Related papers: Multiscale Approximation as a Bias-Reducing Strate…
Variational approaches based on neural networks are showing promise for estimating mutual information (MI) between high dimensional variables. However, they can be difficult to use in practice due to poorly understood bias/variance…
We present a scheme to automatically set the precision of floating point variables in an application. We design a framework that profiles applications to measure undesirable numerical behavior at the floating point operation level. We use…
The paper presents a multiplicative bias reduction estimator for nonparametric regression. The approach consists to apply a multiplicative bias correction to an oversmooth pilot estimator. In Burr et al. [2010], this method has been tested…
Sampling from multimodal distributions is a challenging task in scientific computing. When a distribution has an exact symmetry between the modes, direct jumps among them can accelerate the samplings significantly. However, the…
This paper presents a modified iterative approach to solve the variational inequality problem using the double inertial technique in the context of a real Hilbert space. Our iterative technique involves a projection onto a generalized…
The interaction between two particles with shape or interaction anisotropy can be modeled using a pairwise potential energy function that depends on their relative position and orientation; however, this function is often challenging to…
This paper focuses on scattered data fitting problems on spheres. We study the approximation performance of a class of weighted spectral filter algorithms, including Tikhonov regularization, Landaweber iteration, spectral cut-off, and…
Many large-scale optimization problems arising in science and engineering are naturally defined at multiple levels of discretization or model fidelity. Multilevel methods exploit this hierarchy to accelerate convergence by combining coarse-…
This paper introduces a new computational methodology for determining a-posteriori multi-objective error estimates for finite-element approximations, and for constructing corresponding (quasi-)optimal adaptive refinements of finite-element…
In order to avoid the curse of dimensionality, frequently encountered in Big Data analysis, there was a vast development in the field of linear and nonlinear dimension reduction techniques in recent years. These techniques (sometimes…
We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…
This paper tackles the challenge of parameter calibration in stochastic models, particularly in scenarios where the likelihood function is unavailable in an analytical form. We introduce a gradient-based simulated parameter estimation…
A new result in convex analysis on the calculation of proximity operators in certain scaled norms is derived. We describe efficient implementations of the proximity calculation for a useful class of functions; the implementations exploit…
In this paper, we propose an innovative approach to thoroughly explore dataset features that introduce bias in downstream machine-learning tasks. Depending on the data format, we use different techniques to map instances into a similarity…
It is often possible to perform reduced order modelling by specifying linear subspace which accurately captures the dynamics of the system. This approach becomes especially appealing when linear subspace explicitly depends on parameters of…
An effective two-stage method for an estimation of parameters of the linear regression is considered. For this purpose we introduce a certain quasi-estimator that, in contrast to usual estimator, produces two alternative estimates. It is…
This paper introduces \emph{biased mean regression}, estimating the \emph{biased mean}, i.e., $\mathbb{E}[Y] + x$, where $x \in \mathbb{R}$. The approach addresses a fundamental statistical problem that covers numerous applications. For…
Multivariate regression models are widely used in various fields such as biology and finance. In this paper, we focus on two key challenges: (a) When should we favor a multivariate model over a series of univariate models; (b) If the…
Geodesic distance matrices can reveal shape properties that are largely invariant to non-rigid deformations, and thus are often used to analyze and represent 3-D shapes. However, these matrices grow quadratically with the number of points.…
Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level…