Related papers: Spanning Tree Constrained Determinantal Point Proc…
Decision trees and random forest remain highly competitive for classification on medium-sized, standard datasets due to their robustness, minimal preprocessing requirements, and interpretability. However, a single tree suffers from high…
Spanning trees are an important primitive in many data analysis tasks, when a data set needs to be summarized in terms of its "skeleton", or when a tree-shaped graph over all observations is required for downstream processing. Popular…
This paper makes two main contributions: The first is the construction of a near-minimum spanning tree with constant average distortion. The second is a general equivalence theorem relating two refined notions of distortion: scaling…
In some practical learning tasks, such as traffic video analysis, the number of available training samples is restricted by different factors, such as limited communication bandwidth and computation power. Determinantal Point Process (DPP)…
We introduce tree representations for $ \alpha$-determinantal point processes. The $ \alpha$-determinantal point processes is introduced as a one parameter extension of the determinantal point process. In the previous paper with H.Osada,…
The matrices of spanning rooted forests are studied as a tool for analysing the structure of digraphs and measuring their characteristics. The problems of revealing the basis bicomponents, measuring vertex proximity, and ranking from…
Determinantal point processes (DPPs for short) are a class of repulsive point processes. They have found some statistical applications to model spatial point pattern datasets with repulsion between close points. In the case of DPPs on…
We prove that any graph $G$ with $n$ points has a distribution $\mathcal{T}$ over spanning trees such that for any edge $(u,v)$ the expected stretch $E_{T \sim \mathcal{T}}[d_T(u,v)/d_G(u,v)]$ is bounded by $\tilde{O}(\log n)$. Our result…
We show variants of spectral sparsification routines can preserve the total spanning tree counts of graphs, which by Kirchhoff's matrix-tree theorem, is equivalent to determinant of a graph Laplacian minor, or equivalently, of any SDDM…
We consider the stochastic geometry model where the location of each node is a random point in a given metric space, or the existence of each node is uncertain. We study the problems of computing the expected lengths of several…
Eliciting preferences from human judgements is inherently imprecise, yet most decision analysis methods force a single priority vector from pairwise comparisons, discarding the information embedded in inconsistencies. We instead leverage…
A determinantal point process (DPP) is a probabilistic model of set diversity compactly parameterized by a positive semi-definite kernel matrix. To fit a DPP to a given task, we would like to learn the entries of its kernel matrix by…
Decision trees built with data remain in widespread use for nonparametric prediction. Predicting probability distributions is preferred over point predictions when uncertainty plays a prominent role in analysis and decision-making. We study…
We present a new random sampling strategy for k-bandlimited signals defined on graphs, based on determinantal point processes (DPP). For small graphs, ie, in cases where the spectrum of the graph is accessible, we exhibit a DPP sampling…
Symmetric determinantal point processes (DPP's) are a class of probabilistic models that encode the random selection of items that exhibit a repulsive behavior. They have attracted a lot of attention in machine learning, when returning…
Determinantal Point Processes (DPPs) have attracted significant interest from the machine-learning community due to their ability to elegantly and tractably model the delicate balance between quality and diversity of sets. DPPs are commonly…
Determinantal point processes (DPPs) have garnered attention as an elegant probabilistic model of set diversity. They are useful for a number of subset selection tasks, including product recommendation. DPPs are parametrized by a positive…
Suppose N is a phylogenetic network indicating a complicated relationship among individuals and taxa. Often of interest is a much simpler network, for example, a species tree T, that summarizes the most fundamental relationships. The…
We propose a novel diverse feature selection method based on determinantal point processes (DPPs). Our model enables one to flexibly define diversity based on the covariance of features (similar to orthogonal matching pursuit) or…
Finding spanning trees under various constraints is a classic problem with applications in many fields. Recently, a novel notion of "dense" ("sparse") tree, and in particular spanning tree (DST and SST respectively), is introduced as the…