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Gaussian process regression (GPR) is a popular nonparametric Bayesian method that provides predictive uncertainty estimates and is widely used in safety-critical applications. While prior research has introduced various uncertainty bounds,…
A multiverse analysis evaluates all combinations of "reasonable" analytic decisions to promote robustness and transparency, but can lead to a combinatorial explosion of analyses to compute. Long delays before assessing results prevent users…
In this paper, we will be delving deeper into the connection between the rough theory and the ring theory precisely in the principle and maximal ideal. The rough set theory has shown by Pawlak as good formal tool for modeling and processing…
An important issue in Qualitative Spatial Reasoning is the representation of relative direction. In this paper we present simple geometric rules that enable reasoning about relative direction between oriented points. This framework, the…
Sparse approximation is important in many applications because of concise form of an approximant and good accuracy guarantees. The theory of compressed sensing, which proved to be very useful in the image processing and data sciences, is…
Algorithmic fairness is typically studied from the perspective of predictions. Instead, here we investigate fairness from the perspective of recourse actions suggested to individuals to remedy an unfavourable classification. We propose two…
This paper discusses basic results and recent developments on variational regularization methods, as developed for inverse problems. In a typical setup we review basic properties needed to obtain a convergent regularization scheme and…
Gaussian processes (GPs) provide flexible distributions over functions, with inductive biases controlled by a kernel. However, in many applications Gaussian processes can struggle with even moderate input dimensionality. Learning a low…
Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…
Gaussian processes (GPs) are commonly used as models for functions, time series, and spatial fields, but they are computationally infeasible for large datasets. Focusing on the typical setting of modeling data as a GP plus an additive noise…
Despite recent advances in Visual QuestionAnswering (VQA), it remains a challenge todetermine how much success can be attributedto sound reasoning and comprehension ability.We seek to investigate this question by propos-ing a new task…
The paper is mainly devoted to systematic developments and applications of geometric aspects of second-order variational analysis that are revolved around the concept of parabolic regularity of sets. This concept has been known in…
Variational Gaussian process (GP) approximations have become a standard tool in fast GP inference. This technique requires a user to select variational features to increase efficiency. So far the common choices in the literature are…
It is by now well-established that modern over-parameterized models seem to elude the bias-variance tradeoff and generalize well despite overfitting noise. Many recent works attempt to analyze this phenomenon in the relatively tractable…
Gaussian Processes (GPs) offer an attractive method for regression over small, structured and correlated datasets. However, their deployment is hindered by computational costs and limited guidelines on how to apply GPs beyond simple…
This paper introduces new solvers for efficiently computing solutions to large-scale inverse problems with group sparsity regularization, including both non-overlapping and overlapping groups. Group sparsity regularization refers to a type…
Symbolic regression (SR) with genetic programming (GP) aims to discover interpretable mathematical expressions directly from data. Despite its strong empirical success, the theoretical understanding of why GP-based SR generalizes beyond the…
Regularization has become a primary tool for developing reliable estimators of the covariance matrix in high-dimensional settings. To curb the curse of dimensionality, numerous methods assume that the population covariance (or inverse…
Deep Neural Networks have achieved remarkable success relying on the developing high computation capability of GPUs and large-scale datasets with increasing network depth and width in image recognition, object detection and many other…
The subject of this paper is regularity-preserving aggregation of regular norms on finite-dimensional linear spaces. Regular norms were introduced in [5] and are closely related to ``type 2'' spaces [9, Chapter 9] playing important role in…