Related papers: An Overview of Causal Inference using Kernel Embed…
One of the most natural connections between quantum and classical machine learning has been established in the context of kernel methods. Kernel methods rely on kernels, which are inner products of feature vectors living in large feature…
Coherent, continuous spatial representations are critical for synthesizing physical and perceptual phenomena into a single representational space. Radial basis kernels provide a path forward for this type of distributed representation. In…
Comparing probability distributions is a core challenge across the natural, social, and computational sciences. Existing methods, such as Maximum Mean Discrepancy (MMD), struggle in high-dimensional and non-compact domains. Here we…
In this paper, we present the general theory of embedding independence tests on Hilbert spaces that generalizes the concepts of distance covariance, distance multivariance and HSIC. This is done by defining new types of kernel on an $n$…
Reproducing kernel Hilbert spaces (RKHSs) are key elements of many non-parametric tools successfully used in signal processing, statistics, and machine learning. In this work, we aim to address three issues of the classical RKHS based…
This PhD thesis contains several contributions to the field of statistical causal modeling. Statistical causal models are statistical models embedded with causal assumptions that allow for the inference and reasoning about the behavior of…
Diffusion maps are a commonly used kernel-based method for manifold learning, which can reveal intrinsic structures in data and embed them in low dimensions. However, as with most kernel methods, its implementation requires a heavy…
Various methods in statistical learning build on kernels considered in reproducing kernel Hilbert spaces. In applications, the kernel is often selected based on characteristics of the problem and the data. This kernel is then employed to…
In supervised learning, the output variable to be predicted is often represented as a function, such as a spectrum or probability distribution. Despite its importance, functional output regression remains relatively unexplored. In this…
Diffusion Maps framework is a kernel based method for manifold learning and data analysis that defines diffusion similarities by imposing a Markovian process on the given dataset. Analysis by this process uncovers the intrinsic geometric…
In this paper, we consider the coefficient-based regularized distribution regression which aims to regress from probability measures to real-valued responses over a reproducing kernel Hilbert space (RKHS), where the regularization is put on…
Causal inference is known to be very challenging when only observational data are available. Randomized experiments are often costly and impractical and in instrumental variable regression the number of instruments has to exceed the number…
In this paper we review important aspects of semiparametric theory and empirical processes that arise in causal inference problems. We begin with a brief introduction to the general problem of causal inference, and go on to discuss…
Kernel herding belongs to a family of deterministic quadratures that seek to minimize the worst-case integration error over a reproducing kernel Hilbert space (RKHS). These quadrature rules come with strong experimental evidence that this…
The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…
Optimal experimental design seeks to determine the most informative allocation of experiments to infer an unknown statistical quantity. In this work, we investigate the optimal design of experiments for {\em estimation of linear functionals…
This paper studies the probabilistic function approximation problem over reproducing kernel Hilbert spaces. We show the existence and uniqueness of the optimizer under mild assumptions. Furthermore, we generalize the celebrated representer…
We present several generative and predictive algorithms based on the RKHS (reproducing kernel Hilbert spaces) methodology, which, most importantly, are scale up efficiently with large datasets or high-dimensional data. It is well recognized…
This article presents a quantum computing approach to designing of similarity measures and kernels for classification of stochastic symbolic time series. In the area of machine learning, kernels are important components of various…
To draw scientifically meaningful conclusions and build reliable models of quantitative phenomena, cause and effect must be taken into consideration (either implicitly or explicitly). This is particularly challenging when the measurements…