Related papers: Gauge-optimal approximate learning for small data …

We propose a goal-oriented mesh-adaptive algorithm for a finite element method stabilized via residual minimization on dual discontinuous-Galerkin norms. By solving a saddle-point problem, this residual minimization delivers a stable…

We address the task of identifying densely connected subsets of multivariate Gaussian random variables within a graphical model framework. We propose two novel estimators based on the Ordered Weighted $\ell_1$ (OWL) norm: 1) The Graphical…

In machine learning, nonconvex optimization problems with multiple local optimums are often encountered. Graduated Optimization Algorithm (GOA) is a popular heuristic method to obtain global optimums of nonconvex problems through…

Constrained optimization problems can be difficult because their search spaces have properties not conducive to search, e.g., multimodality, discontinuities, or deception. To address such difficulties, considerable research has been…

Multi-objective reinforcement learning (MORL) algorithms tackle sequential decision problems where agents may have different preferences over (possibly conflicting) reward functions. Such algorithms often learn a set of policies (each…

Out-of-distribution (OOD) generalization has long been a challenging problem that remains largely unsolved. Gaussian processes (GP), as popular probabilistic model classes, especially in the small data regime, presume strong OOD…

Many real-world applications require decision-makers to assess the quality of solutions while considering multiple conflicting objectives. Obtaining good approximation sets for highly constrained many-objective problems is often a difficult…

We present a general technique, based on parametric search with some twist, for solving a variety of optimization problems on a set of semi-algebraic geometric objects of constant complexity. The common feature of these problems is that…

We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…

Graphs are powerful representations for relations among objects, which have attracted plenty of attention. A fundamental challenge for graph learning is how to train an effective Graph Neural Network (GNN) encoder without labels, which are…

Learning on big data brings success for artificial intelligence (AI), but the annotation and training costs are expensive. In future, learning on small data that approximates the generalization ability of big data is one of the ultimate…

We study the task of agnostically learning halfspaces under the Gaussian distribution. Specifically, given labeled examples $(\mathbf{x},y)$ from an unknown distribution on $\mathbb{R}^n \times \{ \pm 1\}$, whose marginal distribution on…

This work proposes a machine-learning framework for constructing statistical models of errors incurred by approximate solutions to parameterized systems of nonlinear equations. These approximate solutions may arise from early termination of…

In this paper, we propose an ensemble learning algorithm called \textit{under-bagging $k$-nearest neighbors} (\textit{under-bagging $k$-NN}) for imbalanced classification problems. On the theoretical side, by developing a new learning…

In this brief paper, we present a naive aggregation algorithm for a typical learning problem with expert advice setting, in which the task of improving generalization, i.e., model validation, is embedded in the learning process as a…

Identifying affordance regions on 3D objects from semantic cues is essential for robotics and human-machine interaction. However, existing 3D affordance learning methods struggle with generalization and robustness due to limited annotated…

We consider non-differentiable dynamic optimization problems such as those arising in robotics and subspace tracking. Given the computational constraints and the time-varying nature of the problem, a low-complexity algorithm is desirable,…

We consider a linear elliptic PDE and a quadratic goal functional. The goal-oriented adaptive FEM algorithm (GOAFEM) solves the primal as well as a dual problem, where the goal functional is always linearized around the discrete primal…

A new challenge for learning algorithms in cyber-physical network systems is the distributed solution of big-data classification problems, i.e., problems in which both the number of training samples and their dimension is high. Motivated by…

Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…