Gaining the ability to make informed decisions on operation and maintenance of structures provides motivation for the implementation of structural health monitoring (SHM) systems. However, descriptive labels for measured data corresponding to health-states of the monitored system are often unavailable. This issue limits the applicability of fully-supervised machine learning paradigms for the development of statistical classifiers to be used in decision-support in SHM systems. One approach to dealing with this problem is risk-based active learning. In such an approach, data-label querying is guided according to the expected value of perfect information for incipient data points. For risk-based active learning in SHM, the value of information is evaluated with respect to a maintenance decision process, and the data-label querying corresponds to the inspection of a structure to determine its health state. In the context of SHM, risk-based active learning has only been considered for generative classifiers. The current paper demonstrates several advantages of using an alternative type of classifier -- discriminative models. Using the Z24 Bridge dataset as a case study, it is shown that discriminative classifiers have benefits, in the context of SHM decision-support, including improved robustness to sampling bias, and reduced expenditure on structural inspections.

Increasingly frequent wildfires significantly affect solar energy production as the atmospheric aerosols generated by wildfires diminish the incoming solar radiation to the earth. Atmospheric aerosols are measured by Aerosol Optical Depth (AOD), and AOD data streams can be retrieved and monitored by geostationary satellites. However, multi-source remote-sensing data streams often present heterogeneous characteristics, including different data missing rates, measurement errors, systematic biases, and so on. To accurately estimate and predict the underlying AOD propagation process, there exist practical needs and theoretical interests to propose a physics-informed statistical approach for modeling wildfire AOD propagation by simultaneously utilizing, or fusing, multi-source heterogeneous satellite remote-sensing data streams. Leveraging a spectral approach, the proposed approach integrates multi-source satellite data streams with a fundamental advection-diffusion equation that governs the AOD propagation process. A bias correction process is included in the statistical model to account for the bias of the physics model and the truncation error of the Fourier series. The proposed approach is applied to California wildfires AOD data streams obtained from the National Oceanic and Atmospheric Administration. Comprehensive numerical examples are provided to demonstrate the predictive capabilities and model interpretability of the proposed approach. Computer code has been made available on GitHub.

Shap explanations are a popular feature-attribution mechanism for explainable AI. They use game-theoretic notions to measure the influence of individual features on the prediction of a machine learning model. Despite a lot of recent interest from both academia and industry, it is not known whether Shap explanations of common machine learning models can be computed efficiently. In this paper, we establish the complexity of computing the Shap explanation in three important settings. First, we consider fully-factorized data distributions, and show that the complexity of computing the Shap explanation is the same as the complexity of computing the expected value of the model. This fully-factorized setting is often used to simplify the Shap computation, yet our results show that the computation can be intractable for commonly used models such as logistic regression. Going beyond fully-factorized distributions, we show that computing Shap explanations is already intractable for a very simple setting: computing Shap explanations of trivial classifiers over naive Bayes distributions. Finally, we show that even computing Shap over the empirical distribution is #P-hard.

The variable you want to predict is called the dependent variable. The variable you are using to predict the other variable's value is called the independent variable. K-NN is a non-parametric algorithm, which means it does not make any assumption on underlying data. It is also called a lazy learner algorithm because it does not learn from the training set immediately instead it stores the dataset and at the time of classification, it performs an action on the dataset. The Naive Bayes classification algorithm is a probabilistic classifier.

We consider the Bayesian calibration of models describing the phenomenon of block copolymer (BCP) self-assembly using image data produced by microscopy or X-ray scattering techniques. To account for the random long-range disorder in BCP equilibrium structures, we introduce auxiliary variables to represent this aleatory uncertainty. These variables, however, result in an integrated likelihood for high-dimensional image data that is generally intractable to evaluate. We tackle this challenging Bayesian inference problem using a likelihood-free approach based on measure transport together with the construction of summary statistics for the image data. We also show that expected information gains (EIGs) from the observed data about the model parameters can be computed with no significant additional cost. Lastly, we present a numerical case study based on the Ohta--Kawasaki model for diblock copolymer thin film self-assembly and top-down microscopy characterization. For calibration, we introduce several domain-specific energy- and Fourier-based summary statistics, and quantify their informativeness using EIG. We demonstrate the power of the proposed approach to study the effect of data corruptions and experimental designs on the calibration results.

We investigate the cold posterior effect through the lens of PAC-Bayes generalization bounds. We argue that in the non-asymptotic setting, when the number of training samples is (relatively) small, discussions of the cold posterior effect should take into account that approximate Bayesian inference does not readily provide guarantees of performance on out-of-sample data. Instead, out-of-sample error is better described through a generalization bound. In this context, we explore the connections between the ELBO objective from variational inference and the PAC-Bayes objectives. We note that, while the ELBO and PAC-Bayes objectives are similar, the latter objectives naturally contain a temperature parameter $\lambda$ which is not restricted to be $\lambda=1$. For both regression and classification tasks, in the case of isotropic Laplace approximations to the posterior, we show how this PAC-Bayesian interpretation of the temperature parameter captures the cold posterior effect.

Most machine learning models are concerned with correlation. In contrast, Causal models are concerned with cause and effect relationships – for example – "How much would a power failure cost to a given manufacturing plant?" A structural causal model (SCM) represents causal dependencies using graphical models. Bayesian Networks are one of the most widely used SCMs. Bayesian Network consists of a DAG(Directed Acyclic Graph), a causal graph where nodes represent random variables and edges represent the relationship between them, and a conditional probability distribution (CPDs) associated with each of the random variables. Models can reflect both statistically significant information (learned from the data) and domain expertise simultaneously.

Robot failures in human-centered environments are inevitable. Therefore, the ability of robots to explain such failures is paramount for interacting with humans to increase trust and transparency. To achieve this skill, the main challenges addressed in this paper are I) acquiring enough data to learn a cause-effect model of the environment and II) generating causal explanations based on that model. We address I) by learning a causal Bayesian network from simulation data. Concerning II), we propose a novel method that enables robots to generate contrastive explanations upon task failures. The explanation is based on setting the failure state in contrast with the closest state that would have allowed for a successful execution. This state is found through breadth-first search and is based on success predictions from the learned causal model. We assessed our method in two different scenarios I) stacking cubes and II) dropping spheres into a container. The obtained causal models reach a sim2real accuracy of 70% and 72%, respectively. We finally show that our novel method scales over multiple tasks and allows real robots to give failure explanations like 'the upper cube was stacked too high and too far to the right of the lower cube.'

In this paper, we study the problem of inferring spatially-varying Gaussian Markov random fields (SV-GMRF) where the goal is to learn a network of sparse, context-specific GMRFs representing network relationships between genes. An important application of SV-GMRFs is in inference of gene regulatory networks from spatially-resolved transcriptomics datasets. The current work on inference of SV-GMRFs are based on the regularized maximum likelihood estimation (MLE) and suffer from overwhelmingly high computational cost due to their highly nonlinear nature. To alleviate this challenge, we propose a simple and efficient optimization problem in lieu of MLE that comes equipped with strong statistical and computational guarantees. Our proposed optimization problem is extremely efficient in practice: we can solve instances of SV-GMRFs with more than 2 million variables in less than 2 minutes. We apply the developed framework to study how gene regulatory networks in Glioblastoma are spatially rewired within tissue, and identify prominent activity of the transcription factor HES4 and ribosomal proteins as characterizing the gene expression network in the tumor peri-vascular niche that is known to harbor treatment resistant stem cells.

Machine learning is one of those fields that anyone learning data science should know. If you're new to data science, you probably must've heard of the words "algorithm" or "model" without knowing how they're related to machine learning. Machine learning algorithms are categorized as supervised or unsupervised. Supervised learning algorithms model the relationship between labeled input and output data (aka target). This model is then used to predict the label of new observations using new labeled input data.