Related papers: Optimal spanning tree reconstruction in symbolic r…
Given a graph $G=(V,E)$, the minimum branch vertices problem consists in finding a spanning tree $T=(V,E')$ of $G$ minimizing the number of vertices with degree greater than two. We consider a simple combinatorial lower bound for the…
Kernel and linear regression have been recently explored in the prediction of graph signals as the output, given arbitrary input signals that are agnostic to the graph. In many real-world problems, the graph expands over time as new nodes…
Learning a regression function using censored or interval-valued output data is an important problem in fields such as genomics and medicine. The goal is to learn a real-valued prediction function, and the training output labels indicate an…
Spanning tree problems with specialized constraints can be difficult to solve in real-world scenarios, often requiring intricate algorithmic design and exponential time. Recently, there has been growing interest in end-to-end deep neural…
The goal of graph inference is to design algorithms for learning properties of a hidden graph using queries to an oracle that returns information about the graph. Graph reconstruction, verification, and property testing are all types of…
Constrained counting is a fundamental problem in artificial intelligence. A promising new algebraic approach to constrained counting makes use of tensor networks, following a reduction from constrained counting to the problem of…
In this paper, we aim to design sparse D-optimal (determinantoptimal) pose-graph SLAM problems through the synthesis of sparse graphs with the maximum weighted number of spanning trees. Characterizing graphs with the maximum number of…
Given an undirected, weighted graph, the minimum spanning tree (MST) is a tree that connects all of the vertices of the graph with minimum sum of edge weights. In real world applications, network designers often seek to quickly find a…
Stacking regressions is an ensemble technique that forms linear combinations of different regression estimators to enhance predictive accuracy. The conventional approach uses cross-validation data to generate predictions from the…
We consider the problem of constructing optimal decision trees: given a collection of tests which can disambiguate between a set of $m$ possible diseases, each test having a cost, and the a-priori likelihood of the patient having any…
In many applications of supervised learning, multiple classification or regression outputs have to be predicted jointly. We consider several extensions of gradient boosting to address such problems. We first propose a straightforward…
This paper addresses the problem of finding a representation of a subtree distance, which is an extension of the tree metric. We show that a minimal representation is uniquely determined by a given subtree distance, and give a linear time…
In recent years there has been a paradigm shift from the study of local task-related activation to the organization and functioning of large-scale functional and structural brain networks. However, a long-standing challenge in this…
Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…
This paper is concerned with the approximation of high-dimensional functions in a statistical learning setting, by empirical risk minimization over model classes of functions in tree-based tensor format. These are particular classes of…
Optimal transport provides a metric which quantifies the dissimilarity between probability measures. For measures supported in discrete metric spaces, finding the optimal transport distance has cubic time complexity in the size of the…
In designing and applying graph neural networks, we often fall into some optimization pitfalls, the most deceptive of which is that we can only build a deep model by solving over-smoothing. The fundamental reason is that we do not…
In this paper, we consider the problem of subsampling and reconstruction of signals that reside on the vertices of a product graph, such as sensor network time series, genomic signals, or product ratings in a social network. Specifically,…
This paper introduces a method to extract a hierarchical tree representation from 3D unorganized polygonal data. The proposed approach first extracts a graph representation of the surface, which serves as the foundation for structural…
We consider the minimum spanning tree problem in a setting where information about the edge weights of the given graph is uncertain. Initially, for each edge $e$ of the graph only a set $A_e$, called an uncertainty area, that contains the…