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Free, publicly-accessible full text available July 11, 2025
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Free, publicly-accessible full text available December 13, 2024
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Free, publicly-accessible full text available December 11, 2024
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Graph-guided learning has well-documented impact in a gamut of network science applications. A prototypical graph-guided learning task deals with semi-supervised learning over graphs, where the goal is to predict the nodal values or labels of unobserved nodes, by leveraging a few nodal observations along with the underlying graph structure. This is particularly challenging under privacy constraints or generally when acquiring nodal observations incurs high cost. In this context, the present work puts forth a Bayesian graph-driven self-supervised learning (Self-SL) approach that: (i) learns powerful nodal embeddings emanating from easier to solve auxiliary tasks that map local to global connectivity information; and, (ii) adopts an ensemble of Gaussian processes (EGPs) with adaptive weights as nodal embeddings are processed online. Unlike most existing deterministic approaches, the novel approach offers accurate estimates of the unobserved nodal values along with uncertainty quantification that is important especially in safety critical applications. Numerical tests on synthetic and real graph datasets showcase merits of the novel EGP-based Self-SL method.more » « lessFree, publicly-accessible full text available December 10, 2024
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Bayesian optimization (BO) has well-documented merits for optimizing black-box functions with an expensive evaluation cost. Such functions emerge in applications as diverse as hyperparameter tuning, drug discovery, and robotics. BO hinges on a Bayesian surrogate model to sequentially select query points so as to balance exploration with exploitation of the search space. Most existing works rely on a single Gaussian process (GP) based surrogate model, where the kernel function form is typically preselected using domain knowledge. To bypass such a design process, this paper leverages an ensemble (E) of GPs to adaptively select the surrogate model fit on-the-fly, yielding a GP mixture posterior with enhanced expressiveness for the sought function. Acquisition of the next evaluation input using this EGP-based function posterior is then enabled by Thompson sampling (TS) that requires no additional design parameters. To endow function sampling with scalability, random feature-based kernel approximation is leveraged per GP model. The novel EGP-TS readily accommodates parallel operation. To further establish convergence of the proposed EGP-TS to the global optimum, analysis is conducted based on the notion of Bayesian regret for both sequential and parallel settings. Tests on synthetic functions and real-world applications showcase the merits of the proposed method.more » « less
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Optimizing a black-box function that is expensive to evaluate emerges in a gamut of machine learning and artifcial intelligence applications including drug discovery, policy optimization in robotics, and hyperparameter tuning of learning models to list a few. Bayesian optimization (BO) provides a principled framework to fnd the global optimum of such functions using a limited number of function evaluations. BO relies on a statistical surrogate model to actively select new query points, that is typically captured by a Gaussian process (GP). Unlike most existing approaches that hinge on a single GP surrogate model with a pre-selected kernel function that may confne the expressiveness of the sought function especially under the limited evaluation budget, the present work puts forth a weighted ensemble of GPs as a surrogate model. Building on the advocated Gaussian mixture (GM) posterior, the EGP framework adapts to the most ftted surrogate model as data arrive on-the-fy, offering a richer function space. For the acquisition of next evaluation points, the EGP-based posterior is coupled with an adaptive expected improvement (EI) criterion to balance exploration and exploitation of the search space. Numerical tests on a set of benchmark synthetic functions and two robotic tasks, demonstrate the impressive benefts of the proposed approach.more » « less
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Assessing set-membership and evaluating distances to the related set boundary are problems of widespread interest, and can often be computationally challenging. Seeking efficient learning models for such tasks, this paper deals with voltage stability margin prediction for power systems. Supervised training of such models is conventionally hard due to high-dimensional feature space, and a cumbersome label-generation process. Nevertheless, one may find related easy auxiliary tasks, such as voltage stability verification, that can aid in training for the hard task. This paper develops a novel approach for such settings by leveraging transfer learning. A Gaussian process-based learning model is efficiently trained using learning- and physics-based auxiliary tasks. Numerical tests demonstrate markedly improved performance that is harnessed alongside the benefit of uncertainty quantification to suit the needs of the considered application.more » « less
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Graph-guided semi-supervised learning (SSL) has gained popularity in several network science applications, including biological, social, and financial ones. SSL becomes particularly challenging when the available nodal labels are scarce, what motivates naturally the active learning (AL) paradigm. AL seeks the most informative nodes to label in order to effectively estimate the nodal values of unobserved nodes. It is also referred to as active sampling, and boils down to learning the sought function mapping, and an acquisition function (AF) to identify the next node(s) to sample. To learn the mapping, this work leverages an adaptive Bayesian model comprising an ensemble (E) of Gaussian Processes (GPs) with enhanced expressiveness of the function space. Unlike most alternatives, the EGP model relies only on the one-hop connectivity of each node. Capitalizing on this EGP model, a suite of novel and intuitive AFs are developed to guide the active sampling process. These AFs are then combined with weights that are adapted incrementally to further robustify performance. Numerical tests on real and synthetic datasets corroborate the merits of the novel methods.more » « less