Surrogate models have shown to be an extremely efficient aid in solving engineering problems that require repeated evaluations of an expensive computational model. They are built by sparsely evaluating the costly original model and have provided a way to solve otherwise intractable problems. A crucial aspect in surrogate modelling is the assumption of smoothness and regularity of the model to approximate. This assumption is however not always met in reality. For instance in civil or mechanical engineering, some models may present discontinuities or non-smoothness, e.g., in case of instability patterns such as buckling or snap-through. Building a single surrogate model capable of accounting for these fundamentally different behaviors or discontinuities is not an easy task. In this paper, we propose a three-stage approach for the approximation of non-smooth functions which combines clustering, classification and regression. The idea is to split the space following the localized behaviors or regimes of the system and build local surrogates that are eventually assembled. A sequence of well-known machine learning techniques are used: Dirichlet process mixtures models (DPMM), support vector machines and Gaussian process modelling. The approach is tested and validated on two analytical functions and a finite element model of a tensile membrane structure.

Learning causal structure from observational data often assumes that we observe independent and identically distributed (i.\,i.\,d) data. The traditional approach aims to find a graphical representation that encodes the same set of conditional independence relationships as those present in the observed distribution. It is known that under i.\,i.\,d assumption, even with infinite data, there is a limit to how fine-grained a causal structure we can identify. To overcome this limitation, recent work has explored using data originating from different, related environments to learn richer causal structure. These approaches implicitly rely on the independent causal mechanisms (ICM) principle, which postulates that the mechanism giving rise to an effect given its causes and the mechanism which generates the causes do not inform or influence each other. Thus, components of the causal model can independently change from environment to environment. Despite its wide application in machine learning and causal inference, there is a lack of statistical formalization of the ICM principle and how it enables identification of richer causal structures from grouped data. Here we present new causal de Finetti theorems which offer a first statistical formalization of ICM principle and show how causal structure identification is possible from exchangeable data. Our work provides theoretical justification for a broad range of techniques leveraging multi-environment data to learn causal structure.

An influence diagram is a graphical model of a Bayesian decision problem that is solved by finding a strategy that maximizes expected utility. When an influence diagram is solved by variable elimination or a related dynamic programming algorithm, it is traditional to represent a strategy as a sequence of policies, one for each decision variable, where a policy maps the relevant history for a decision to an action. We propose an alternative representation of a strategy as a graph, called a strategy graph, and show how to modify a variable elimination algorithm so that it constructs a strategy graph. We consider both a classic variable elimination algorithm for influence diagrams and a recent extension of this algorithm that has more relaxed constraints on elimination order that allow improved performance. We consider the advantages of representing a strategy as a graph and, in particular, how to simplify a strategy graph so that it is easier to interpret and analyze.

We develop a Bayesian semi-parametric model for the estimating the impact of dynamic treatment rules on survival among patients diagnosed with pediatric acute myeloid leukemia (AML). The data consist of a subset of patients enrolled in the phase III AAML1031 clinical trial in which patients move through a sequence of four treatment courses. At each course, they undergo treatment that may or may not include anthracyclines (ACT). While ACT is known to be effective at treating AML, it is also cardiotoxic and can lead to early death for some patients. Our task is to estimate the potential survival probability under hypothetical dynamic ACT treatment strategies, but there are several impediments. First, since ACT was not randomized in the trial, its effect on survival is confounded over time. Second, subjects initiate the next course depending on when they recover from the previous course, making timing potentially informative of subsequent treatment and survival. Third, patients may die or drop out before ever completing the full treatment sequence. We develop a generative Bayesian semi-parametric model based on Gamma Process priors to address these complexities. At each treatment course, the model captures subjects' transition to subsequent treatment or death in continuous time under a given rule. A g-computation procedure is used to compute a posterior over potential survival probability that is adjusted for time-varying confounding. Using this approach, we conduct posterior inference for the efficacy of hypothetical treatment rules that dynamically modify ACT based on evolving cardiac function.

Predictive monitoring is a subfield of process mining that aims to predict how a running case will unfold in the future. One of its main challenges is forecasting the sequence of activities that will occur from a given point in time -- suffix prediction -- . Most approaches to the suffix prediction problem learn to predict the suffix by learning how to predict the next activity only, not learning from the whole suffix during the training phase. This paper proposes a novel architecture based on an encoder-decoder model with an attention mechanism that decouples the representation learning of the prefixes from the inference phase, predicting only the activities of the suffix. During the inference phase, this architecture is extended with a heuristic search algorithm that improves the selection of the activity for each index of the suffix. Our approach has been tested using 12 public event logs against 6 different state-of-the-art proposals, showing that it significantly outperforms these proposals.

Temporal exponential random graph models (TERGM) are powerful statistical models that can be used to infer the temporal pattern of edge formation and elimination in complex networks (e.g., social networks). TERGMs can also be used in a generative capacity to predict longitudinal time series data in these evolving graphs. However, parameter estimation within this framework fails to capture many real-world properties of social networks, including: triadic relationships, small world characteristics, and social learning theories which could be used to constrain the probabilistic estimation of dyadic covariates. Here, we propose triadic temporal exponential random graph models (TTERGM) to fill this void, which includes these hierarchical network relationships within the graph model. We represent social network learning theory as an additional probability distribution that optimizes Markov chains in the graph vector space. The new parameters are then approximated via Monte Carlo maximum likelihood estimation. We show that our TTERGM model achieves improved fidelity and more accurate predictions compared to several benchmark methods on GitHub network data.

Analyzing the behavior of complex interdependent networks requires complete information about the network topology and the interdependent links across networks. For many applications such as critical infrastructure systems, understanding network interdependencies is crucial to anticipate cascading failures and plan for disruptions. However, data on the topology of individual networks are often publicly unavailable due to privacy and security concerns. Additionally, interdependent links are often only revealed in the aftermath of a disruption as a result of cascading failures. We propose a scalable nonparametric Bayesian approach to reconstruct the topology of interdependent infrastructure networks from observations of cascading failures. Metropolis-Hastings algorithm coupled with the infrastructure-dependent proposal are employed to increase the efficiency of sampling possible graphs. Results of reconstructing a synthetic system of interdependent infrastructure networks demonstrate that the proposed approach outperforms existing methods in both accuracy and computational time. We further apply this approach to reconstruct the topology of one synthetic and two real-world systems of interdependent infrastructure networks, including gas-power-water networks in Shelby County, TN, USA, and an interdependent system of power-water networks in Italy, to demonstrate the general applicability of the approach.

Bayesian adaptive experimental design is a form of active learning, which chooses samples to maximize the information they give about uncertain parameters. Prior work has shown that other forms of active learning can suffer from active learning bias, where unrepresentative sampling leads to inconsistent parameter estimates. We show that active learning bias can also afflict Bayesian adaptive experimental design, depending on model misspecification. We analyze the case of estimating a linear model, and show that worse misspecification implies more severe active learning bias. At the same time, model classes incorporating more "noise" -- i.e., specifying higher inherent variance in observations -- suffer less from active learning bias. Finally, we demonstrate empirically that insights from the linear model can predict the presence and degree of active learning bias in nonlinear contexts, namely in a (simulated) preference learning experiment. Statistical theory often assumes learners' access to large amounts of representative training data, drawn from the distribution which is the target of inference or prediction. Nonetheless, such access is not feasible for many applications. Training data may be scarce (e.g., learning to identify a rare medical condition; Henry, Hager, Pronovost, and Saria (2015)), difficult or expensive to obtain (e.g., requiring human coders for text; Chen, Lasko, Mei, Denny, and Xu (2015)), or time-consuming to collect (e.g., obtaining user preferences online; Cavagnaro, Gonzalez, Myung, and Pitt (2013); Golovin, Krause, and Ray (2010)). One response is to abandon random sampling for adaptive sampling methods, choosing data points in sequence to be as informative as possible.

This report summarises the outcomes of a systematic literature search to identify Bayesian network models used to support decision making in healthcare. After describing the search methodology, the selected research papers are briefly reviewed, with the view to identify publicly available models and datasets that are well suited to analysis using the causal interventional analysis software tool developed in Wang B, Lyle C, Kwiatkowska M (2021). Finally, an experimental evaluation of applying the software on a selection of models is carried out and preliminary results are reported.

Hierarchical Bayesian Poisson regression models (HBPRMs) provide a flexible modeling approach of the relationship between predictors and count response variables. The applications of HBPRMs to large-scale datasets require efficient inference algorithms due to the high computational cost of inferring many model parameters based on random sampling. Although Markov Chain Monte Carlo (MCMC) algorithms have been widely used for Bayesian inference, sampling using this class of algorithms is time-consuming for applications with large-scale data and time-sensitive decision-making, partially due to the non-conjugacy of many models. To overcome this limitation, this research develops an approximate Gibbs sampler (AGS) to efficiently learn the HBPRMs while maintaining the inference accuracy. In the proposed sampler, the data likelihood is approximated with Gaussian distribution such that the conditional posterior of the coefficients has a closed-form solution. Numerical experiments using real and synthetic datasets with small and large counts demonstrate the superior performance of AGS in comparison to the state-of-the-art sampling algorithm, especially for large datasets.