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1. Reliable Post hoc Explanations: Modeling Uncertainty in Explainability

   Slack, Dylan; Hilgard, Anna; Singh, Sameer; Lakkaraju, Himabindu. (January 2021, Advances in neural information processing systems)

   As black box explanations are increasingly being employed to establish model credibility in high-stakes settings, it is important to ensure that these explanations are accurate and reliable. However, prior work demonstrates that explanations generated by state-of-the-art techniques are inconsistent, unstable, and provide very little insight into their correctness and reliability. In addition, these methods are also computationally inefficient, and require significant hyper-parameter tuning. In this paper, we address the aforementioned challenges by developing a novel Bayesian framework for generating local explanations along with their associated uncertainty. We instantiate this framework to obtain Bayesian versions of LIME and KernelSHAP which output credible intervals for the feature importances, capturing the associated uncertainty. The resulting explanations not only enable us to make concrete inferences about their quality (e.g., there is a 95% chance that the feature importance lies within the given range), but are also highly consistent and stable. We carry out a detailed theoretical analysis that leverages the aforementioned uncertainty to estimate how many perturbations to sample, and how to sample for faster convergence. This work makes the first attempt at addressing several critical issues with popular explanation methods in one shot, thereby generating consistent, stable, and reliable explanations with guarantees in a computationally efficient manner. Experimental evaluation with multiple real world datasets and user studies demonstrate that the efficacy of the proposed framework. 

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2. A Bayesian Multiplex Graph Classifier of Functional Brain Connectivity Across Diverse Tasks of Cognitive Control

   https://doi.org/10.1007/s12021-024-09670-w  

   Guha, Sharmistha; Rodriguez-Acosta, Jose; Dinov, Ivo D (October 2024, Neuroinformatics)

   This article seeks to investigate the impact of aging on functional connectivity across different cognitive control scenarios, particularly emphasizing the identification of brain regions significantly associated with early aging. By conceptualizing functional connectivity within each cognitive control scenario as a graph, with brain regions as nodes, the statistical challenge revolves around devising a regression framework to predict a binary scalar outcome (aging or normal) using multiple graph predictors. Popular regression methods utilizing multiplex graph predictors often face limitations in effectively harnessing information within and across graph layers, leading to potentially less accurate inference and predictive accuracy, especially for smaller sample sizes. To address this challenge, we propose the Bayesian Multiplex Graph Classifier (BMGC). Accounting for multiplex graph topology, our method models edge coefficients at each graph layer using bilinear interactions between the latent effects associated with the two nodes connected by the edge. This approach also employs a variable selection framework on node-specific latent effects from all graph layers to identify influential nodes linked to observed outcomes. Crucially, the proposed framework is computationally efficient and quantifies the uncertainty in node identification, coefficient estimation, and binary outcome prediction. BMGC outperforms alternative methods in terms of the aforementioned metrics in simulation studies. An additional BMGC validation was completed using an fMRI study of brain networks in adults. The proposed BMGC technique identified that sensory motor brain network obeys certain lateral symmetries, whereas the default mode network exhibits significant brain asymmetries associated with early aging. 

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3. Bayesian Proper Orthogonal Decomposition for Learnable Reduced-Order Models with Uncertainty Quantification

   https://doi.org/10.1109/TAI.2023.3268609  

   Boluki, Shahin; Dadaneh, Siamak Zamani; Dougherty, Edward R.; Qian, Xiaoning (January 2023, IEEE Transactions on Artificial Intelligence)

   Designing and/or controlling complex systems in science and engineering relies on appropriate mathematical modeling of systems dynamics. Classical differential equation based solutions in applied and computational mathematics are often computationally demanding. Recently, the connection between reduced-order models of high-dimensional differential equation systems and surrogate machine learning models has been explored. However, the focus of both existing reduced-order and machine learning models for complex systems has been how to best approximate the high fidelity model of choice. Due to high complexity and often limited training data to derive reduced-order or machine learning surrogate models, it is critical for derived reduced-order models to have reliable uncertainty quantification at the same time. In this paper, we propose such a novel framework of Bayesian reduced-order models naturally equipped with uncertainty quantification as it learns the distributions of the parameters of the reduced-order models instead of their point estimates. In particular, we develop learnable Bayesian proper orthogonal decomposition (BayPOD) that learns the distributions of both the POD projection bases and the mapping from the system input parameters to the projected scores/coefficients so that the learned BayPOD can help predict high-dimensional systems dynamics/fields as quantities of interest in different setups with reliable uncertainty estimates. The developed learnable BayPOD inherits the capability of embedding physics constraints when learning the POD-based surrogate reduced-order models, a desirable feature when studying complex systems in science and engineering applications where the available training data are limited. Furthermore, the proposed BayPOD method is an end-to-end solution, which unlike other surrogate-based methods, does not require separate POD and machine learning steps. The results from a real-world case study of the pressure field around an airfoil. 

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4. Reliable Confidence Intervals for RelTime Estimates of Evolutionary Divergence Times

   https://doi.org/10.1093/molbev/msz236  

   Tao, Qiqing; Tamura, Koichiro; Mello, Beatriz; Kumar, Sudhir (October 2019, Molecular Biology and Evolution)

   Su, Bing (Ed.)

   Abstract Confidence intervals (CIs) depict the statistical uncertainty surrounding evolutionary divergence time estimates. They capture variance contributed by the finite number of sequences and sites used in the alignment, deviations of evolutionary rates from a strict molecular clock in a phylogeny, and uncertainty associated with clock calibrations. Reliable tests of biological hypotheses demand reliable CIs. However, current non-Bayesian methods may produce unreliable CIs because they do not incorporate rate variation among lineages and interactions among clock calibrations properly. Here, we present a new analytical method to calculate CIs of divergence times estimated using the RelTime method, along with an approach to utilize multiple calibration uncertainty densities in dating analyses. Empirical data analyses showed that the new methods produce CIs that overlap with Bayesian highest posterior density intervals. In the analysis of computer-simulated data, we found that RelTime CIs show excellent average coverage probabilities, that is, the actual time is contained within the CIs with a 94% probability. These developments will encourage broader use of computationally efficient RelTime approaches in molecular dating analyses and biological hypothesis testing. 

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5. Towards Unifying Feature Attribution and Counterfactual Explanations: Different Means to the Same End

   https://doi.org/10.1145/3461702.3462597  

   Kommiya Mothilal, Ramaravind; Mahajan, Divyat; Tan, Chenhao; Sharma, Amit (May 2021, Proceedings of the 2021 AAAI/ACM Conference on AI, Ethics, and Society)

   null (Ed.)

   Feature attributions and counterfactual explanations are popular approaches to explain a ML model. The former assigns an importance score to each input feature, while the latter provides input examples with minimal changes to alter the model's predictions. To unify these approaches, we provide an interpretation based on the actual causality framework and present two key results in terms of their use. First, we present a method to generate feature attribution explanations from a set of counterfactual examples. These feature attributions convey how important a feature is to changing the classification outcome of a model, especially on whether a subset of features is necessary and/or sufficient for that change, which attribution-based methods are unable to provide. Second, we show how counterfactual examples can be used to evaluate the goodness of an attribution-based explanation in terms of its necessity and sufficiency. As a result, we highlight the complimentary of these two approaches. Our evaluation on three benchmark datasets --- Adult-Income, LendingClub, and German-Credit --- confirms the complimentary. Feature attribution methods like LIME and SHAP and counterfactual explanation methods like Wachter et al. and DiCE often do not agree on feature importance rankings. In addition, by restricting the features that can be modified for generating counterfactual examples, we find that the top-k features from LIME or SHAP are often neither necessary nor sufficient explanations of a model's prediction. Finally, we present a case study of different explanation methods on a real-world hospital triage problem. 

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