Rethink Tree Traversal

• URL: http://arxiv.org/abs/2209.04825v5
• Date: Mon, 17 Jun 2024 16:34:32 GMT
• Title: Rethink Tree Traversal
• Authors: Jinxiong Zhang,
• Abstract summary: Key idea is to travel the binary decision tree by maximum inner product search. We not only implement decision tree methods without the recursive traverse but also delve into the partitioning nature of tree-based methods.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We will show how to implement binary decision tree traversal in the language of matrix computation. Our main contribution is to propose some equivalent algorithms of binary tree traversal based on a novel matrix representation of the hierarchical structure of the decision tree. Our key idea is to travel the binary decision tree by maximum inner product search. We not only implement decision tree methods without the recursive traverse but also delve into the partitioning nature of tree-based methods.

Related papers

• ReTreever: Tree-based Coarse-to-Fine Representations for Retrieval [64.44265315244579]
  We propose a tree-based method for organizing and representing reference documents at various granular levels. Our method, called ReTreever, jointly learns a routing function per internal node of a binary tree such that query and reference documents are assigned to similar tree branches. Our evaluations show that ReTreever generally preserves full representation accuracy.
  arXiv  Detail & Related papers  (2025-02-11T21:35:13Z)
• Learning a Decision Tree Algorithm with Transformers [75.96920867382859]
  We introduce MetaTree, a transformer-based model trained via meta-learning to directly produce strong decision trees. We fit both greedy decision trees and globally optimized decision trees on a large number of datasets, and train MetaTree to produce only the trees that achieve strong generalization performance.
  arXiv  Detail & Related papers  (2024-02-06T07:40:53Z)
• TreeDQN: Learning to minimize Branch-and-Bound tree [78.52895577861327]
  Branch-and-Bound is a convenient approach to solving optimization tasks in the form of Mixed Linear Programs. The efficiency of the solver depends on the branchning used to select a variable for splitting. We propose a reinforcement learning method that can efficiently learn the branching.
  arXiv  Detail & Related papers  (2023-06-09T14:01:26Z)
• Phylo2Vec: a vector representation for binary trees [0.49478969093606673]
  We present Phylo2Vec, a parsimonious encoding for phylogenetic trees. It serves as a unified approach for both manipulating and representing phylogenetic trees. As a proof of concept, we use Phylo2Vec for maximum likelihood inference on five real-world datasets.
  arXiv  Detail & Related papers  (2023-04-25T09:54:35Z)
• Structure-Unified M-Tree Coding Solver for MathWord Problem [57.825176412485504]
  In previous work, models designed by taking into account the properties of the binary tree structure of mathematical expressions at the output side have achieved better performance. In this paper, we propose the Structure-Unified M-Tree Coding Coding (S-UMCr), which applies a tree with any M branches (M-tree) to unify the output structures. Experimental results on the widely used MAWPS and Math23K datasets have demonstrated that SUMC-r not only outperforms several state-of-the-art models but also performs much better under low-resource conditions.
  arXiv  Detail & Related papers  (2022-10-22T12:20:36Z)
• Robustifying Algorithms of Learning Latent Trees with Vector Variables [92.18777020401484]
  We present the sample complexities of Recursive Grouping (RG) and Chow-Liu Recursive Grouping (CLRG) We robustify RG, CLRG, Neighbor Joining (NJ) and Spectral NJ (SNJ) by using the truncated inner product. We derive the first known instance-dependent impossibility result for structure learning of latent trees.
  arXiv  Detail & Related papers  (2021-06-02T01:37:52Z)
• Decision Machines: Congruent Decision Trees [0.0]
  We propose Decision Machines, which embed Boolean tests into a binary vector space and represent the tree structure as a matrices. We explore the congruence of decision trees and attention mechanisms, opening new avenues for optimizing decision trees and potentially enhancing their predictive power.
  arXiv  Detail & Related papers  (2021-01-27T12:23:24Z)
• Yet Another Representation of Binary Decision Trees: A Mathematical Demonstration [0.0]
  A decision tree looks like a simple directed acyclic computational graph, where only the leaf nodes specify the output values. From the numerical perspective, we express decision trees in the language of computational graph.
  arXiv  Detail & Related papers  (2021-01-18T13:50:14Z)
• Recursive Top-Down Production for Sentence Generation with Latent Trees [77.56794870399288]
  We model the production property of context-free grammars for natural and synthetic languages. We present a dynamic programming algorithm that marginalises over latent binary tree structures with $N$ leaves. We also present experimental results on German-English translation on the Multi30k dataset.
  arXiv  Detail & Related papers  (2020-10-09T17:47:16Z)
• Learning Binary Decision Trees by Argmin Differentiation [34.9154848754842]
  We learn binary decision trees that partition data for some downstream task. We do so by relaxing a mixed-integer program for the discrete parameters. We derive customized algorithms to efficiently compute the forward and backward passes.
  arXiv  Detail & Related papers  (2020-10-09T15:11:28Z)
• MurTree: Optimal Classification Trees via Dynamic Programming and Search [61.817059565926336]
  We present a novel algorithm for learning optimal classification trees based on dynamic programming and search. Our approach uses only a fraction of the time required by the state-of-the-art and can handle datasets with tens of thousands of instances.
  arXiv  Detail & Related papers  (2020-07-24T17:06:55Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.