A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Proves homology of mapping class groups for infinite-type surfaces.
Quantum circuits represent binary classification trees with binary features.
New method learns binary decision trees efficiently.
CEDA analyzes large categorical datasets using tree geometry and binary codes.
Kauri is a novel unsupervised binary tree for clustering that outperforms existing methods.
Study infers tree topology from customer data using contrastive learning.
A new clustering algorithm for functional data using binary trees.
Infinite fractal tree solves shortest connection problem.
Paper addresses limitations of traditional hierarchical clustering methods.
Researchers improve tree model recovery from noisy data.
We characterize and study variable importance (VIMP) and pairwise variable associations in binary regression trees. A key component involves the node mean squared error for a quantity we refer to as a maximal subtree. The theory naturally extends from single trees to ensembles of trees and applies to methods like rando…
We introduce the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering, a generalization of the Dirichlet Diffusion Tree (Neal, 2001) which removes the restriction to binary branching structure. The generative process is described and shown to result in an exchangeable distribution over data points. We prove som…
Hierarchical structure is ubiquitous in data across many domains. There are many hierarchical clustering methods, frequently used by domain experts, which strive to discover this structure. However, most of these methods limit discoverable hierarchies to those with binary branching structure. This limitation, while com…
Decision tree learning is a popular classification technique most commonly used in machine learning applications. Recent work has shown that decision trees can be used to represent provably-correct controllers concisely. Compared to representations using lookup tables or binary decision diagrams, decision trees are sma…
Probit Monotone BART estimates binary outcomes using monotonic functions.
Paper studies multiclass classifiers from binary classifiers, proving methods and demonstrating advantages.
Develops a binary tree model for option pricing with skew dynamics.
The Mondrian process represents an elegant and powerful approach for space partition modelling. However, as it restricts the partitions to be axis-aligned, its modelling flexibility is limited. In this work, we propose a self-consistent Binary Space Partitioning (BSP)-Tree process to generalize the Mondrian process. Th…
Enhanced Random Forests outperform XGBoost across binary classification datasets.
We introduce canonical correlation forests (CCFs), a new decision tree ensemble method for classification and regression. Individual canonical correlation trees are binary decision trees with hyperplane splits based on local canonical correlation coefficients calculated during training. Unlike axis-aligned alternatives…
One-class classifiers are trained with target class only samples. Intuitively, their conservative modelling of the class description may benefit classical classification tasks where classes are difficult to separate due to overlapping and data imbalance. In this work, three methods are proposed which leverage on the co…
We study the natural map eta between a group of binary planar trees whose leaves are labeled by elements of a free abelian group H and a certain group D(H) derived from the free Lie algebra over H. Both of these groups arise in several different topological contexts. The map eta is known to be an isomorphism over Q, bu…
Ensemble of regression trees have become popular statistical tools for the estimation of conditional mean given a set of predictors. However, quantile regression trees and their ensembles have not yet garnered much attention despite the increasing popularity of the linear quantile regression model. This work proposes a…
The Binary Space Partitioning-Tree~(BSP-Tree) process was recently proposed as an efficient strategy for space partitioning tasks. Because it uses more than one dimension to partition the space, the BSP-Tree Process is more efficient and flexible than conventional axis-aligned cutting strategies. However, due to its ba…
Decision Machines embeds decision trees into vector spaces for improved optimization.
The Binary Space Partitioning~(BSP)-Tree process is proposed to produce flexible 2-D partition structures which are originally used as a Bayesian nonparametric prior for relational modelling. It can hardly be applied to other learning tasks such as regression trees because extending the BSP-Tree process to a higher dim…
Risk bounds for Classification and Regression Trees (CART, Breiman et. al. 1984) classifiers are obtained under a margin condition in the binary supervised classification framework. These risk bounds are obtained conditionally on the construction of the maximal deep binary tree and permit to prove that the linear penal…
This research sets limits on how complex multi-class learning problems can be.
We present an alternative layer to convolution layers in convolutional neural networks (CNNs). Our approach reduces the complexity of convolutions by replacing it with binary decisions. Those binary decisions are used as indexes to conditional distributions where each weight represents a leaf in a decision tree. This m…
We propose a new splitting criterion for a meta-learning approach to multiclass classifier design that adaptively merges the classes into a tree-structured hierarchy of increasingly difficult binary classification problems. The classification tree is constructed from empirical estimates of the Henze-Penrose bounds on t…
New split rules improve subpopulation targeting in policy-making.
Decision trees with binary splits are popularly constructed using Classification and Regression Trees (CART) methodology. For binary classification and regression models, this approach recursively divides the data into two near-homogenous daughter nodes according to a split point that maximizes the reduction in sum of …
In this paper, we propose a compositional nonparametric method in which a model is expressed as a labeled binary tree of nodes, where each node is either a summation, a multiplication, or the application of one of the basis functions to one of the covariates. We show that in order to recover a labeled bi…
Tree ensembles like RF and GBT can be seen as kernels, improving regression and classification performance.
FairUDT uses uplift decision trees to detect and mitigate discrimination in training data.
Non-proper surface group action on product of trees found.
New method uses binary quadratic forms to classify Seifert surfaces in 4-ball.
We consider the problem of estimating the conditional probability of a label in time O(log n), where n is the number of possible labels. We analyze a natural reduction of this problem to a set of binary regression problems organized in a tree structure, proving a regret bound that scales with the depth of the tree. Mot…
The study analyzes decision trees on real and categorical features, deriving bounds on their VC dimension and proposing improved pruning algorithms.
Paper extends tree bijection for hyperbolic surfaces without requiring cusps.
We consider the problem of learning optimal binary classification trees. Literature on the topic has burgeoned in recent years, motivated both by the empirical suboptimality of heuristic approaches and the tremendous improvements in mixed-integer programming (MIP) technology. Yet, existing approaches from the literatur…
Paper analyzes soft tree ensembles using NTK, finding only leaf count matters.
Space partitioning methods such as random forests and the Mondrian process are powerful machine learning methods for multi-dimensional and relational data, and are based on recursively cutting a domain. The flexibility of these methods is often limited by the requirement that the cuts be axis aligned. The Ostomachion p…
Counting HCMU sphere components using weighted trees.
Spaces of circle embeddings in curved surfaces indexed by trees.
Non-ergodic geodesic flow on Cantor tree surfaces found.
Decision tree algorithms have been among the most popular algorithms for interpretable (transparent) machine learning since the early 1980's. The problem that has plagued decision tree algorithms since their inception is their lack of optimality, or lack of guarantees of closeness to optimality: decision tree algorithm…
Analytic patch trees reveal new geometric structures and dimension fields.