相关论文: Partial orders and monotonicity of logarithmic dep…
We investigate the gradual emergence of the disorder-related phenomena in intermediate regimes between a deterministic periodic Bragg grating and a fully random grating and highlight two critical properties of partially disordered Bragg…
Random forests remain among the most popular off-the-shelf supervised machine learning tools with a well-established track record of predictive accuracy in both regression and classification settings. Despite their empirical success as well…
A rooted tree is balanced if the degree of a vertex depends only on its distance to the root. In this paper we determine the sharp threshold for the appearance of a large family of balanced spanning trees in the random geometric graph…
The data arrangement problem on regular trees (DAPT) consists in assigning the vertices of a given graph G to the leaves of a d-regular tree T such that the sum of the pairwise distances of all pairs of leaves in T which correspond to edges…
This paper derives a unifying theorem establishing consistency results for a broad class of tree-based algorithms. It improves current results in two aspects. First of all, it can be applied to algorithms that vary from traditional Random…
Reciprocity characterizes the information exchange between users in a network, and some empirical studies have revealed that social networks have a high proportion of reciprocal edges. Classical directed preferential attachment (PA) models,…
One of the most important classes of even $\Delta$-matroids arises from orientable ribbon graphs, which play a role analogous to that of graphic matroids in matroid theory. Motivated by a natural correspondence between strong…
We introduce the notion of quota trees in directed graphs. Given a nonnegative integer ``quota'' for each vertex of a directed multigraph $G$, a quota tree is an immersed rooted tree which hits each vertex of $G$ the prescribed number of…
The purpose of this paper is to provide further understanding into the structure of the sequential allocation ("stochastic multi-armed bandit", or MAB) problem by establishing probability one finite horizon bounds and convergence rates for…
In 1993 van den Berg and Kesten proved a strict monotonicity theorem for first passage percolation on $\mathbb{Z}^d$, $d \ge 2$: given two probability measures $\nu$ and $\tilde{\nu}$ with finite mean, if $\tilde{\nu}$ is strictly more…
Quasi-trees generalize trees in that the unique "path" between two nodes may be infinite and have any countable order type. They are used to define the rank-width of a countable graph in such a way that it is equal to the least upper-bound…
In this paper we study a variation of the accessibility percolation model, this is also motivated by evolutionary biology and evolutionary computation. Consider a tree whose vertices are labeled with random numbers. We study the probability…
We introduce a new matroid (graph) invariant, the arboricity polynomial. Given a matroid, the arboricity polynomial enumerates the number of covers of the ground set by disjoint independent sets. We establish the polynomiality of the…
Learning monotonic models with respect to a subset of the inputs is a desirable feature to effectively address the fairness, interpretability, and generalization issues in practice. Existing methods for learning monotonic neural networks…
We consider a sequence $\mathbf{T} = (\mathcal{T}_n : n \in \mathbb{N}^+)$ of trees $\mathcal{T}_n$ where, for some $\Delta \in \mathbb{N}^+$ every $\mathcal{T}_n$ has height at most $\Delta$ and as $n \to \infty$ the minimal number of…
Stochastic gradient descent (SGD), a widely used algorithm in deep-learning neural networks has attracted continuing studies for the theoretical principles behind its success. A recent work reports an anomaly (inverse) relation between the…
We study the growth of bipartite networks in which the number of nodes in one of the partitions is kept fixed while the other partition is allowed to grow. We study random and preferential attachment as well as combination of both. We…
Often in the analysis of first-order methods, assuming the existence of a quadratic growth bound (a generalization of strong convexity) facilitates much stronger convergence analysis. Hence the analysis is done twice, once for the general…
An influential line of recent work has focused on the generalization properties of unregularized gradient-based learning procedures applied to separable linear classification with exponentially-tailed loss functions. The ability of such…
In recent years, machine learning and AI have been introduced in many industrial fields. In fields such as finance, medicine, and autonomous driving, where the inference results of a model may have serious consequences, high…