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We consider the use of Gaussian process (GP) priors for solving inverse problems in a Bayesian framework. As is well known, the computational complexity of GPs scales cubically in the number of datapoints. We here show that in the context…

Real-time trajectory optimization for nonlinear constrained autonomous systems is critical and typically performed by CPU-based sequential solvers. Specifically, reliance on global sparse linear algebra or the serial nature of dynamic…

The study of biological systems witnessed a pervasive cross-fertilization between experimental investigation and computational methods. This gave rise to the development of new methodologies, able to tackle the complexity of biological…

Last several years, GPUs are used to accelerate computations in many computer science domains. We focused on GPU accelerated Support Vector Machines (SVM) training with non-linear kernel functions. We had searched for all available GPU…

Bayesian spatial modeling provides a flexible framework for whole-brain fMRI analysis by explicitly incorporating spatial dependencies, overcoming the limitations of traditional massive univariate approaches that lead to information waste.…

In recent years, the Hamiltonian Monte Carlo (HMC) algorithm has been found to work more efficiently compared to other popular Markov Chain Monte Carlo (MCMC) methods (such as random walk Metropolis-Hastings) in generating samples from a…

This dissertation presents the design, implementation and evaluation of GPU-accelerated simulation frameworks for Evolutionary Spatial Cyclic Games (ESCGs), a class of agent-based models used to study ecological and evolutionary dynamics.…

Modeling data sharing in GPU programs is a challenging task because of the massive parallelism and complex data sharing patterns provided by GPU architectures. Better GPU caching efficiency can be achieved through careful task scheduling…

Large spatial datasets with non-Gaussian responses are increasingly common in environmental monitoring, ecology, and remote sensing, yet scalable Bayesian inference for such data remains challenging. Markov chain Monte Carlo (MCMC) methods…

Block iterative methods are extremely important as smoothers for multigrid methods, as preconditioners for Krylov methods, and as solvers for diagonally dominant linear systems. Developing robust and efficient algorithms suitable for…

We introduce a GPU-accelerated Monte Carlo framework for nonconvex, free-final-time trajectory optimization problems. This framework makes use of the prox-linear method, which belongs to the larger family of sequential convex programming…

We present high performance implementations of the QR and the singular value decomposition of a batch of small matrices hosted on the GPU with applications in the compression of hierarchical matrices. The one-sided Jacobi algorithm is used…

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,…

Meta-learning is a powerful approach that exploits historical data to quickly solve new tasks from the same distribution. In the low-data regime, methods based on the closed-form posterior of Gaussian processes (GP) together with Bayesian…

We propose efficient computational methods to fit multivariate Gaussian additive models, where the mean vector and the covariance matrix are allowed to vary with covariates, in an empirical Bayes framework. To guarantee the…

Bayesian methods for learning Gaussian graphical models offer a principled framework for quantifying model uncertainty and incorporating prior knowledge. However, their scalability is constrained by the computational cost of jointly…

In this work, we study scaling limits of shallow Bayesian neural networks (BNNs) via their connection to Gaussian processes (GPs), with an emphasis on statistical modeling, identifiability, and scalable inference. We first establish a…

Gaussian processes (GP) are a well studied Bayesian approach for the optimization of black-box functions. Despite their effectiveness in simple problems, GP-based algorithms hardly scale to high-dimensional functions, as their per-iteration…

Gaussian process are a widely-used statistical tool for conducting non-parametric inference in applied sciences, with many computational packages available to fit to data and predict future observations. We study the use of the Greta…

Stochastic gradient descent (SGD) is a widely adopted iterative method for optimizing differentiable objective functions. In this paper, we propose and discuss a novel approach to scale up SGD in applications involving non-convex functions…