Related papers: A General $\mathcal{O}(n^2)$ Hyper-Parameter Optim…

We present a new polynomial-free prolongation scheme for Adaptive Mesh Refinement (AMR) simulations of compressible and incompressible computational fluid dynamics. The new method is constructed using a multi-dimensional kernel-based…

We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…

Regularization is a popular technique in machine learning for model estimation and avoiding overfitting. Prior studies have found that modern ordered regularization can be more effective in handling highly correlated, high-dimensional data…

Distributed optimization is fundamental to large-scale machine learning and control applications. Among existing methods, the alternating direction method of multipliers (ADMM) has gained popularity due to its strong convergence guarantees…

Gaussian processes (GPs) are non-linear probabilistic models popular in many applications. However, na\"ive GP realizations require quadratic memory to store the covariance matrix and cubic computation to perform inference or evaluate the…

Multi-robot systems require scalable and federated methods to model complex environments under computational and communication constraints. Gaussian Processes (GPs) offer robust probabilistic modeling, but suffer from cubic computational…

The asymptotic optimality (a.o.) of various hyper-parameter estimators with different optimality criteria has been studied in the literature for regularized least squares regression problems. The estimators include e.g., the maximum…

The recent emergence of deep learning has led to a great deal of work on designing supervised deep semantic segmentation algorithms. As in many tasks sufficient pixel-level labels are very difficult to obtain, we propose a method which…

Model selection in Gaussian processes scales prohibitively with the size of the training dataset, both in time and memory. While many approximations exist, all incur inevitable approximation error. Recent work accounts for this error in the…

Gaussian process (GP) regression is a powerful probabilistic modeling technique with built-in uncertainty quantification. When one has access to multiple correlated simulations (tasks), it is common to fit a multitask GP (MTGP) surrogate…

Alternating Direction Method of Multipliers (ADMM) has recently been proposed as a potential alternative optimizer to the Stochastic Gradient Descent(SGD) for deep learning problems. This is because ADMM can solve gradient vanishing and…

Sequential learning with Gaussian processes (GPs) is challenging when access to past data is limited, for example, in continual and active learning. In such cases, errors can accumulate over time due to inaccuracies in the posterior,…

When the data are sparse, optimization of hyperparameters of the kernel in Gaussian process regression by the commonly used maximum likelihood estimation (MLE) criterion often leads to overfitting. We show that choosing hyperparameters (in…

We propose a distributed nonparametric algorithm for solving measure-valued optimization problems with additive objectives. Such problems arise in several contexts in stochastic learning and control including Langevin sampling from an…

This work is a part of ICLR Reproducibility Challenge 2019, we try to reproduce the results in the conference submission PADAM: Closing The Generalization Gap of Adaptive Gradient Methods In Training Deep Neural Networks. Adaptive gradient…

Although Gaussian processes (GPs) with deep kernels have been successfully used for meta-learning in regression tasks, its uncertainty estimation performance can be poor. We propose a meta-learning method for calibrating deep kernel GPs for…

Data-driven Model Predictive Control (MPC), where the system model is learned from data with machine learning, has recently gained increasing interests in the control community. Gaussian Processes (GP), as a type of statistical models, are…

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…

Gaussian processes (GPs) are flexible non-parametric models, with a capacity that grows with the available data. However, computational constraints with standard inference procedures have limited exact GPs to problems with fewer than about…

We propose a novel sparse spectrum approximation of Gaussian process (GP) tailored for Bayesian optimization. Whilst the current sparse spectrum methods provide desired approximations for regression problems, it is observed that this…