相关论文: On the total variation regularized estimator over …

Given a graph $G=(V,E)$ with two distinguished vertices $s,t\in V$ and an integer parameter $L>0$, an {\em $L$-bounded cut} is a subset $F$ of edges (vertices) such that the every path between $s$ and $t$ in $G\setminus F$ has length more…

Let $G$ be a connected graph with vertex set $V(G)$, and denote by $d_G(u,v)$ the distance from $u$ to $v$ in $G$, for any $u,v \in V(G)$. The average distance of an $n$-vertex connected graph $G$, denoted by $\mu(G)$, is defined to be the…

We provide a set of probabilistic laws for estimating the quadratic variation of continuous semimartingales with realized range-based variance -- a statistic that replaces every squared return of realized variance with a normalized squared…

We investigate the tractability of a simple fusion of two fundamental structures on graphs, a spanning tree and a perfect matching. Specifically, we consider the following problem: given an edge-weighted graph, find a minimum-weight…

Large graphs abound in machine learning, data mining, and several related areas. A useful step towards analyzing such graphs is that of obtaining certain summary statistics - e.g., or the expected length of a shortest path between two…

In this paper we consider alignment of sparse graphs, for which we introduce the Neighborhood Tree Matching Algorithm (NTMA). For correlated Erd\H{o}s-R\'{e}nyi random graphs, we prove that the algorithm returns -- in polynomial time -- a…

We study high-dimensional linear models and the $\ell_1$-penalized least squares estimator, also known as the Lasso estimator. In literature, oracle inequalities have been derived under restricted eigenvalue or compatibility conditions. In…

A compositional tree refers to a tree structure on a set of random variables where each random variable is a node and composition occurs at each non-leaf node of the tree. As a generalization of compositional data, compositional trees…

In this paper, we present a new simple degree-based estimator for the size of maximum matching in bounded arboricity graphs. When the arboricity of the graph is bounded by $\alpha$, the estimator gives a $\alpha+2$ factor approximation of…

This paper investigates the partial linear model by Least Absolute Deviation (LAD) regression. We parameterize the nonparametric term using Deep Neural Networks (DNNs) and formulate a penalized LAD problem for estimation. Specifically, our…

We propose a model of random walks on weighted graphs where the weights are interval valued, and connect it to reversible imprecise Markov chains. While the theory of imprecise Markov chains is now well established, this is a first attempt…

We study the problem of sharing as many branching conditions of a given forest classifier or regressor as possible while keeping classification performance. As a constraint for preventing from accuracy degradation, we first consider the one…

In this paper, we provide finite sample results to assess the consistency of Generalized Pareto regression trees, as tools to perform extreme value regression. The results that we provide are obtained from concentration inequalities, and…

A fundamental problem in network science is the normalization of the topological or physical distance between vertices, that requires understanding the range of variation of the unnormalized distances. Here we investigate the limits of the…

We prove that among all graphs of order n, the path uniquely minimises the average order of its connected induced subgraphs. This confirms a conjecture of Kroeker, Mol and Oellermann, and generalises a classical result of Jamison for trees,…

We consider the statistical inference problem of recovering an unknown perfect matching, hidden in a weighted random graph, by exploiting the information arising from the use of two different distributions for the weights on the edges…

Decision trees are important both as interpretable models amenable to high-stakes decision-making, and as building blocks of ensemble methods such as random forests and gradient boosting. Their statistical properties, however, are not well…

We enumerate factorisations of the complete graph into spanning regular graphs in several cases, including when the degrees of all the factors except for one or two are small. The resulting asymptotic behaviour is seen to generalise the…

Comparative analysis of scalar fields is an important problem with various applications including feature-directed visualization and feature tracking in time-varying data. Comparing topological structures that are abstract and succinct…

We give the first non-trivial fully dynamic probabilistic tree embedding algorithm for weighted graphs undergoing edge insertions and deletions. We obtain a trade-off between amortized update time and expected stretch against an oblivious…