, quantify affinity, recognize dynamic changes and structural breaks... However, unlike traditional databases, similarity search in time series data is a complex issue that cannot be addressed with conventional methods.

Deep generative models trained by maximum likelihood remain very popular methods for reasoning about data probabilistically. However, it has been observed that they can assign higher likelihoods to out-of-distribution (OOD) data than in-distribution data, thus calling into question the meaning of these likelihood values. In this work we provide a novel perspective on this phenomenon, decomposing the average likelihood into a KL divergence term and an entropy term. We argue that the latter can explain the curious OOD behaviour mentioned above, suppressing likelihood values on datasets with higher entropy. Although our idea is simple, we have not seen it explored yet in the literature. This analysis provides further explanation for the success of OOD detection methods based on likelihood ratios, as the problematic entropy term cancels out in expectation. Finally, we discuss how this observation relates to recent success in OOD detection with manifold-supported models, for which the above decomposition does not hold.

Identification of nonlinear dynamic systems remains a significant challenge across engineering. This work suggests an approach based on Bayesian filtering to extract and identify the contribution of an unknown nonlinear term in the system which can be seen as an alternative viewpoint on restoring force surface type approaches. To achieve this identification, the contribution which is the nonlinear restoring force is modelled, initially, as a Gaussian process in time. That Gaussian process is converted into a state-space model and combined with the linear dynamic component of the system. Then, by inference of the filtering and smoothing distributions, the internal states of the system and the nonlinear restoring force can be extracted. In possession of these states a nonlinear model can be constructed. The approach is demonstrated to be effective in both a simulated case study and on an experimental benchmark dataset.

In many fields of science and engineering, models with different fidelities are available. Physical experiments or detailed simulations that accurately capture the behavior of the system are regarded as high-fidelity models with low model uncertainty, however, they are expensive to run. On the other hand, simplified physical experiments or numerical models are seen as low-fidelity models that are cheaper to evaluate. Although low-fidelity models are often not suitable for direct use in reliability analysis due to their low accuracy, they can offer information about the trend of the high-fidelity model thus providing the opportunity to explore the design space at a low cost. This study presents a new approach called adaptive multi-fidelity Gaussian process for reliability analysis (AMGPRA). Contrary to selecting training points and information sources in two separate stages as done in state-of-the-art mfEGRA method, the proposed approach finds the optimal training point and information source simultaneously using the novel collective learning function (CLF). CLF is able to assess the global impact of a candidate training point from an information source and it accommodates any learning function that satisfies a certain profile. In this context, CLF provides a new direction for quantifying the impact of new training points and can be easily extended with new learning functions to adapt to different reliability problems. The performance of the proposed method is demonstrated by three mathematical examples and one engineering problem concerning the wind reliability of transmission towers. It is shown that the proposed method achieves similar or higher accuracy with reduced computational costs compared to state-of-the-art single and multi-fidelity methods. A key application of AMGPRA is high-fidelity fragility modeling using complex and costly physics-based computational models.

The Van Wijngaarden Awards 2021 are awarded to computer scientist Marta Kwiatkowska and mathematician Susan A. Murphy for the numerous and highly significant contributions they made to their respective research areas: preventing software faults and improving decision making in health. The five-yearly award is established by CWI, the national research institute for mathematics and computer science in the Netherlands, and is named after former CWI director Aad van Wijngaarden. The winners receive the prize during a festive soirée on 18 November in Amsterdam. Marta Kwiatkowska (University of Oxford) is a computer scientist who pioneered research on modelling, verification, and synthesis of probabilistic systems. She led the development of the highly influential PRISM probabilistic model checker, which is widely used for research and teaching and which has been downloaded over 80,000 times. In her research Kwiatkowska showed the relevance of PRISM by applying it in several areas, including ubiquitous computing, system biology, DNA computing, and most recently, safety for AI.