Related papers: Adaptive Priors based on Splines with Random Knots

Reliable models should not only predict correctly, but also justify decisions with acceptable evidence. Yet conventional supervised learning typically provides only class-level labels, allowing models to achieve high accuracy through…

A novel block prior is proposed for adaptive Bayesian estimation. The prior does not depend on the smoothness of the function or the sample size. It puts sufficient prior mass near the true signal and automatically concentrates on its…

We study homoclinic snaking of one-dimensional, localised states on two-dimensional, bistable lattices via the method of exponential asymptotics. Within a narrow region of parameter space, fronts connecting the two stable states are pinned…

Prompt-Tuning is an efficient method for adapting pre-trained language models to new tasks with minimal computational overhead by modifying prompt embeddings. In this work, we investigate how crucial the phenomenon of embedding collapse,…

A noise-reduction algorithm for time-series of non-linear systems is presented. The algorithm smoothes the attractors in phase space using B-splines, allowing a more accurate measure of their dynamics. The algorithm is tested on numerical…

Procrustes Analysis is a Morphometric method based on Configurations of Landmarks that estimates the superimposition parameters by least-squares; for this reason, the procedure is very sensitive to outliers. In the first part of the paper…

We investigate the frequentist posterior contraction rate of nonparametric Bayesian procedures in linear inverse problems in both the mildly and severely ill-posed cases. A theorem is proved in a general Hilbert space setting under…

Recent advancements in recurrent neural network (RNN) research have demonstrated the superiority of utilizing multiscale structures in learning temporal representations of time series. Currently, most of multiscale RNNs use fixed scales,…

We consider the problems of variable selection and estimation in nonparametric additive regression models for high-dimensional data. In recent years, several methods have been proposed to model nonlinear relationships when the number of…

In this article, we study the binary classification problem with supervised data, in the case where the covariate-to-probability-of-success map is possibly spatially inhomogeneous. We devise nonparametric Bayesian procedures with…

We develop likelihood-based bias reduction for nonlinear panel models with additive individual and time effects. In two-way panels, integrated-likelihood corrections are attractive but challenging because the required integration is high…

In this paper we propose a general method to derive an upper bound for the contraction rate of the posterior distribution for nonparametric inverse problems. We present a general theorem that allows us to derive con- traction rates for the…

During the past decade, shrinkage priors have received much attention in Bayesian analysis of high-dimensional data. This paper establishes the posterior consistency for high-dimensional linear regression with a class of shrinkage priors,…

Approximating data points in three or higher dimension space based on cubic B-spline curve is presented. Representations for planar curves, are merged and extended to the higher dimension. The curve is fitted to the order of data points, or…

Many applications in machine learning or signal processing involve nonsmooth optimization problems. This nonsmoothness brings a low-dimensional structure to the optimal solutions. In this paper, we propose a randomized proximal gradient…

Proteins with nontrivial topology, containing knots and slipknots, have the ability to fold to their native states without any additional external forces invoked. A mechanism is suggested for folding of these proteins, such as YibK and…

This study investigates the potential for drag-reduction of low-mechanical-order, self-adaptive control systems, consisting of hinged flaps attached along the edges of the rectangular base of a canonical blunt body. Comparative experiments…

A piecewise Chebyshevian spline space is good for design when it possesses a B-spline basis and this property is preserved under knot insertion. The interest in such kind of spaces is justified by the fact that, similarly as for polynomial…

We investigate the problem of deriving posterior concentration rates under different loss functions in nonparametric Bayes. We first provide a lower bound on posterior coverages of shrinking neighbourhoods that relates the metric or loss…

We propose a method for adaptive nonlinear sequential modeling of vector-time series data. Data is modeled as a nonlinear function of past values corrupted by noise, and the underlying non-linear function is assumed to be approximately…