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Extracting compact, physically interpretable representations from high-dimensional scientific data is a persistent challenge due to the complex, nonlinear structures inherent in physical systems. We propose a Gaussian Mixture Variational…

Logic-Geometric Programming (LGP) is a powerful motion and manipulation planning framework, which represents hierarchical structure using logic rules that describe discrete aspects of problems, e.g., touch, grasp, hit, or push, and solves…

Latent manifolds provide a compact characterization of neural population activity and of shared co-variability across brain areas. Nonetheless, existing statistical tools for extracting neural manifolds face limitations in terms of…

Gaussian processes (GPs) are widely used for regression and optimization tasks such as Bayesian optimization (BO) due to their expressiveness and principled uncertainty estimates. However, in settings with large datasets corrupted by…

Gaussian graphical models (GGM) have been widely used in many high-dimensional applications ranging from biological and financial data to recommender systems. Sparsity in GGM plays a central role both statistically and computationally.…

In this work, a Gaussian process regression(GPR) model incorporated with given physical information in partial differential equations(PDEs) is developed: physics-assisted Gaussian processes(PAGP). The targets of this model can be divided…

This study utilized the Gaussian Processes (GPs) regression framework to establish stochastic error bounds between the actual and predicted state evolution of nonlinear systems. These systems are embedded in the linear parameter-varying…

Machine learning based solvers have garnered much attention in physical simulation and scientific computing, with a prominent example, physics-informed neural networks (PINNs). However, PINNs often struggle to solve high-frequency and…

We introduce a novel stochastic variational inference method for Gaussian process ($\mathcal{GP}$) regression, by deriving a posterior over a learnable set of coresets: i.e., over pseudo-input/output, weighted pairs. Unlike former free-form…

Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…

Estimating covariances between financial assets plays an important role in risk management. In practice, when the sample size is small compared to the number of variables, the empirical estimate is known to be very unstable. Here, we…

This work presents an efficient framework to generate a motion plan of a robot with high degrees of freedom (e.g., a humanoid robot). High-dimensionality of the robot configuration space often leads to difficulties in utilizing the…

Learning uncertain dynamics models using Gaussian process~(GP) regression has been demonstrated to enable high-performance and safety-aware control strategies for challenging real-world applications. Yet, for computational tractability,…

Gaussian processes (GPs) are important models in supervised machine learning. Training in Gaussian processes refers to selecting the covariance functions and the associated parameters in order to improve the outcome of predictions, the core…

A common problem in neuroscience is to elucidate the collective neural representations of behaviorally important variables such as head direction, spatial location, upcoming movements, or mental spatial transformations. Often, these latent…

In this letter, we present a novel Gaussian Process Learning-based Probabilistic Optimal Power Flow (GP-POPF) for solving POPF under renewable and load uncertainties of arbitrary distribution. The proposed method relies on a non-parametric…

Gaussian processes provide a compact representation for modeling and estimating an unknown function, that can be updated as new measurements of the function are obtained. This paper extends this powerful framework to the case where the…

Gaussian processes (GPs) are nonparametric priors over functions. Fitting a GP implies computing a posterior distribution of functions consistent with the observed data. Similarly, deep Gaussian processes (DGPs) should allow us to compute a…

We introduce a methodology for nonlinear inverse problems using a variational Bayesian approach where the unknown quantity is a spatial field. A structured Bayesian Gaussian process latent variable model is used both to construct a…

In sensing applications, sensors cannot always measure the latent quantity of interest at the required resolution, sometimes they can only acquire a blurred version of it due the sensor's transfer function. To recover latent signals when…