Nonlocal, integral operators have become an efficient surrogate for bottom-up homogenization, due to their ability to represent long-range dependence and multiscale effects. However, the nonlocal homogenized model has unavoidable discrepancy from the microscale model. Such errors accumulate and propagate in long-term simulations, making the resultant prediction unreliable. To develop a robust and reliable bottom-up homogenization framework, we propose a new framework, which we coin Embedded Nonlocal Operator Regression (ENOR), to learn a nonlocal homogenized surrogate model and its structural model error. This framework provides discrepancy-adaptive uncertainty quantification for homogenized material response predictions in long-term simulations. The method is built on Nonlocal Operator Regression (NOR), an optimization-based nonlocal kernel learning approach, together with an embedded model error term in the trainable kernel. Then, Bayesian inference is employed to infer the model error term parameters together with the kernel parameters. To make the problem computationally feasible, we use a multilevel delayed acceptance Markov chain Monte Carlo (MLDA-MCMC) method, enabling efficient Bayesian model calibration and model error estimation. We apply this technique to predict long-term wave propagation in a heterogeneous one-dimensional bar, and compare its performance with additive noise models. Owing to its ability to capture model error, the learned ENOR achieves improved estimation of posterior predictive uncertainty.

Discovering the underlying Directed Acyclic Graph (DAG) from time series observational data is highly challenging due to the dynamic nature and complex nonlinear interactions between variables. Existing methods often struggle with inefficiency and the handling of high-dimensional data. To address these research gap, we propose LOCAL, a highly efficient, easy-to-implement, and constraint-free method for recovering dynamic causal structures. LOCAL is the first attempt to formulate a quasi-maximum likelihood-based score function for learning the dynamic DAG equivalent to the ground truth. On this basis, we propose two adaptive modules for enhancing the algebraic characterization of acyclicity with new capabilities: Asymptotic Causal Mask Learning (ACML) and Dynamic Graph Parameter Learning (DGPL). ACML generates causal masks using learnable priority vectors and the Gumbel-Sigmoid function, ensuring the creation of DAGs while optimizing computational efficiency. DGPL transforms causal learning into decomposed matrix products, capturing the dynamic causal structure of high-dimensional data and enhancing interpretability. Extensive experiments on synthetic and real-world datasets demonstrate that LOCAL significantly outperforms existing methods, and highlight LOCAL's potential as a robust and efficient method for dynamic causal discovery. Our code will be available soon.

This study explores the limitations of image-based structural health monitoring (SHM) techniques in detecting structural damage. Leveraging machine learning and computer vision, image-based SHM offers a scalable and efficient alternative to manual inspections. However, its reliability is impacted by challenges such as false positives, false negatives, and environmental variability, particularly in low base rate damage scenarios. The Base Rate Bias plays a significant role, as low probabilities of actual damage often lead to misinterpretation of positive results. This study uses both Bayesian analysis and a frequentist approach to evaluate the precision of damage detection systems, revealing that even highly accurate models can yield misleading results when the occurrence of damage is rare. Strategies for mitigating these limitations are discussed, including hybrid systems that combine multiple data sources, human-in-the-loop approaches for critical assessments, and improving the quality of training data. These findings provide essential insights into the practical applicability of image-based SHM techniques, highlighting both their potential and their limitations for real-world infrastructure monitoring.

Exemplar-Free Class Incremental Learning (EFCIL) tackles the problem of training a model on a sequence of tasks without access to past data. Existing state-of-the-art methods represent classes as Gaussian distributions in the feature extractor's latent space, enabling Bayes classification or training the classifier by replaying pseudo features. However, we identify two critical issues that compromise their efficacy when the feature extractor is updated on incremental tasks. First, they do not consider that classes' covariance matrices change and must be adapted after each task. Second, they are susceptible to a task-recency bias caused by dimensionality collapse occurring during training. In this work, we propose AdaGauss -- a novel method that adapts covariance matrices from task to task and mitigates the task-recency bias owing to the additional anti-collapse loss function. AdaGauss yields state-of-the-art results on popular EFCIL benchmarks and datasets when training from scratch or starting from a pre-trained backbone. The code is available at: https://github.com/grypesc/AdaGauss.

Bayesian Additive Regression Trees (BART) is a nonparametric Bayesian regression technique of rising fame. It is a sum-of-decision-trees model, and is in some sense the Bayesian version of boosting. In the limit of infinite trees, it becomes equivalent to Gaussian process (GP) regression. This limit is known but has not yet led to any useful analysis or application. For the first time, I derive and compute the exact BART prior covariance function. With it I implement the infinite trees limit of BART as GP regression. Through empirical tests, I show that this limit is worse than standard BART in a fixed configuration, but also that tuning the hyperparameters in the natural GP way yields a competitive method, although a properly tuned BART is still superior. The advantage of using a GP surrogate of BART is the analytical likelihood, which simplifies model building and sidesteps the complex BART MCMC. More generally, this study opens new ways to understand and develop BART and GP regression. The implementation of BART as GP is available in the Python package https://github.com/Gattocrucco/lsqfitgp .

Causal discovery is a fundamental problem with applications spanning various areas in science and engineering. It is well understood that solely using observational data, one can only orient the causal graph up to its Markov equivalence class, necessitating interventional data to learn the complete causal graph. Most works in the literature design causal discovery policies with perfect interventions, i.e., they have access to infinite interventional samples. This study considers a Bayesian approach for learning causal graphs with limited interventional samples, mirroring real-world scenarios where such samples are usually costly to obtain. By leveraging the recent result of Wien\"obst et al. (2023) on uniform DAG sampling in polynomial time, we can efficiently enumerate all the cut configurations and their corresponding interventional distributions of a target set, and further track their posteriors. Given any number of interventional samples, our proposed algorithm randomly intervenes on a set of target vertices that cut all the edges in the graph and returns a causal graph according to the posterior of each target set. When the number of interventional samples is large enough, we show theoretically that our proposed algorithm will return the true causal graph with high probability. We compare our algorithm against various baseline methods on simulated datasets, demonstrating its superior accuracy measured by the structural Hamming distance between the learned DAG and the ground truth. Additionally, we present a case study showing how this algorithm could be modified to answer more general causal questions without learning the whole graph. As an example, we illustrate that our method can be used to estimate the causal effect of a variable that cannot be intervened.

Over the past few years, several approaches utilizing score-based diffusion have been proposed to sample from probability distributions, that is without having access to exact samples and relying solely on evaluations of unnormalized densities. In practice, the performance of these methods heavily depends on key hyperparameters that require ground truth samples to be accurately tuned. Our work aims to highlight and address this fundamental issue, focusing in particular on multimodal distributions, which pose significant challenges for existing sampling methods. Building on existing approaches, we introduce Learned Reference-based Diffusion Sampler (LRDS), a methodology specifically designed to leverage prior knowledge on the location of the target modes in order to bypass the obstacle of hyperparameter tuning. LRDS proceeds in two steps by (i) learning a reference diffusion model on samples located in high-density space regions and tailored for multimodality, and (ii) using this reference model to foster the training of a diffusion-based sampler. We experimentally demonstrate that LRDS best exploits prior knowledge on the target distribution compared to competing algorithms on a variety of challenging distributions. We consider the problem of sampling from a probability density known up to a normalizing constant. In particular, we are interested in sampling from multimodal distributions, i.e., distributions whose density admits multiple local maxima, called modes. Finding the modes of such distributions is a notoriously hard problem, yet, maybe surprisingly, even if the location of the modes is known, sampling π remains a very challenging problem (Noé et al., 2019; Pompe et al., 2020; Grenioux et al., 2023). In this work, we aim to address this specific issue and will assume that we have access to the location of the modes as prior information on π. However, we do not assume to have access a priori to ground truth samples from π. Annealed MCMC. Markov Chain Monte Carlo (MCMC) samplers are among the most popular approaches for sampling. In particular, gradient-based methods based on discretizations of Langevin or Hamiltonian dynamics (Roberts & Tweedie, 1996; Neal, 2012; Hoffman & Gelman, 2014) are guaranteed to be efficient for high-dimensional target distributions that are log-concave or satisfy or functional inequalities (Dalalyan, 2017; Durmus & Moulines, 2017).

Home robots performing personalized tasks must adeptly balance user preferences with environmental affordances. We focus on organization tasks within constrained spaces, such as arranging items into a refrigerator, where preferences for placement collide with physical limitations. The robot must infer user preferences based on a small set of demonstrations, which is easier for users to provide than extensively defining all their requirements. While recent works use Large Language Models (LLMs) to learn preferences from user demonstrations, they encounter two fundamental challenges. First, there is inherent ambiguity in interpreting user actions, as multiple preferences can often explain a single observed behavior. Second, not all user preferences are practically feasible due to geometric constraints in the environment. To address these challenges, we introduce APRICOT, a novel approach that merges LLM-based Bayesian active preference learning with constraint-aware task planning. APRICOT refines its generated preferences by actively querying the user and dynamically adapts its plan to respect environmental constraints. We evaluate APRICOT on a dataset of diverse organization tasks and demonstrate its effectiveness in real-world scenarios, showing significant improvements in both preference satisfaction and plan feasibility. The project website is at https://portal-cornell.github.io/apricot/

Agent-Based Model (ABM) validation is crucial as it helps ensuring the reliability of simulations, and causal discovery has become a powerful tool in this context. However, current causal discovery methods often face accuracy and robustness challenges when applied to complex and noisy time series data, which is typical in ABM scenarios. This study addresses these issues by proposing a Robust Cross-Validation (RCV) approach to enhance causal structure learning for ABM validation. We develop RCV-VarLiNGAM and RCV-PCMCI, novel extensions of two prominent causal discovery algorithms. These aim to reduce the impact of noise better and give more reliable causal relation results, even with high-dimensional, time-dependent data. The proposed approach is then integrated into an enhanced ABM validation framework, which is designed to handle diverse data and model structures. The approach is evaluated using synthetic datasets and a complex simulated fMRI dataset. The results demonstrate greater reliability in causal structure identification. The study examines how various characteristics of datasets affect the performance of established causal discovery methods. These characteristics include linearity, noise distribution, stationarity, and causal structure density. This analysis is then extended to the RCV method to see how it compares in these different situations. This examination helps confirm whether the results are consistent with existing literature and also reveals the strengths and weaknesses of the novel approaches. By tackling key methodological challenges, the study aims to enhance ABM validation with a more resilient valuation framework presented. These improvements increase the reliability of model-driven decision making processes in complex systems analysis.

We are interested in studying how heterogeneous agents can learn to communicate and cooperate with each other without being explicitly pre-programmed to do so. Motivated by this goal, we present and analyze a distributed solution to a two-player signaler-responder game which is defined as follows. The signaler agent has a random, exogenous need and can choose from four different strategies: never signal, always signal, signal when need, and signal when no need. The responder agent can choose to either ignore or respond to the signal. We define a reward to both agents when they cooperate to satisfy the signaler's need, and costs associated with communication, response and unmet needs. We identify pure Nash equilibria of the game and the conditions under which they occur. As a solution for this game, we propose two new distributed Bayesian learning algorithms, one for each agent, based on the classic Thompson Sampling policy for multi-armed bandits. These algorithms allow both agents to update beliefs about both the exogenous need and the behavior of the other agent and optimize their own expected reward. We show that by using these policies, the agents are able to intelligently adapt their strategies over multiple iterations to attain efficient, reward-maximizing equilibria under different settings, communicating and cooperating when it is rewarding to do so, and not communicating or cooperating when it is too expensive.