Related papers: Learning in Function Spaces: An Unified Functional…

Resource allocation and transceivers in wireless networks are usually designed by solving optimization problems subject to specific constraints, which can be formulated as variable or functional optimization. If the objective and constraint…

By selecting different filter functions, spectral algorithms can generate various regularization methods to solve statistical inverse problems within the learning-from-samples framework. This paper combines distributed spectral algorithms…

Statistical inference, a central tool of science, revolves around the study and the usage of statistical estimators: functions that map finite samples to predictions about unknown distribution parameters. In the frequentist framework,…

In principle, meta-reinforcement learning algorithms leverage experience across many tasks to learn fast reinforcement learning (RL) strategies that transfer to similar tasks. However, current meta-RL approaches rely on manually-defined…

All famous machine learning algorithms that comprise both supervised and semi-supervised learning work well only under a common assumption: the training and test data follow the same distribution. When the distribution changes, most…

Supervised learning is classically formulated as training a model to minimize a fixed loss function over a fixed distribution, or task. However, an emerging paradigm instead views model training as extracting enough information from data so…

We present a novel framework for learning system design with neural feature extractors. First, we introduce the feature geometry, which unifies statistical dependence and feature representations in a function space equipped with inner…

In this paper, we introduce a new functional point of view on bilevel optimization problems for machine learning, where the inner objective is minimized over a function space. These types of problems are most often solved by using methods…

Performative learning addresses the increasingly pervasive situations in which algorithmic decisions may induce changes in the data distribution as a consequence of their public deployment. We propose a novel view in which these…

Multi-task learning aims to learn multiple tasks jointly by exploiting their relatedness to improve the generalization performance for each task. Traditionally, to perform multi-task learning, one needs to centralize data from all the tasks…

Unsupervised and self-supervised learning approaches have become a crucial tool to learn representations for downstream prediction tasks. While these approaches are widely used in practice and achieve impressive empirical gains, their…

In large-scale distributed scenarios, increasingly complex tasks demand more intelligent collaboration across networks, requiring the joint extraction of structural representations from data samples. However, conventional task-specific…

Classification is a core topic in functional data analysis. A large number of functional classifiers have been proposed in the literature, most of which are based on functional principal component analysis or functional regression. In…

Standard supervised machine learning assumes that the distribution of the source samples used to train an algorithm is the same as the one of the target samples on which it is supposed to make predictions. However, as any data scientist…

The literature on machine learning in the context of data streams is vast and growing. However, many of the defining assumptions regarding data-stream learning tasks are too strong to hold in practice, or are even contradictory such that…

Mathematical optimization is widely used in various research fields. With a carefully-designed objective function, mathematical optimization can be quite helpful in solving many problems. However, objective functions are usually…

Distribution regression refers to the supervised learning problem where labels are only available for groups of inputs instead of individual inputs. In this paper, we develop a rigorous mathematical framework for distribution regression…

Operator learning offers a robust framework for approximating mappings between infinite-dimensional function spaces. It has also become a powerful tool for solving inverse problems in the computational sciences. This chapter surveys…

Learning mappings of data on manifolds is an important topic in contemporary machine learning, with applications in astrophysics, geophysics, statistical physics, medical diagnosis, biochemistry, 3D object analysis. This paper studies the…

In scientific machine learning, models are routinely deployed with parameter values or boundary conditions far from those used in training. This paper studies the learning-where-to-learn problem of designing a training data distribution…