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.

The rise of AI methods to make predictions and decisions has led to a pressing need for more explainable artificial intelligence (XAI) methods. One common approach for XAI is to produce a post-hoc explanation, explaining why a black box ML model made a certain prediction. Formal approaches to post-hoc explanations provide succinct reasons for why a prediction was made, as well as why not another prediction was made. But these approaches assume that features are independent and uniformly distributed. While this means that "why" explanations are correct, they may be longer than required. It also means the "why not" explanations may be suspect as the counterexamples they rely on may not be meaningful. In this paper, we show how one can apply background knowledge to give more succinct "why" formal explanations, that are presumably easier to interpret by humans, and give more accurate "why not" explanations. In addition, we show how to use existing rule induction techniques to efficiently extract background information from a dataset, and also how to report which background information was used to make an explanation, allowing a human to examine it if they doubt the correctness of the explanation.

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.

The prediction of protein structures from sequences is an important task for function prediction, drug design, and related biological processes understanding. Recent advances have proved the power of language models (LMs) in processing the protein sequence databases, which inherit the advantages of attention networks and capture useful information in learning representations for proteins. The past two years have witnessed remarkable success in tertiary protein structure prediction (PSP), including evolution-based and single-sequence-based PSP. It seems that instead of using energy-based models and sampling procedures, protein language model (pLM)-based pipelines have emerged as mainstream paradigms in PSP. Despite the fruitful progress, the PSP community needs a systematic and up-to-date survey to help bridge the gap between LMs in the natural language processing (NLP) and PSP domains and introduce their methodologies, advancements and practical applications. To this end, in this paper, we first introduce the similarities between protein and human languages that allow LMs extended to pLMs, and applied to protein databases. Then, we systematically review recent advances in LMs and pLMs from the perspectives of network architectures, pre-training strategies, applications, and commonly-used protein databases. Next, different types of methods for PSP are discussed, particularly how the pLM-based architectures function in the process of protein folding. Finally, we identify challenges faced by the PSP community and foresee promising research directions along with the advances of pLMs. This survey aims to be a hands-on guide for researchers to understand PSP methods, develop pLMs and tackle challenging problems in this field for practical purposes.

A reliable pose estimator robust to environmental disturbances is desirable for mobile robots. To this end, inertial measurement units (IMUs) play an important role because they can perceive the full motion state of the vehicle independently. However, it suffers from accumulative error due to inherent noise and bias instability, especially for low-cost sensors. In our previous studies on Wheel-INS \cite{niu2021, wu2021}, we proposed to limit the error drift of the pure inertial navigation system (INS) by mounting an IMU to the wheel of the robot to take advantage of rotation modulation. However, Wheel-INS still drifted over a long period of time due to the lack of external correction signals. In this letter, we propose to exploit the environmental perception ability of Wheel-INS to achieve simultaneous localization and mapping (SLAM) with only one IMU. To be specific, we use the road bank angles (mirrored by the robot roll angles estimated by Wheel-INS) as terrain features to enable the loop closure with a Rao-Blackwellized particle filter. The road bank angle is sampled and stored according to the robot position in the grid maps maintained by the particles. The weights of the particles are updated according to the difference between the currently estimated roll sequence and the terrain map. Field experiments suggest the feasibility of the idea to perform SLAM in Wheel-INS using the robot roll angle estimates. In addition, the positioning accuracy is improved significantly (more than 30\%) over Wheel-INS. The source code of our implementation is publicly available (https://github.com/i2Nav-WHU/Wheel-SLAM).

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.