Related papers: Nearest Embedded and Embedding Self-Nested Trees
We study the NP-hard problem of approximating a Minimum Routing Cost Spanning Tree in the message passing model with limited bandwidth (CONGEST model). In this problem one tries to find a spanning tree of a graph $G$ over $n$ nodes that…
Tree structures have been shown to provide an efficient framework for propagating beliefs [Pearl,1986]. This paper studies the problem of finding an optimal approximating tree. The star decomposition scheme for sets of three binary…
We adopt data structure in the form of cover trees and iteratively apply approximate nearest neighbour (ANN) searches for fast compressed sensing reconstruction of signals living on discrete smooth manifolds. Levering on the recent…
In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an…
The number of embeddings of a partially ordered set $S$ in a partially ordered set $T$ is the number of subposets of $T$ isomorphic to $S$. If both, $S$ and $T$, have only one unique maximal element, we define good embeddings as those in…
In this paper we introduce a simple and intuitive adaptive k nearest neighbours classifier, and explore its utility within the context of bootstrap aggregating ("bagging"). The approach is based on finding discriminant subspaces which are…
Given a graph $G = (V, E)$, we wish to compute a spanning tree whose maximum vertex degree, i.e. tree degree, is as small as possible. Computing the exact optimal solution is known to be NP-hard, since it generalizes the Hamiltonian path…
Recently, deep neural networks have expanded the state-of-art in various scientific fields and provided solutions to long standing problems across multiple application domains. Nevertheless, they also suffer from weaknesses since their…
We investigate approximating joint distributions of random processes with causal dependence tree distributions. Such distributions are particularly useful in providing parsimonious representation when there exists causal dynamics among…
A variety of algorithms have been proposed for reconstructing trees that show the evolutionary relationships between species by comparing differences in genetic data across present-day taxa. If the leaf-to-leaf distances in a tree can be…
A new synthesis scheme is proposed to effectively generate a random vector with prescribed joint density that induces a (latent) Gaussian tree structure. The quality of synthesis is measured by total variation distance between the…
We propose an algorithm named best-scored random forest for binary classification problems. The terminology "best-scored" means to select the one with the best empirical performance out of a certain number of purely random tree candidates…
A simple linear-time algorithm for constructing a linear context-free tree grammar of size O(rg + r g log (n/r g))for a given input tree T of size n is presented, where g is the size of a minimal linear context-free tree grammar for T, and…
The Steiner Tree problem is a classical problem in combinatorial optimization: the goal is to connect a set $T$ of terminals in a graph $G$ by a tree of minimum size. Karpinski and Zelikovsky (1996) studied the $\delta$-dense version of…
We consider the indirect covering subtree problem (Kim et al., 1996). The input is an edge weighted tree graph along with customers located at the nodes. Each customer is associated with a radius and a penalty. The goal is to locate a…
Binary neural networks (BNNs) have been widely adopted to reduce the computational cost and memory storage on edge-computing devices by using one-bit representation for activations and weights. However, as neural networks become…
Let $T$ be a tree space (or tree network) represented by a weighted tree with $t$ vertices, and $S$ be a set of $n$ stochastic points in $T$, each of which has a fixed location with an independent existence probability. We investigate two…
In this paper, we propose a concept of approximate bisimulation relation for feedforward neural networks. In the framework of approximate bisimulation relation, a novel neural network merging method is developed to compute the approximate…
We give an algorithm that, given an $n$-vertex graph $G$ and an integer $k$, in time $2^{O(k)} n$ either outputs a tree decomposition of $G$ of width at most $2k + 1$ or determines that the treewidth of $G$ is larger than $k$. This is the…
We present the self-encoder, a neural network trained to guess the identity of each data sample. Despite its simplicity, it learns a very useful representation of data, in a self-supervised way. Specifically, the self-encoder learns to…