Related papers: Mean Nystr\"om Embeddings for Adaptive Compressive…

This paper deals with the speed of convergence of the learning curve in a Gaussian process regression framework. The learning curve describes the average generalization error of the Gaussian process used for the regression. More…

This paper presents a novel information-theoretic perspective on generalization in machine learning by framing the learning problem within the context of lossy compression and applying finite blocklength analysis. In our approach, the…

In Programming by Demonstration, the robot learns novel skills from human demonstrations. After learning, the robot should be able not only to reproduce the skill, but also to generalize it to shifted domains without collecting new training…

We study prediction and estimation problems using empirical risk minimization, relative to a general convex loss function. We obtain sharp error rates even when concentration is false or is very restricted, for example, in heavy-tailed…

Active learning parallelization is widely used, but typically relies on fixing the batch size throughout experimentation. This fixed approach is inefficient because of a dynamic trade-off between cost and speed -- larger batches are more…

A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…

In this paper, we address learning problems for high dimensional data. Previously, oblivious random projection based approaches that project high dimensional features onto a random subspace have been used in practice for tackling…

For a tall $n\times d$ matrix $A$ and a random $m\times n$ sketching matrix $S$, the sketched estimate of the inverse covariance matrix $(A^\top A)^{-1}$ is typically biased: $E[(\tilde A^\top\tilde A)^{-1}]\ne(A^\top A)^{-1}$, where…

In this paper, we investigate effective sketching schemes via sparsification for high dimensional multilinear arrays or tensors. More specifically, we propose a novel tensor sparsification algorithm that retains a subset of the entries of a…

We establish a general form of explicit, input-dependent, measure-valued warpings for learning nonstationary kernels. While stationary kernels are ubiquitous and simple to use, they struggle to adapt to functions that vary in smoothness…

We consider least-squares problems with quadratic regularization and propose novel sketching-based iterative methods with an adaptive sketch size. The sketch size can be as small as the effective dimension of the data matrix to guarantee…

The problem of adaptive noisy clustering is investigated. Given a set of noisy observations $Z_i=X_i+\epsilon_i$, $i=1,...,n$, the goal is to design clusters associated with the law of $X_i$'s, with unknown density $f$ with respect to the…

The simulation of complex nonlinear engineering systems such as compressible fluid flows may be targeted to make more efficient and accurate the approximation of a specific (scalar) quantity of interest of the system. Putting aside modeling…

Data availability has dramatically increased in recent years, driving model-based control methods to exploit learning techniques for improving the system description, and thus control performance. Two key factors that hinder the practical…

This paper studies transfer learning for estimating the mean of random functions based on discretely sampled data, where, in addition to observations from the target distribution, auxiliary samples from similar but distinct source…

Nonparametric learning is a fundamental concept in machine learning that aims to capture complex patterns and relationships in data without making strong assumptions about the underlying data distribution. Owing to simplicity and…

In multi-objective optimization, multiple loss terms are weighted and added together to form a single objective. These weights are chosen to properly balance the competing losses according to some meta-goal. For example, in physics-informed…

In this paper we study constrained subspace approximation problem. Given a set of $n$ points $\{a_1,\ldots,a_n\}$ in $\mathbb{R}^d$, the goal of the {\em subspace approximation} problem is to find a $k$ dimensional subspace that best…

Preventing catastrophic forgetting while continually learning new tasks is an essential problem in lifelong learning. Structural regularization (SR) refers to a family of algorithms that mitigate catastrophic forgetting by penalizing the…

In this paper, we propose a randomly projected convex clustering model for clustering a collection of $n$ high dimensional data points in $\mathbb{R}^d$ with $K$ hidden clusters. Compared to the convex clustering model for clustering…