Related papers: Flexible Expectile Regression in Reproducing Kerne…

A Hilbert space embedding of a distribution---in short, a kernel mean embedding---has recently emerged as a powerful tool for machine learning and inference. The basic idea behind this framework is to map distributions into a reproducing…

In this paper, the flexibility, versatility and predictive power of kernel regression are combined with now lavishly available network data to create regression models with even greater predictive performances. Building from previous work…

Many machine learning approaches for decision making, such as reinforcement learning, rely on simulators or predictive models to forecast the time-evolution of quantities of interest, e.g., the state of an agent or the reward of a policy.…

Traditional linear methods for forecasting multivariate time series are not able to satisfactorily model the non-linear dependencies that may exist in non-Gaussian series. We build on the theory of learning vector-valued functions in the…

The linear conditional expectation (LCE) provides a best linear (or rather, affine) estimate of the conditional expectation and hence plays an important r\^ole in approximate Bayesian inference, especially the Bayes linear approach. This…

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…

We propose a nonlinear function-on-function regression model where both the covariate and the response are random functions. The nonlinear regression is carried out in two steps: we first construct Hilbert spaces to accommodate the…

In this paper we present a nonparametric method for extending functional regression methodology to the situation where more than one functional covariate is used to predict a functional response. Borrowing the idea from Kadri et al.…

Kernel methods approximate nonlinear maps in a data-driven manner by projecting the target map onto a finite-dimensional Hilbert space called the solution space. Traditionally, this space is a subspace of a fixed ambient reproducing kernel…

Matrix approximations are a key element in large-scale algebraic machine learning approaches. The recently proposed method MEKA (Si et al., 2014) effectively employs two common assumptions in Hilbert spaces: the low-rank property of an…

These notes provide a self-contained introduction to kernel methods and their geometric foundations in machine learning. Starting from the construction of Hilbert spaces, we develop the theory of positive definite kernels, reproducing…

High-dimensional data can often display heterogeneity due to heteroscedastic variance or inhomogeneous covariate effects. Penalized quantile and expectile regression methods offer useful tools to detect heteroscedasticity in…

This paper addresses the problem of learning the impulse responses characterizing forward models by means of a regularized kernel-based Prediction Error Method (PEM). The common approach to accomplish that is to approximate the system with…

We consider the theory of bond discounts, defined as the difference between the terminal payoff of the contract and its current price. Working in the setting of finite-dimensional realizations in the HJM framework, under suitable notions of…

The distribution regression problem encompasses many important statistics and machine learning tasks, and arises in a large range of applications. Among various existing approaches to tackle this problem, kernel methods have become a method…

The functional generalized additive model (FGAM) provides a more flexible nonlinear functional regression model than the well-studied functional linear regression model. This paper restricts attention to the FGAM with identity link and…

A key challenge in probabilistic regression is ensuring that predictive distributions accurately reflect true empirical uncertainty. Minimizing overall prediction error often encourages models to prioritize informativeness over calibration,…

We recently introduced a scale of kernel-based greedy schemes for approximating the solutions of elliptic boundary value problems. The procedure is based on a generalized interpolation framework in reproducing kernel Hilbert spaces and was…

This paper derives error bounds for regression in continuous time over subsets of certain types of Riemannian manifolds.The regression problem is typically driven by a nonlinear evolution law taking values on the manifold, and it is cast as…

Recent progress in variational inference has paid much attention to the flexibility of variational posteriors. One promising direction is to use implicit distributions, i.e., distributions without tractable densities as the variational…