Related papers: Flexible Expectile Regression in Reproducing Kerne…

This paper studies a very flexible model that can be used widely to analyze the relation between a response and multiple covariates. The model is nonparametric, yet renders easy interpretation for the effects of the covariates. The model…

Consider the problem: given the data pair $(\mathbf{x}, \mathbf{y})$ drawn from a population with $f_*(x) = \mathbf{E}[\mathbf{y} | \mathbf{x} = x]$, specify a neural network model and run gradient flow on the weights over time until…

A nonparametric kernel-based method for realizing Bayes' rule is proposed, based on representations of probabilities in reproducing kernel Hilbert spaces. Probabilities are uniquely characterized by the mean of the canonical map to the…

New local linear estimators are proposed for a wide class of nonparametric regression models. The estimators are uniformly consistent regardless of satisfying traditional conditions of depen\-dence of design elements. The estimators are the…

We consider conditions on a given system $\mathcal{F}$ of vectors in Hilbert space $\mathcal{H}$, forming a frame, which turn $\mathcal{H}$ into a reproducing kernel Hilbert space. It is assumed that the vectors in $\mathcal{F}$ are…

In the on-line Explore and Exploit literature, central to Machine Learning, a central planner is faced with a set of alternatives, each yielding some unknown reward. The planner's goal is to learn the optimal alternative as soon as…

Factor modeling is a powerful statistical technique that permits to capture the common dynamics in a large panel of data with a few latent variables, or factors, thus alleviating the curse of dimensionality. Despite its popularity and…

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,…

Obtaining reliable, adaptive confidence sets for prediction functions (hypotheses) is a central challenge in sequential decision-making tasks, such as bandits and model-based reinforcement learning. These confidence sets typically rely on…

A key assumption in the theory of nonlinear adaptive control is that the uncertainty of the system can be expressed in the linear span of a set of known basis functions. While this assumption leads to efficient algorithms, it limits…

This survey is an introduction to positive definite kernels and the set of methods they have inspired in the machine learning literature, namely kernel methods. We first discuss some properties of positive definite kernels as well as…

Tree structured graphical models are powerful at expressing long range or hierarchical dependency among many variables, and have been widely applied in different areas of computer science and statistics. However, existing methods for…

We propose a new supervised learning algorithm, for classification and regression problems where two or more preliminary predictors are available. We introduce \texttt{KernelCobra}, a non-linear learning strategy for combining an arbitrary…

The problem of estimating a parametric or nonparametric regression function in a model with normal errors is considered. For this purpose, a novel objective prior for the regression function is proposed, defined as the distribution…

Mixed-effects regression models represent a useful subclass of regression models for grouped data; the introduction of random effects allows for the correlation between observations within each group to be conveniently captured when…

The polynomial kernels are widely used in machine learning and they are one of the default choices to develop kernel-based classification and regression models. However, they are rarely used and considered in numerical analysis due to their…

A new algorithm named EXPected Similarity Estimation (EXPoSE) was recently proposed to solve the problem of large-scale anomaly detection. It is a non-parametric and distribution free kernel method based on the Hilbert space embedding of…

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…

Clinical risk prediction models are regularly updated as new data, often with additional covariates, become available. We propose CARE (Convex Aggregation of relative Risk Estimators) as a general approach for combining existing "external"…

Kernel methods are an incredibly popular technique for extending linear models to non-linear problems via a mapping to an implicit, high-dimensional feature space. While kernel methods are computationally cheaper than an explicit feature…