Related papers: Denoising Flows on Trees
We consider linear regression problems with a varying number of random projections, where we provably exhibit a double descent curve for a fixed prediction problem, with a high-dimensional analysis based on random matrix theory. We first…
Whereas most plants are flexible structures that undergo large deformations under flow, another process can occur when the plant is broken by heavy fluid-loading. We investigate here the mechanism of such possible breakage, focusing on the…
The time process of transport on randomly evolving trees is investigated. By introducing the notions of living and dead nodes a model of random tree evolution is constructed which describes the spreading in time of objects corresponding to…
An extension of the regularized least-squares in which the estimation parameters are stretchable is introduced and studied in this paper. The solution of this ridge regression with stretchable parameters is given in primal and dual spaces…
We prove a lower bound on the number of spanning two-forests in a graph, in terms of the number of vertices, edges, and spanning trees. This implies an upper bound on the average cut size of a random two-forest. The main tool is an identity…
In this work, we present a new approach to analyze the gradient flow for a positive semi-definite matrix denoising problem in an extensive-rank and high-dimensional regime. We use recent linear pencil techniques of random matrix theory to…
Energy networks should strive for reliability. How can it be assessed, measured, and improved? What are the best trade-offs between investments and their worth? The flow-based framework for the reliability assessment of energy networks…
We study fragmentation of a random recursive tree into a forest by repeated removal of nodes. The initial tree consists of N nodes and it is generated by sequential addition of nodes with each new node attaching to a randomly-selected…
We study the minimal spanning arborescence which is the directed analogue of the minimal spanning tree, with a particular focus on its infinite volume limit and its geometric properties. We prove that in a certain large class of transient…
Two approaches to the problem of transition to turbulence of shear flows are popular in the literature. The first is the linear one of transient growth which focuses on the likely form of the most 'dangerous' (lowest energy)…
We investigate the statistics of trees grown from some initial tree by attaching links to preexisting vertices, with attachment probabilities depending only on the valence of these vertices. We consider the asymptotic mass distribution that…
We study the implicit bias of gradient flow (i.e., gradient descent with infinitesimal step size) on linear neural network training. We propose a tensor formulation of neural networks that includes fully-connected, diagonal, and…
The rotor walk on a graph is a deterministic analogue of random walk. Each vertex is equipped with a rotor, which routes the walker to the neighbouring vertices in a fixed cyclic order on successive visits. We consider rotor walk on an…
Decision trees are widely used for classification and regression tasks in a variety of application fields due to their interpretability and good accuracy. During the past decade, growing attention has been devoted to globally optimized…
Motivated by recent success in the dynamical systems approach to transitional flow, we study the efficiency and effectiveness of extracting simple invariant sets (recurrent flows) directly from chaotic/turbulent flows and the potential of…
Consider a tree network T, where each edge acts as an independent copy of a given channel M, and information is propagated from the root. For which T and M does the configuration obtained at level n of T typically contain significant…
We consider the behaviour of minimax recursions defined on random trees. Such recursions give the value of a general class of two-player combinatorial games. We examine in particular the case where the tree is given by a Galton-Watson…
We consider three different schemes for signal routing on a tree. The vertices of the tree represent transceivers that can transmit and receive signals, and are equipped with i.i.d. weights representing the strength of the transceivers. The…
We introduce a novel interpretable tree based algorithm for prediction in a regression setting. Our motivation is to estimate the unknown regression function from a functional decomposition perspective in which the functional components…
Regression trees have emerged as a preeminent tool for solving real-world regression problems due to their ability to deal with nonlinearities, interaction effects and sharp discontinuities. In this article, we rather study regression trees…