Related papers: Consistent Kernel Mean Estimation for Functions of…
A mean function in a reproducing kernel Hilbert space (RKHS), or a kernel mean, is central to kernel methods in that it is used by many classical algorithms such as kernel principal component analysis, and it also forms the core inference…
Kernel mean embeddings have recently attracted the attention of the machine learning community. They map measures $\mu$ from some set $M$ to functions in a reproducing kernel Hilbert space (RKHS) with kernel $k$. The RKHS distance of two…
This paper introduces an approach for detecting differences in the first-order structures of spatial point patterns. The proposed approach leverages the kernel mean embedding in a novel way by introducing its approximate version tailored to…
Standard kernels such as Mat\'ern or RBF kernels only encode simple monotonic dependencies within the input space. Spectral mixture kernels have been proposed as general-purpose, flexible kernels for learning and discovering more…
The problem of nonparametric inference on a monotone function has been extensively studied in many particular cases. Estimators considered have often been of so-called Grenander type, being representable as the left derivative of the…
Functional data analysis has attracted considerable interest and is facing new challenges, one of which is the increasingly available data in a streaming manner. In this article we develop an online nonparametric method to dynamically…
The performance of kernel density estimators is usually studied via Taylor expansions and asymptotic approximation arguments, in which the bandwidth parameter tends to zero with increasing sample size. In contrast, this paper focusses…
We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…
We describe a method to perform functional operations on probability distributions of random variables. The method uses reproducing kernel Hilbert space representations of probability distributions, and it is applicable to all operations…
We consider statistical models where functional data are artificially contaminated by independent Wiener processes in order to satisfy privacy constraints. We show that the corrupted observations have a Wiener density which determines the…
Contextualized embeddings vary by context, even for the same token, and form a distribution in the embedding space. To analyze this distribution, we focus on the norm of the mean embedding and the variance of the embeddings. In this study,…
Representing, comparing, and measuring the distance between probability distributions is a key task in computational statistics and machine learning. The choice of representation and the associated distance determine properties of the…
This paper considers extensions of minimum-disparity estimators to the problem of estimating parameters in a regression model that is conditionally specified; that is where a parametric model describes the distribution of a response $y$…
The semivarying coefficient models are widely used in the application of finance, economics, medical science and many other areas. The functional coefficients are commonly estimated by local smoothing methods, e.g. local linear estimator.…
Kernel mean embedding is a useful tool to represent and compare probability measures. Despite its usefulness, kernel mean embedding considers infinite-dimensional features, which are challenging to handle in the context of differentially…
Creating accurate meta-embeddings from pre-trained source embeddings has received attention lately. Methods based on global and locally-linear transformation and concatenation have shown to produce accurate meta-embeddings. In this paper,…
We provide new asymptotic theory for kernel density estimators, when these are applied to autoregressive processes exhibiting moderate deviations from a unit root. This fills a gap in the existing literature, which has to date considered…
Motivated by applications, we consider here new operator theoretic approaches to Conditional mean embeddings (CME). Our present results combine a spectral analysis-based optimization scheme with the use of kernels, stochastic processes, and…
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…
We study uniform consistency in nonparametric mixture models as well as closely related mixture of regression (also known as mixed regression) models, where the regression functions are allowed to be nonparametric and the error…