Related papers: Towards regularized learning from functional data …
Random feature approximation is arguably one of the most widely used techniques for kernel methods in large-scale learning algorithms. In this work, we analyze the generalization properties of random feature methods, extending previous…
This paper develops a theory of graph classification under domain shift through a random-graph generative lens, where we consider intra-class graphs sharing the same random graph model (RGM) and the domain shift induced by changes in RGM…
Ensemble learning is traditionally justified as a variance-reduction strategy, explaining its strong performance for unstable predictors such as decision trees. This explanation, however, does not account for ensembles constructed from…
We consider a class of statistical inverse problems involving the estimation of a regression operator from a Polish space to a separable Hilbert space, where the target lies in a vector-valued reproducing kernel Hilbert space induced by an…
Convolution neural networks have achieved remarkable performance in many tasks of computing vision. However, CNN tends to bias to low frequency components. They prioritize capturing low frequency patterns which lead them fail when suffering…
The performance of adaptive estimators that employ embedding in reproducing kernel Hilbert spaces (RKHS) depends on the choice of the location of basis kernel centers. Parameter convergence and error approximation rates depend on where and…
The support vector machine (SVM) is a popular machine learning classification method which produces a nonlinear decision boundary in a feature space by constructing linear boundaries in a transformed Hilbert space. It is well known that…
We propose new reproducing kernel-based tests for model checking in conditional moment restriction models. By regressing estimated residuals on kernel functions via kernel ridge regression (KRR), we obtain a coefficient function in a…
Multiscale Models are known to be successful in uncovering and analyzing the structures in data at different resolutions. In the current work we propose a feature driven Reproducing Kernel Hilbert space (RKHS), for which the associated…
Learning models whose predictions are invariant under multiple environments is a promising approach for out-of-distribution generalization. Such models are trained to extract features $X_{\text{inv}}$ where the conditional distribution $Y…
Domain generalization (DG) aims to learn a model on several source domains, hoping that the model can generalize well to unseen target domains. The distribution shift between domains contains the covariate shift and conditional shift, both…
We propose a new data-driven approach for learning the fundamental solutions (Green's functions) of various linear partial differential equations (PDEs) given sample pairs of input-output functions. Building off the theory of functional…
This paper proposes a new nonlinear approach for additive functional regression with functional response based on kernel methods along with some slight reformulation and implementation of the linear regression and the spectral additive…
People typically learn through exposure to visual concepts associated with linguistic descriptions. For instance, teaching visual object categories to children is often accompanied by descriptions in text or speech. In a machine learning…
Covariate shift, a widely used assumption in tackling {\it distributional shift} (when training and test distributions differ), focuses on scenarios where the distribution of the labels conditioned on the feature vector is the same, but the…
In the setting of supervised learning using reproducing kernel methods, we propose a data-dependent regularization parameter selection rule that is adaptive to the unknown regularity of the target function and is optimal both for the…
We focus on the distribution regression problem: regressing to vector-valued outputs from probability measures. Many important machine learning and statistical tasks fit into this framework, including multi-instance learning and point…
In this paper, we study the online learning algorithm without explicit regularization terms. This algorithm is essentially a stochastic gradient descent scheme in a reproducing kernel Hilbert space (RKHS). The polynomially decaying step…
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…
Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…