Trunc-Opt vine building algorithms

• URL: http://arxiv.org/abs/2512.14399v1
• Date: Tue, 16 Dec 2025 13:37:00 GMT
• Title: Trunc-Opt vine building algorithms
• Authors: Dániel Pfeifer, Edith Alice Kovács,
• Abstract summary: This paper introduces a new score for fitting truncated vines to given data, called Weight of truncated vine.<n>We give algorithms for constructing and encoding truncated vines which do exploit them.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Vine copula models have become highly popular and practical tools for modelling multivariate probability distributions due to their flexibility in modelling different kinds of dependences between the random variables involved. However, their flexibility comes with the drawback of a high-dimensional parameter space. To tackle this problem, truncated vine copulas were introduced by Kurowicka (2010) (Gaussian case) and Brechmann and Czado (2013) (general case). Truncated vine copulas contain conditionally independent pair copulas after the truncation level. So far, in the general case, truncated vine constructing algorithms started from the lowest tree in order to encode the largest dependences in the lower trees. The novelty of this paper starts from the observation that a truncated vine is determined by the first tree after the truncation level (see Kovács and Szántai (2017)). This paper introduces a new score for fitting truncated vines to given data, called the Weight of the truncated vine. Then we propose a completely new methodology for constructing truncated vines. We prove theorems which motivate this new approach. While earlier algorithms did not use conditional independences, we give algorithms for constructing and encoding truncated vines which do exploit them. Finally, we illustrate the algorithms on real datasets and compare the results with well-known methods included in R packages. Our method generally compare favorably to previously known methods.

Related papers

• Birch SGD: A Tree Graph Framework for Local and Asynchronous SGD Methods [51.54704494242525]
  We propose a new unifying framework, Birch SGD, for analyzing and designing distributed SGD methods.<n>Using Birch SGD, we design eight new methods and analyze them alongside previously known ones, with at least six of the new methods shown to have optimal computational time complexity.<n>Our research leads to two key insights: (i) all methods share the same "iteration rate" of $Oleft(frac(R + 1) L Deltavarepsilon + fracsigma2 L Deltavarepsilon2right)$, where $R$
  arXiv  Detail & Related papers  (2025-05-14T08:37:45Z)
• Free Lunch in the Forest: Functionally-Identical Pruning of Boosted Tree Ensembles [45.962492329047215]
  We introduce a method to prune a tree ensemble into a reduced version that is "functionally identical" to the original model.<n>We formalize the problem of functionally identical pruning on ensembles, introduce an exact optimization model, and provide a fast yet highly effective method to prune large ensembles.
  arXiv  Detail & Related papers  (2024-08-28T23:15:46Z)
• SUnAA: Sparse Unmixing using Archetypal Analysis [62.997667081978825]
  This paper introduces a new geological error map technique using archetypal sparse analysis (SUnAA) First, we design a new model based on archetypal sparse analysis (SUnAA)
  arXiv  Detail & Related papers  (2023-08-09T07:58:33Z)
• Bayesian Decision Trees via Tractable Priors and Probabilistic Context-Free Grammars [7.259767735431625]
  We propose a new criterion for training Bayesian Decision Trees. BCART-PCFG can efficiently sample decision trees from a posterior distribution across trees given the data. We find that trees sampled via BCART-PCFG perform comparable to or better than greedily-constructed Decision Trees.
  arXiv  Detail & Related papers  (2023-02-15T00:17:41Z)
• A Robust Hypothesis Test for Tree Ensemble Pruning [2.4923006485141284]
  We develop and present a novel theoretically justified hypothesis test of split quality for gradient boosted tree ensembles. We show that using this method instead of the common penalty terms leads to a significant reduction in out of sample loss. We also present several innovative extensions to the method, opening the door for a wide variety of novel tree pruning algorithms.
  arXiv  Detail & Related papers  (2023-01-24T16:31:49Z)
• Lassoed Tree Boosting [53.56229983630983]
  We prove that a gradient boosted tree algorithm with early stopping faster than $n-1/4$ L2 convergence in the large nonparametric space of cadlag functions of bounded sectional variation. Our convergence proofs are based on a novel, general theorem on early stopping with empirical loss minimizers of nested Donsker classes.
  arXiv  Detail & Related papers  (2022-05-22T00:34:41Z)
• On multivariate randomized classification trees: $l_0$-based sparsity, VC~dimension and decomposition methods [0.9346127431927981]
  We investigate the nonlinear continuous optimization formulation proposed in Blanquero et al. We first consider alternative methods to sparsify such trees based on concave approximations of the $l_0$ norm" We propose a general decomposition scheme and an efficient version of it. Experiments on larger datasets show that the proposed decomposition method is able to significantly reduce the training times without compromising the accuracy.
  arXiv  Detail & Related papers  (2021-12-09T22:49:08Z)
• A cautionary tale on fitting decision trees to data from additive models: generalization lower bounds [9.546094657606178]
  We study the generalization performance of decision trees with respect to different generative regression models. This allows us to elicit their inductive bias, that is, the assumptions the algorithms make (or do not make) to generalize to new data. We prove a sharp squared error generalization lower bound for a large class of decision tree algorithms fitted to sparse additive models.
  arXiv  Detail & Related papers  (2021-10-18T21:22:40Z)
• SGA: A Robust Algorithm for Partial Recovery of Tree-Structured Graphical Models with Noisy Samples [75.32013242448151]
  We consider learning Ising tree models when the observations from the nodes are corrupted by independent but non-identically distributed noise. Katiyar et al. (2020) showed that although the exact tree structure cannot be recovered, one can recover a partial tree structure. We propose Symmetrized Geometric Averaging (SGA), a more statistically robust algorithm for partial tree recovery.
  arXiv  Detail & Related papers  (2021-01-22T01:57:35Z)
• 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.