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We develop a skew-adaptive extension of split conformal prediction for regression. The method starts from an asymmetric interval family centered at a point prediction and uses the gauge approach to deduce the conformity score induced by…
The low statistical errors on cosmological parameters promised by future galaxy surveys will only be realised with the development of new, fast, analysis methods that reduce potential systematic problems to low levels. We present an…
A possible gluon-condensate-induced modified-gravity model with f(R) \propto |R|^{1/2} has been suggested previously. Here, a simplified version is presented using the constant flat-spacetime equilibrium value of the QCD gluon condensate…
We consider the problem of nonparametric regression when the covariate is $d$-dimensional, where $d \geq 1$. In this paper we introduce and study two nonparametric least squares estimators (LSEs) in this setting---the entirely monotonic LSE…
Stochastic evolution equations with compensated Poisson noise are considered in the variational approach with monotone and coercive coefficients. Here the Poisson noise is assumed to be time-homogeneous with $\sigma$-finite intensity…
Effective properties of composite materials are defined as the ensemble average of property-specific PDE solutions over the underlying microstructure distributions. Traditionally, predicting such properties can be done by solving PDEs…
The paper introduces a new estimation method for the standard linear regression model. The procedure is not driven by the optimisation of any objective function rather, it is a simple weighted average of slopes from observation pairs. The…
Bilinear Matrix Inequalities (BMIs) are fundamental to control system design but are notoriously difficult to solve due to their nonconvexity. This study addresses BMI-based control optimization problems by adapting and integrating advanced…
We study nonasymptotic minimax estimation of the linear functional $L(\theta)=\eta^\top \theta$ for a high-dimensional $s$-sparse mean vector with an arbitrary loading vector $\eta$. For symmetric noise with exponentially decaying tails, we…
By using the underlying theory of proper scoring rules, we design a family of noise-contrastive estimation (NCE) methods that are tractable for latent variable models. Both terms in the underlying NCE loss, the one using data samples and…
Foundational vision models, such as the Segment Anything Model (SAM), have achieved significant breakthroughs through extensive pre-training on large-scale visual datasets. Despite their general success, these models may fall short in…
This paper proposes Covariate-Balanced Weighted Stacked Difference-in-Differences (CBWSDID), a design-based extension of weighted stacked DID for settings in which untreated trends may be conditionally rather than unconditionally parallel.…
Edge detection (ED) is a fundamental perceptual process in computer vision, forming the structural basis for high-level reasoning tasks such as segmentation, recognition, and scene understanding. Despite substantial progress achieved by…
We develop the mathematical foundations of the stochastic modified equations (SME) framework for analyzing the dynamics of stochastic gradient algorithms, where the latter is approximated by a class of stochastic differential equations with…
Recent advancements in learning algorithms have demonstrated that the sharpness of the loss surface is an effective measure for improving the generalization gap. Building upon this concept, Sharpness-Aware Minimization (SAM) was proposed to…
Consider the problem of estimating a multivariate normal mean with a known variance matrix, which is not necessarily proportional to the identity matrix. The coordinates are shrunk directly in proportion to their variances in Efron and…
This paper considers a practical scenario where a classical estimation method might have already been implemented on a certain platform when one tries to apply more advanced techniques such as moving horizon estimation (MHE). We are…
Functions with discontinuities appear in many applications such as image reconstruction, signal processing, optimal control problems, interface problems, engineering applications and so on. Accurate approximation and interpolation of these…
A novel estimation approach for a general class of semi-parametric multivariate time series models is introduced where the conditional mean is modeled through parametric functions. The focus of the estimation is the conditional mean…
We propose the Variation Calibration Error (VCE) metric for assessing the calibration of machine learning classifiers. The metric can be viewed as an extension of the well-known Expected Calibration Error (ECE) which assesses the…