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.

We characterize homotopical equivalences between causal DAG models, exploiting the close connections between partially ordered set representations of DAGs (posets) and finite Alexandroff topologies. Alexandroff spaces yield a directional topological space: the topology is defined by a unique minimal basis defined by an open set for each variable x, specified as the intersection of all open sets containing x. Alexandroff spaces induce a (reflexive, transitive) preorder. Alexandroff spaces satisfying the Kolmogorov T0 separation criterion, where open sets distinguish variables, converts the preordering into a partial ordering. Our approach broadly is to construct a topological representation of posets from data, and then use the poset representation to build a conventional DAG causal model. We illustrate our framework by showing how it unifies disparate algorithms and case studies proposed previously. Topology plays two key roles in causal discovery. First, topological separability constraints on datasets have been used in several previous approaches to infer causal structure from observations and interventions. Second, a diverse range ofgraphical models used to represent causal structures can be represented in a unified way in terms of a topological representation of the induced poset structure. We show that the homotopy theory of Alexandroff spaces can be exploited to significantly efficiently reduce the number of possible DAG structures, reducing the search space by several orders of magnitude.

Causal effect estimation for dynamic treatment regimes (DTRs) contributes to sequential decision making. However, censoring and time-dependent confounding under DTRs are challenging as the amount of observational data declines over time due to a reducing sample size but the feature dimension increases over time. Long-term follow-up compounds these challenges. Another challenge is the highly complex relationships between confounders, treatments, and outcomes, which causes the traditional and commonly used linear methods to fail. We combine outcome regression models with treatment models for high dimensional features using uncensored subjects that are small in sample size and we fit deep Bayesian models for outcome regression models to reveal the complex relationships between confounders, treatments, and outcomes. Also, the developed deep Bayesian models can model uncertainty and output the prediction variance which is essential for the safety-aware applications, such as self-driving cars and medical treatment design. The experimental results on medical simulations of HIV treatment show the ability of the proposed method to obtain stable and accurate dynamic causal effect estimation from observational data, especially with long-term follow-up. Our technique provides practical guidance for sequential decision making, and policy-making.

In recent years, machine learning (ML) algorithms have been deployed in safety-critical and high-stake decision-making, where the fairness of algorithms is of paramount importance. Fairness in ML centers on detecting bias towards certain demographic populations induced by an ML classifier and proposes algorithmic solutions to mitigate the bias with respect to different fairness definitions. To this end, several fairness verifiers have been proposed that compute the bias in the prediction of an ML classifier -- essentially beyond a finite dataset -- given the probability distribution of input features. In the context of verifying linear classifiers, existing fairness verifiers are limited by accuracy due to imprecise modelling of correlations among features and scalability due to restrictive formulations of the classifiers as SSAT or SMT formulas or by sampling. In this paper, we propose an efficient fairness verifier, called FVGM, that encodes the correlations among features as a Bayesian network. In contrast to existing verifiers, FVGM proposes a stochastic subset-sum based approach for verifying linear classifiers. Experimentally, we show that FVGM leads to an accurate and scalable assessment for more diverse families of fairness-enhancing algorithms, fairness attacks, and group/causal fairness metrics than the state-of-the-art. We also demonstrate that FVGM facilitates the computation of fairness influence functions as a stepping stone to detect the source of bias induced by subsets of features.

We investigate novel parameter estimation and goodness-of-fit (GOF) assessment methods for large-scale confirmatory item factor analysis (IFA) with many respondents, items, and latent factors. For parameter estimation, we extend Urban and Bauer's (2021) deep learning algorithm for exploratory IFA to the confirmatory setting by showing how to handle user-defined constraints on loadings and factor correlations. For GOF assessment, we explore new simulation-based tests and indices. In particular, we consider extensions of the classifier two-sample test (C2ST), a method that tests whether a machine learning classifier can distinguish between observed data and synthetic data sampled from a fitted IFA model. The C2ST provides a flexible framework that integrates overall model fit, piece-wise fit, and person fit. Proposed extensions include a C2ST-based test of approximate fit in which the user specifies what percentage of observed data can be distinguished from synthetic data as well as a C2ST-based relative fit index that is similar in spirit to the relative fit indices used in structural equation modeling. Via simulation studies, we first show that the confirmatory extension of Urban and Bauer's (2021) algorithm produces more accurate parameter estimates as the sample size increases and obtains comparable estimates to a state-of-the-art confirmatory IFA estimation procedure in less time. We next show that the C2ST-based test of approximate fit controls the empirical type I error rate and detects when the number of latent factors is misspecified. Finally, we empirically investigate how the sampling distribution of the C2ST-based relative fit index depends on the sample size.

Natural language inference (NLI) aims to determine the logical relationship between two sentences among the target labels Entailment, Contradiction, and Neutral. In recent years, deep learning models have become a prevailing approach to NLI, but they lack interpretability and explainability. In this work, we address the explainability for NLI by weakly supervised logical reasoning, and propose an Explainable Phrasal Reasoning (EPR) approach. Our model first detects phrases as the semantic unit and aligns corresponding phrases. Then, the model predicts the NLI label for the aligned phrases, and induces the sentence label by fuzzy logic formulas. Our EPR is almost everywhere differentiable and thus the system can be trained end-to-end in a weakly supervised manner. We annotated a corpus and developed a set of metrics to evaluate phrasal reasoning. Results show that our EPR yields much more meaningful explanations in terms of F scores than previous studies. To the best of our knowledge, we are the first to develop a weakly supervised phrasal reasoning model for the NLI task.