相关论文: The Cascading Metric Tree
Computing $k$-Nearest Neighbors (KNN) is one of the core kernels used in many machine learning, data mining and scientific computing applications. Although kd-tree based $O(\log n)$ algorithms have been proposed for computing KNN, due to…
Optimal 3-way comparison search trees (3WCST's) can be computed using standard dynamic programming in time O(n^3), and this can be further improved to O(n^2) by taking advantage of the Monge property. In contrast, the fastest algorithm in…
As a modern ensemble technique, Deep Forest (DF) employs a cascading structure to construct deep models, providing stronger representational power compared to traditional decision forests. However, its greedy multi-layer learning procedure…
We present a novel algorithm for the minimum-depth elimination tree problem, which is equivalent to the optimal treedepth decomposition problem. Our algorithm makes use of two cheaply-computed lower bound functions to prune the search tree,…
We consider a covariate shift problem where one has access to several different training datasets for the same learning problem and a small validation set which possibly differs from all the individual training distributions. This covariate…
This work presents novel algorithms for learning Bayesian network structures with bounded treewidth. Both exact and approximate methods are developed. The exact method combines mixed-integer linear programming formulations for structure…
In this work, we investigate how exploiting symmetry when creating and modifying structural models may speed up global atomistic structure optimization. We propose a search strategy in which models start from high symmetry configurations…
Many fundamental statistical methods have become critical tools for scientific data analysis yet do not scale tractably to modern large datasets. This paper will describe very recent algorithms based on computational geometry which have…
The recently introduced graph parameter tree-cut width plays a similar role with respect to immersions as the graph parameter treewidth plays with respect to minors. In this paper, we provide the first algorithmic applications of tree-cut…
Recent advances in Neural Machine Translation (NMT) show that adding syntactic information to NMT systems can improve the quality of their translations. Most existing work utilizes some specific types of linguistically-inspired tree…
We introduce K-tree in an information retrieval context. It is an efficient approximation of the k-means clustering algorithm. Unlike k-means it forms a hierarchy of clusters. It has been extended to address issues with sparse…
We present linear-time algorithms for partitioning a path or a tree with weights on the vertices by removing $k$ edges to maximize the minimum-weight component. We also use the same framework to partition a path with weight on the vertices,…
High-performance implementations of $k$-Nearest Neighbor Search ($k$NN) in low dimensions use tree-based data structures. Tree algorithms are hard to parallelize on GPUs due to their irregularity. However, newer Nvidia GPUs offer hardware…
In this paper we present novel algorithmic techniques with a O(H(N)+N/H(N)) time complexity for performing several types of queries and updates on general rooted trees, binary search trees and lists of size N. For rooted trees we introduce…
Numerous analysis methods for quantitative attack tree analysis have been proposed. These algorithms compute relevant security metrics, i.e. performance indicators that quantify how good the security of a system is; typical metrics being…
Quantum machine learning (QML) has attracted considerable research interest, yet whether it offers practical benefits over classical approaches remains an open question. The choice of data encoding significantly influences QML performance,…
Computing an optimal classification tree that provably maximizes training performance within a given size limit, is NP-hard, and in practice, most state-of-the-art methods do not scale beyond computing optimal trees of depth three.…
This paper presents an efficient algorithm for retrieving from a database of trees, all trees that match a given query tree approximately, that is, within a certain error tolerance. It has natural language processing applications in…
Decision tree (DT) attracts persistent research attention due to its impressive empirical performance and interpretability in numerous applications. However, the growth of traditional yet widely-used univariate decision trees (UDTs) is…
Nearest neighbor searching of large databases in high-dimensional spaces is inherently difficult due to the curse of dimensionality. A flavor of approximation is, therefore, necessary to practically solve the problem of nearest neighbor…