Related papers: Adaptive Priors based on Splines with Random Knots

P-splines are penalized B-splines, in which finite order differences in coefficients are typically penalized with an $\ell_2$ norm. P-splines can be used for semiparametric regression and can include random effects to account for…

In this paper, we approach the challenging problem of motion planning for knot tying. We propose a hierarchical approach in which the top layer produces a topological plan and the bottom layer translates this plan into continuous robot…

Prediction of dynamical time series with additive noise using support vector machines or kernel based regression has been proved to be consistent for certain classes of discrete dynamical systems. Consistency implies that these methods are…

We focus on the increasingly important area of sparse regression problems where there are many variables and the effects of a large subset of these are negligible. This paper describes the construction of hierarchical prior distributions…

Completely random measures (CRMs) provide a broad class of priors, arguably, the most popular, for Bayesian nonparametric (BNP) analysis of trait allocations. As a peculiar property, CRM priors lead to predictive distributions that share…

Spatio-temporal receptive field (STRF) models are frequently used to approximate the computation implemented by a sensory neuron. Typically, such STRFs are assumed to be smooth and sparse. Current state-of-the-art approaches for estimating…

This paper investigates sparse high-dimensional linear regression, particularly examining the properties of the posterior under conditions of random design and unknown error variance. We provide consistency results for the posterior and…

Projected priors were originally introduced to accommodate parameter constraints, but have recently regained popularity due to their ability to assign probability mass to low-dimensional parameter sets, such as the spaces of sparse vectors,…

In pattern-forming systems, localized patterns are states of intermediate complexity between fully extended ordered patterns and completely irregular patterns. They are formed by stationary fronts enclosing an ordered pattern inside an…

Structured additive regression provides a general framework for complex Gaussian and non-Gaussian regression models, with predictors comprising arbitrary combinations of nonlinear functions and surfaces, spatial effects, varying…

This paper presents an adaptive discretization strategy for level set topology optimization of structures based on hierarchical B-splines. This work focuses on the influence of the discretization approach and the adaptation strategy on the…

We study how the posterior contraction rate under a Gaussian process (GP) prior depends on the intrinsic dimension of the predictors and the smoothness of the regression function. An open question is whether a generic GP prior that does not…

Isotonic regression or monotone function estimation is a problem of estimating function values under monotonicity constraints, which appears naturally in many scientific fields. This paper proposes a new Bayesian method with global-local…

The paper considers functional linear regression, where scalar responses $Y_1,...,Y_n$ are modeled in dependence of random functions $X_1,...,X_n$. We propose a smoothing splines estimator for the functional slope parameter based on a…

The first Bayesian results for the sparse normal means problem were proven for spike-and-slab priors. However, these priors are less convenient from a computational point of view. In the meanwhile, a large number of continuous shrinkage…

We study posterior contraction rates for sparse Bayesian Kolmogorov-Arnold networks (KANs) over anisotropic Besov spaces, providing a statistical foundation of KANs from a Bayesian point of view. We show that sparse Bayesian KANs equipped…

This paper studies posterior contraction rates in multi-category logit models with priors incorporating group sparse structures. We consider a general class of logit models that includes the well-known multinomial logit models as a special…

We propose a new Bayesian strategy for adaptation to smoothness in nonparametric models based on heavy tailed series priors. We illustrate it in a variety of settings, showing in particular that the corresponding Bayesian posterior…

We propose a regression model for count data when the classical generalized linear model approach is too rigid due to a high outcome of zero counts and a nonlinear influence of continuous covariates. Zero-Inflation is applied to take into…

In this paper we consider adaptive sampling's local-feature size, used in surface reconstruction and geometric inference, with respect to an arbitrary landmark set rather than the medial axis and relate it to a path-based adaptive metric on…