Conditional Density Estimation with Histogram Trees

• URL: http://arxiv.org/abs/2410.11449v1
• Date: Tue, 15 Oct 2024 09:53:24 GMT
• Title: Conditional Density Estimation with Histogram Trees
• Authors: Lincen Yang, Matthijs van Leeuwen,
• Abstract summary: Conditional density estimation (CDE) goes beyond regression by modeling the full conditional distribution. Current methods typically employ kernel-based approaches, using kernel functions directly for kernel density estimation or as basis functions in linear models. We propose the Conditional Density Tree (CDTree), a fully non-parametric model consisting of a decision tree in which each leaf is formed by a histogram model.
• Score: 3.5297361401370044
• License:
• Abstract: Conditional density estimation (CDE) goes beyond regression by modeling the full conditional distribution, providing a richer understanding of the data than just the conditional mean in regression. This makes CDE particularly useful in critical application domains. However, interpretable CDE methods are understudied. Current methods typically employ kernel-based approaches, using kernel functions directly for kernel density estimation or as basis functions in linear models. In contrast, despite their conceptual simplicity and visualization suitability, tree-based methods -- which are arguably more comprehensible -- have been largely overlooked for CDE tasks. Thus, we propose the Conditional Density Tree (CDTree), a fully non-parametric model consisting of a decision tree in which each leaf is formed by a histogram model. Specifically, we formalize the problem of learning a CDTree using the minimum description length (MDL) principle, which eliminates the need for tuning the hyperparameter for regularization. Next, we propose an iterative algorithm that, although greedily, searches the optimal histogram for every possible node split. Our experiments demonstrate that, in comparison to existing interpretable CDE methods, CDTrees are both more accurate (as measured by the log-loss) and more robust against irrelevant features. Further, our approach leads to smaller tree sizes than existing tree-based models, which benefits interpretability.

Related papers

• Latent Semantic Consensus For Deterministic Geometric Model Fitting [109.44565542031384]
  We propose an effective method called Latent Semantic Consensus (LSC) LSC formulates the model fitting problem into two latent semantic spaces based on data points and model hypotheses. LSC is able to provide consistent and reliable solutions within only a few milliseconds for general multi-structural model fitting.
  arXiv  Detail & Related papers  (2024-03-11T05:35:38Z)
• Mixtures of All Trees [28.972995038976745]
  We propose a novel class of generative models called mixtures of all trees: that is, a mixture over all possible ($nn-2$) tree-shaped graphical models over $n$ variables. We show that it is possible to parameterize this Mixture of All Trees (MoAT) model compactly in a way that allows for tractable likelihood and optimization via gradient descent.
  arXiv  Detail & Related papers  (2023-02-27T23:37:03Z)
• Discrete Tree Flows via Tree-Structured Permutations [5.929956715430168]
  discrete flow-based models cannot be straightforwardly optimized with conventional deep learning methods because gradients of discrete functions are undefined or zero. Our approach seeks to reduce computational burden and remove the need for pseudo-gradients by developing a discrete flow based on decision trees.
  arXiv  Detail & Related papers  (2022-07-04T23:11:04Z)
• Hierarchical Shrinkage: improving the accuracy and interpretability of tree-based methods [10.289846887751079]
  We introduce Hierarchical Shrinkage (HS), a post-hoc algorithm that does not modify the tree structure. HS substantially increases the predictive performance of decision trees, even when used in conjunction with other regularization techniques. All code and models are released in a full-fledged package available on Github.
  arXiv  Detail & Related papers  (2022-02-02T02:43:23Z)
• Scaling Structured Inference with Randomization [64.18063627155128]
  We propose a family of dynamic programming (RDP) randomized for scaling structured models to tens of thousands of latent states. Our method is widely applicable to classical DP-based inference. It is also compatible with automatic differentiation so can be integrated with neural networks seamlessly.
  arXiv  Detail & Related papers  (2021-12-07T11:26:41Z)
• 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)
• Spectral Top-Down Recovery of Latent Tree Models [13.681975313065477]
  Spectral Top-Down Recovery (STDR) is a divide-and-conquer approach for inference of large latent tree models. STDR's partitioning step is non-random. Instead, it is based on the Fiedler vector of a suitable Laplacian matrix related to the observed nodes. We prove that STDR is statistically consistent, and bound the number of samples required to accurately recover the tree with high probability.
  arXiv  Detail & Related papers  (2021-02-26T02:47:42Z)
• Visualizing hierarchies in scRNA-seq data using a density tree-biased autoencoder [50.591267188664666]
  We propose an approach for identifying a meaningful tree structure from high-dimensional scRNA-seq data. We then introduce DTAE, a tree-biased autoencoder that emphasizes the tree structure of the data in low dimensional space.
  arXiv  Detail & Related papers  (2021-02-11T08:48:48Z)
• Autoregressive Score Matching [113.4502004812927]
  We propose autoregressive conditional score models (AR-CSM) where we parameterize the joint distribution in terms of the derivatives of univariable log-conditionals (scores) For AR-CSM models, this divergence between data and model distributions can be computed and optimized efficiently, requiring no expensive sampling or adversarial training. We show with extensive experimental results that it can be applied to density estimation on synthetic data, image generation, image denoising, and training latent variable models with implicit encoders.
  arXiv  Detail & Related papers  (2020-10-24T07:01:24Z)
• Convex Polytope Trees [57.56078843831244]
  convex polytope trees (CPT) are proposed to expand the family of decision trees by an interpretable generalization of their decision boundary. We develop a greedy method to efficiently construct CPT and scalable end-to-end training algorithms for the tree parameters when the tree structure is given.
  arXiv  Detail & Related papers  (2020-10-21T19:38:57Z)
• ENTMOOT: A Framework for Optimization over Ensemble Tree Models [57.98561336670884]
  ENTMOOT is a framework for integrating tree models into larger optimization problems. We show how ENTMOOT allows a simple integration of tree models into decision-making and black-box optimization.
  arXiv  Detail & Related papers  (2020-03-10T14:34:07Z)

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.