Related papers: Wavelet Tree Ensembles for Triangulable Manifolds

General circulation models (GCMs) are essential tools for climate studies. Such climate models may have varying accuracy across the input domain, but no model is uniformly best. One can improve climate model prediction performance by…

This paper introduces a new extension of Riemannian elastic curve matching to a general class of geometric structures, which we call (weighted) shape graphs, that allows for shape registration with partial matching constraints and…

Random forests are a statistical learning method widely used in many areas of scientific research because of its ability to learn complex relationships between input and output variables and also its capacity to handle high-dimensional…

Wavelet trees are widely used in the representation of sequences, permutations, text collections, binary relations, discrete points, and other succinct data structures. We show, however, that this still falls short of exploiting all of the…

While statistical learning methods have proved powerful tools for predictive modeling, the black-box nature of the models they produce can severely limit their interpretability and the ability to conduct formal inference. However, the…

Persistent homology is a central methodology in topological data analysis that has been successfully implemented in many fields and is becoming increasingly popular and relevant. The output of persistent homology is a persistence diagram --…

Phylogenetic comparative methods are well established tools for using inter-species variation to analyse phenotypic evolution and adaptation. They are generally hampered, however, by predominantly univariate approaches and failure to…

In this work, we propose the Haar wavelet method for the coupled degenerate reaction-diffusion PDEs and the ODEs having non-linear a source with Neumann boundary, applicable in various fields of the natural sciences, engineering, and…

We consider a wavelet thresholding approach to adaptive variance function estimation in heteroscedastic nonparametric regression. A data-driven estimator is constructed by applying wavelet thresholding to the squared first-order differences…

Tree ensembles can be well-suited for black-box optimization tasks such as algorithm tuning and neural architecture search, as they achieve good predictive performance with little or no manual tuning, naturally handle discrete feature…

A general machine learning architecture is introduced that uses wavelet scattering coefficients of an inputted three dimensional signal as features. Solid harmonic wavelet scattering transforms of three dimensional signals were previously…

Recent technological advancements have enabled detailed investigation of associations between the molecular architecture and tumor heterogeneity, through multi-source integration of radiological imaging and genomic (radiogenomic) data. In…

Unoriented surface reconstruction is an important task in computer graphics and has extensive applications. Based on the compact support of wavelet and orthogonality properties, classic wavelet surface reconstruction achieves good and fast…

To improve the uncertainty quantification of variance networks, we propose a novel tree-structured local neural network model that partitions the feature space into multiple regions based on uncertainty heterogeneity. A tree is built upon…

The construction of adaptive nonparametric procedures by means of wavelet thresholding techniques is now a classical topic in modern mathematical statistics. In this paper, we extend this framework to the analysis of nonparametric…

Bayesian Additive Regression Trees (BART) is a tree-based machine learning method that has been successfully applied to regression and classification problems. BART assumes regularisation priors on a set of trees that work as weak learners…

We propose a novel Riemannian geometric framework for variational inference in Bayesian models based on the nonparametric Fisher-Rao metric on the manifold of probability density functions. Under the square-root density representation, the…

The metric space of phylogenetic trees defined by Billera, Holmes, and Vogtmann, which we refer to as BHV space, provides a natural geometric setting for describing collections of trees on the same set of taxa. However, it is sometimes…

It is increasingly being realised that many real world time series are not stationary and exhibit evolving second-order autocovariance or spectral structure. This article introduces a Bayesian approach for modelling the evolving wavelet…

This paper investigates the nonparametric estimation of a heteroskedastic variance function on the sphere in a regression framework, assuming the variance belongs to a Besov regularity class. A needlet-based estimator is proposed, combining…