Related papers: Computational Efficiency under Covariate Shift in …
This paper addresses the problem of regression to reconstruct functions, which are observed with superimposed errors at random locations. We address the problem in reproducing kernel Hilbert spaces. It is demonstrated that the estimator,…
Consider a scenario where we have access to train data with both covariates and outcomes while test data only contains covariates. In this scenario, our primary aim is to predict the missing outcomes of the test data. With this objective in…
In this paper, an online learning algorithm is proposed as sequential stochastic approximation of a regularization path converging to the regression function in reproducing kernel Hilbert spaces (RKHSs). We show that it is possible to…
The ability to generalize under distributional shifts is essential to reliable machine learning, while models optimized with empirical risk minimization usually fail on non-$i.i.d$ testing data. Recently, invariant learning methods for…
Machine learning models used in medical applications often face challenges due to the covariate shift, which occurs when there are discrepancies between the distributions of training and target data. This can lead to decreased predictive…
The primary hyperparameter in kernel regression (KR) is the choice of kernel. In most theoretical studies of KR, one assumes the kernel is fixed before seeing the training data. Under this assumption, it is known that the optimal kernel is…
Traditional functional linear regression usually takes a one-dimensional functional predictor as input and estimates the continuous coefficient function. Modern applications often generate two-dimensional covariates, which become matrices…
In this paper, we study an online learning algorithm with a robust loss function $\mathcal{L}_{\sigma}$ for regression over a reproducing kernel Hilbert space (RKHS). The loss function $\mathcal{L}_{\sigma}$ involving a scaling parameter…
We propose estimators based on kernel ridge regression for nonparametric causal functions such as dose, heterogeneous, and incremental response curves. Treatment and covariates may be discrete or continuous in general spaces. Due to a…
Data depth is a statistical function that generalizes order and quantiles to the multivariate setting and beyond, with applications spanning over descriptive and visual statistics, anomaly detection, testing, etc. The celebrated halfspace…
The notion of reproducing kernel Hilbert space (RKHS) has emerged in system identification during the past decade. In the resulting framework, the impulse response estimation problem is formulated as a regularized optimization defined on an…
An important feature of kernel mean embeddings (KME) is that the rate of convergence of the empirical KME to the true distribution KME can be bounded independently of the dimension of the space, properties of the distribution and smoothness…
A common pursuit in modern statistical learning is to attain satisfactory generalization out of the source data distribution (OOD). In theory, the challenge remains unsolved even under the canonical setting of covariate shift for the linear…
Covariate shift may impact the operational safety performance of neural networks. A re-evaluation of the safety performance, however, requires collecting new operational data and creating corresponding ground truth labels, which often is…
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…
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 develop semiparametrically efficient inference for kernel measures of noise heterogeneity in additive noise models. In many applications, the regression function is estimated using flexible machine learning methods. Downstream procedures…
In this work we revisit two classic high-dimensional online learning problems, namely linear regression and contextual bandits, from the perspective of adversarial robustness. Existing works in algorithmic robust statistics make strong…
Nonlinear kernel regression models are often used in statistics and machine learning because they are more accurate than linear models. Variable selection for kernel regression models is a challenge partly because, unlike the linear…
Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation…