Causal discovery can be computationally demanding for large numbers of variables. If we only wish to estimate the causal effects on a small subset of target variables, we might not need to learn the causal graph for all variables, but only a small subgraph that includes the targets and their adjustment sets. In this paper, we focus on identifying causal effects between target variables in a computationally and statistically efficient way. This task combines causal discovery and effect estimation, aligning the discovery objective with the effects to be estimated. We show that definite non-ancestors of the targets are unnecessary to learn causal relations between the targets and to identify efficient adjustments sets. We sequentially identify and prune these definite non-ancestors with our Sequential Non-Ancestor Pruning (SNAP) framework, which can be used either as a preprocessing step to standard causal discovery methods, or as a standalone sound and complete causal discovery algorithm. Our results on synthetic and real data show that both approaches substantially reduce the number of independence tests and the computation time without compromising the quality of causal effect estimations.

Minimizing the inclusive Kullback-Leibler (KL) divergence with stochastic gradient descent (SGD) is challenging since its gradient is defined as an integral over the posterior. Recently, multiple methods have been proposed to run SGD with biased gradient estimates obtained from a Markov chain. This paper provides the first non-asymptotic convergence analysis of these methods by establishing their mixing rate and gradient variance. To do this, we demonstrate that these methods-which we collectively refer to as Markov chain score ascent (MCSA) methods-can be cast as special cases of the Markov chain gradient descent framework. Furthermore, by leveraging this new understanding, we develop a novel MCSA scheme, parallel MCSA (pMCSA), that achieves a tighter bound on the gradient variance. We demonstrate that this improved theoretical result translates to superior empirical performance.

Stochastic variational inference (SVI) uses stochastic optimization to scale up Bayesian computation to massive data. We present an alternative perspective on SVI as approximate parallel coordinate ascent. SVI trades-off bias and variance to step close to the unknown true coordinate optimum given by batch variational Bayes (VB). We define a model to automate this process.

It was recently proved using graph covers (Ruozzi, 2012) that the Bethe partition function is upper bounded by the true partition function for a binary pairwise model that is attractive. Here we provide a new, arguably simpler proof from first principles. We make use of the idea of clamping a variable to a particular value. For an attractive model, we show that summing over the Bethe partition functions for each sub-model obtained after clamping any variable can only raise (and hence improve) the approximation. In fact, we derive a stronger result that may have other useful implications. Repeatedly clamping until we obtain a model with no cycles, where the Bethe approximation is exact, yields the result. We also provide a related lower bound on a broad class of approximate partition functions of general pairwise multi-label models that depends only on the topology. We demonstrate that clamping a few wisely chosen variables can be of practical value by dramatically reducing approximation error.

In many problem settings, parameter vectors are not merely sparse, but dependent in such a way that non-zero coefficients tend to cluster together. We refer to this form of dependency as "region sparsity". Classical sparse regression methods, such as the lasso and automatic relevance determination (ARD), model parameters as independent a priori, and therefore do not exploit such dependencies. Here we introduce a hierarchical model for smooth, region-sparse weight vectors and tensors in a linear regression setting. Our approach represents a hierarchical extension of the relevance determination framework, where we add a transformed Gaussian process to model the dependencies between the prior variances of regression weights. We combine this with a structured model of the prior variances of Fourier coefficients, which eliminates unnecessary high frequencies. The resulting prior encourages weights to be region-sparse in two different bases simultaneously. We develop efficient approximate inference methods and show substantial improvements over comparable methods (e.g., group lasso and smooth RVM) for both simulated and real datasets from brain imaging.

The problem of f-divergence estimation is important in the fields of machine learning, information theory, and statistics. While several nonparametric divergence estimators exist, relatively few have known convergence properties. In particular, even for those estimators whose MSE convergence rates are known, the asymptotic distributions are unknown. We establish the asymptotic normality of a recently proposed ensemble estimator of f-divergence between two distributions from a finite number of samples.

Solving parametric partial differential equations (PDEs) and associated PDE-based, inverse problems is a central task in engineering and physics, yet existing neural operator methods struggle with high-dimensional, discontinuous inputs and require large amounts of {\em labeled} training data. We propose the Deep Generative Neural Operator (DGNO), a physics-aware framework that addresses these challenges by leveraging a deep, generative, probabilistic model in combination with a set of lower-dimensional, latent variables that simultaneously encode PDE-inputs and PDE-outputs. This formulation can make use of unlabeled data and significantly improves inverse problem-solving, particularly for discontinuous or discrete-valued input functions. DGNO enforces physics constraints without labeled data by incorporating as virtual observables, weak-form residuals based on compactly supported radial basis functions (CSRBFs). These relax regularity constraints and eliminate higher-order derivatives from the objective function. We also introduce MultiONet, a novel neural operator architecture, which is a more expressive generalization of the popular DeepONet that significantly enhances the approximating power of the proposed model. These innovations make DGNO particularly effective for challenging forward and inverse, PDE-based problems, such as those involving multi-phase media. Numerical experiments demonstrate that DGNO achieves higher accuracy across multiple benchmarks while exhibiting robustness to noise and strong generalization to out-of-distribution cases. Its adaptability, and the ability to handle sparse, noisy data while providing probabilistic estimates, make DGNO a powerful tool for scientific and engineering applications.

Hard computing generally deals with precise data, which provides ideal solutions to problems. However, in the civil engineering field, amongst other disciplines, that is not always the case as real-world systems are continuously changing. Here lies the need to explore soft computing methods and artificial intelligence to solve civil engineering shortcomings. The integration of advanced computational models, including Artificial Neural Networks (ANNs), Fuzzy Logic, Genetic Algorithms (GAs), and Probabilistic Reasoning, has revolutionized the domain of civil engineering. These models have significantly advanced diverse sub-fields by offering innovative solutions and improved analysis capabilities. Sub-fields such as: slope stability analysis, bearing capacity, water quality and treatment, transportation systems, air quality, structural materials, etc. ANNs predict non-linearities and provide accurate estimates. Fuzzy logic uses an efficient decision-making process to provide a more precise assessment of systems. Lastly, while GAs optimizes models (based on evolutionary processes) for better outcomes, probabilistic reasoning lowers their statistical uncertainties.

Model Predictive Control has emerged as a popular tool for robots to generate complex motions. However, the real-time requirement has limited the use of hard constraints and large preview horizons, which are necessary to ensure safety and stability. In practice, practitioners have to carefully design cost functions that can imitate an infinite horizon formulation, which is tedious and often results in local minima. In this work, we study how to approximate the infinite horizon value function of constrained optimal control problems with neural networks using value iteration and trajectory optimization. Furthermore, we demonstrate how using this value function approximation as a terminal cost provides global stability to the model predictive controller. The approach is validated on two toy problems and a real-world scenario with online obstacle avoidance on an industrial manipulator where the value function is conditioned to the goal and obstacle.

Geological Carbon Storage (GCS) is a key technology for achieving global climate goals by capturing and storing CO2 in deep geological formations. Its effectiveness and safety rely on accurate monitoring of subsurface CO2 migration using advanced time-lapse seismic imaging. A Digital Shadow framework integrates field data, including seismic and borehole measurements, to track CO2 saturation over time. Machine learning-assisted data assimilation techniques, such as generative AI and nonlinear ensemble Bayesian filtering, update a digital model of the CO2 plume while incorporating uncertainties in reservoir properties. Compared to 2D approaches, 3D monitoring enhances the spatial accuracy of GCS assessments, capturing the full extent of CO2 migration. This study extends the uncertainty-aware 2D Digital Shadow framework by incorporating 3D seismic imaging and reservoir modeling, improving decision-making and risk mitigation in CO2 storage projects.