Related papers: Online Learning with Multiple Operator-valued Kern…
Much recent work has addressed the solution of a family of partial differential equations by computing the inverse operator map between the input and solution space. Toward this end, we incorporate function-valued reproducing kernel Hilbert…
Positive definite operator-valued kernels generalize the well-known notion of reproducing kernels, and are naturally adapted to multi-output learning situations. This paper addresses the problem of learning a finite linear combination of…
In recent years, functional linear models have attracted growing attention in statistics and machine learning, with the aim of recovering the slope function or its functional predictor. This paper considers online regularized learning…
In this paper we consider the problems of supervised classification and regression in the case where attributes and labels are functions: a data is represented by a set of functions, and the label is also a function. We focus on the use of…
Pairwise learning usually refers to a learning task which involves a loss function depending on pairs of examples, among which most notable ones include ranking, metric learning and AUC maximization. In this paper, we study an online…
Online learning from a stream of data is a defining feature of intelligence, yet modern machine learning systems often struggle in this setting, especially under distributional shift. To understand its basic properties, we study the…
We consider the problem of approximating the regression function $f_\mu:\, \Omega \to Y$ from noisy $\mu$-distributed vector-valued data $(\omega_m,y_m)\in\Omega\times Y$ by an online learning algorithm using a reproducing kernel Hilbert…
Recent advances in operator learning theory have improved our knowledge about learning maps between infinite dimensional spaces. However, for large-scale engineering problems such as concurrent multiscale simulation for mechanical…
We consider the problem of learning a nonlinear function over a network of learners in a fully decentralized fashion. Online learning is additionally assumed, where every learner receives continuous streaming data locally. This learning…
The performance of reproducing kernel Hilbert space-based methods is known to be sensitive to the choice of the reproducing kernel. Choosing an adequate reproducing kernel can be challenging and computationally demanding, especially in…
Higher-order learning is fundamentally rooted in exploiting compositional features. It clearly hinges on enriching the representation by more elaborate interactions of the data which, in turn, tends to increase the model complexity of…
In this paper, we demonstrate how to learn the objective function of a decision-maker while only observing the problem input data and the decision-maker's corresponding decisions over multiple rounds. We present exact algorithms for this…
This expository article presents the approach to statistical machine learning based on reproducing kernel Hilbert spaces. The basic framework is introduced for scalar-valued learning and then extended to operator learning. Finally, learning…
We review machine learning methods employing positive definite kernels. These methods formulate learning and estimation problems in a reproducing kernel Hilbert space (RKHS) of functions defined on the data domain, expanded in terms of a…
We consider the problem of operator-valued kernel learning and investigate the possibility of going beyond the well-known separable kernels. Borrowing tools and concepts from the field of quantum computing, such as partial trace and…
In this paper, we address the problem of adaptive learning for autoregressive moving average (ARMA) model in the quaternion domain. By transforming the original learning problem into a full information optimization task without explicit…
We propose a novel online learning paradigm for nonlinear-function estimation tasks based on the iterative projections in the L2 space with probability measure reflecting the stochastic property of input signals. The proposed learning…
Online federated learning (OFL) becomes an emerging learning framework, in which edge nodes perform online learning with continuous streaming local data and a server constructs a global model from the aggregated local models. Online…
We investigate online kernel algorithms which simultaneously process multiple classification tasks while a fixed constraint is imposed on the size of their active sets. We focus in particular on the design of algorithms that can efficiently…
In contrast to offline working fashions, two research paradigms are devised for online learning: (1) Online Meta Learning (OML) learns good priors over model parameters (or learning to learn) in a sequential setting where tasks are revealed…