Related papers: The linear conditional expectation in Hilbert spac…
The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied. However, nonlinear partial differential equations (PDEs) pose substantial challenges from an…
We give a finite-sample analysis of predictive inference procedures after model selection in regression with random design. The analysis is focused on a statistically challenging scenario where the number of potentially important…
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…
We consider an incremental approximation method for solving variational problems in infinite-dimensional Hilbert spaces, where in each step a randomly and independently selected subproblem from an infinite collection of subproblems is…
Autonomous service robots require computational frameworks that allow them to generalize knowledge to new situations in a manner that models uncertainty while scaling to real-world problem sizes. The Robot Common Sense Embedding (RoboCSE)…
The fundamental problem of line spectral estimation (LSE) using the expectation propagation (EP) method is studied. Previous approaches estimate the model order sequentially, limiting their practical utility in scenarios with large…
Although deep learning has achieved appealing results on several machine learning tasks, most of the models are deterministic at inference, limiting their application to single-modal settings. We propose a novel general-purpose framework…
In this paper we consider the problem of inference in statistical models characterized by moment restrictions by casting the problem within the Exponentially Tilted Empirical Likelihood (ETEL) framework. Because the ETEL function has a well…
We show that moment inequalities in a wide variety of economic applications have a particular linear conditional structure. We use this structure to construct uniformly valid confidence sets that remain computationally tractable even in…
In this note we study the problem of sampling and reconstructing signals which are assumed to lie on or close to one of several subspaces of a Hilbert space. Importantly, we here consider a very general setting in which we allow infinitely…
Mechanistic models with differential equations are a key component of scientific applications of machine learning. Inference in such models is usually computationally demanding, because it involves repeatedly solving the differential…
We consider the problem of unfair discrimination between two groups and propose a pre-processing method to achieve fairness. Corrective methods like statistical parity usually lead to bad accuracy and do not really achieve fairness in…
The concept of conditional expectation is important in applications of probability and statistics in many areas such as reliability engineering, economy, finance, and actuarial sciences due to its property of being the best predictor of a…
We introduce and study the persuasive calibration problem, where a principal aims to provide trustworthy predictions about underlying events to a downstream agent to make desired decisions. We adopt the standard calibration framework that…
Parameter-space regularization in neural network optimization is a fundamental tool for improving generalization. However, standard parameter-space regularization methods make it challenging to encode explicit preferences about desired…
In applications it is common that the exact form of a conditional expectation is unknown and having flexible functional forms can lead to improvements. Series method offers that by approximating the unknown function based on $k$ basis…
Empirical Bayes (EB) improves the accuracy of simultaneous inference "by learning from the experience of others" (Efron, 2012). Classical EB theory focuses on latent variables that are iid draws from a fitted prior (Efron, 2019). Modern…
In this paper, we prove optimal convergence rates results for regularisation methods for solving linear ill-posed operator equations in Hilbert spaces. The result generalises existing convergence rates results on optimality to general…
Network Embeddings (NEs) map the nodes of a given network into $d$-dimensional Euclidean space $\mathbb{R}^d$. Ideally, this mapping is such that `similar' nodes are mapped onto nearby points, such that the NE can be used for purposes such…
We assume the direct sum <A> o <B> for the signal subspace. As a result of post- measurement, a number of operational contexts presuppose the a priori knowledge of the LB -dimensional "interfering" subspace <B> and the goal is to estimate…