Related papers: Random Frame Decompositions from Weighted Residual…
Given an edge-weighted tree $T$ with $n$ leaves, sample the leaves uniformly at random without replacement and let $W_k$, $2 \le k \le n$, be the length of the subtree spanned by the first $k$ leaves. We consider the question, "Can $T$ be…
Deep learning approaches to optical flow estimation have seen rapid progress over the recent years. One common trait of many networks is that they refine an initial flow estimate either through multiple stages or across the levels of a…
Random spanning trees are among the most prominent determinantal point processes. We give four examples of random spanning trees on ladder-like graphs whose rungs form stationary renewal processes or regenerative processes of order two,…
Dynamic sampling mechanisms in deep learning architectures have demonstrated utility across many computer vision models, though the theoretical analysis of these structures has not yet been unified. In this paper we connect the various…
The past decade has witnessed the development and success of coarse-grained network models of proteins for predicting many equilibrium properties related to collective modes of motion. Curiously, the results are usually robust towards the…
Weighted recursive trees are built by adding successively vertices with predetermined weights to a tree: each new vertex is attached to a parent chosen randomly proportionally to its weight. Under some assumptions on the sequence of…
D. Wilson~\cite{[Wi]} in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a…
Normalizing flows are a powerful tool for generative modelling, density estimation and posterior reconstruction in Bayesian inverse problems. In this paper, we introduce proximal residual flows, a new architecture of normalizing flows.…
A treedepth decomposition of an undirected graph $G$ is a rooted forest $F$ on the vertex set of $G$ such that every edge $uv\in E(G)$ is in ancestor-descendant relationship in $F$. Given a weight function $w\colon V(G)\rightarrow…
The issue of estimating residual variance in regression models has experienced relatively little attention in the machine learning community. However, the estimate is of primary interest in many practical applications, e.g. as a primary…
We consider growing random recursive trees in random environment, in which at each step a new vertex is attached (by an edge of a random length) to an existing tree vertex according to a probability distribution that assigns the tree…
In this paper, orthogonal to the existing data and model studies, we instead resort our efforts to investigate the potential of loss function in a new perspective and present our belief ``Random Weights Networks can Be Acted as Loss Prior…
We introduce a new framework for the analysis of the dynamics of networks, based on randomly reinforced urn (RRU) processes, in which the weight of the edges is determined by a reinforcement mechanism. We rigorously explain the empirical…
Motivated by the study of pattern avoidance in the context of permutations and ordered partitions, we consider the enumeration of weak-ordering chains obtained as leaves of certain restricted rooted trees. A tree of order $n$ is generated…
Motivated by a recently introduced network growth mechanism that rely on the ranking of node prestige measures [S. Fortunato \emph{et al}., Phys. Rev. Lett. \textbf{96}, 218701 (2006)], a rank-based model for weighted network evolution is…
A new class of (not necessarily bounded) operators related to (mainly infinite) directed trees is introduced and investigated. Operators in question are to be considered as a generalization of classical weighted shifts, on the one hand, and…
We study effective randomness-preserving transformations of path-incompressible trees. Some path-incompressible trees with infinitely many paths do not compute perfect path-random trees with computable oracle-use. Sparse perfect…
This paper addresses the understanding and characterization of residual networks (ResNet), which are among the state-of-the-art deep learning architectures for a variety of supervised learning problems. We focus on the mapping component of…
We first establish a kernel theorem that characterizes all linear shift-invariant (LSI) operators acting on discrete multicomponent signals. This result naturally leads to the identification of the Parseval convolution operators as the…
A mechanism deriving new well-posed evolutionary equations from given ones is inspected. It turns out that there is one particular spatial operator from which many of the standard evolutionary problems of mathematical physics can be…