GLMM trees identify subgroups with different growth patterns in longitudinal data.
problem Identifying subgroups with distinct growth trajectories in longitudinal studies.
method Extended GLMM trees for longitudinal data.
result Extended GLMM trees outperform other methods in accuracy and speed.
Paper develops federated GLMM algorithms for analyzing hierarchical data.
problem Analyzing hierarchical data with non-independent observations in a federated setting.
method Developed two federated GLMM algorithms using Laplace and Gaussian Hermite approximations.
result Federated GLMM can handle hierarchical data and achieve comparable or superior performance.
Conjugate gradient methods improve efficiency for high-dimensional GLMMs.
problem Efficiency bottleneck in computing high-dimensional GLMM precision matrices.
method Combining spectral analysis and random graph theory with conjugate gradient methods.
result CG-based methods achieve linear scaling in cost with model parameters and observations.
Neural models improve GLMMs for complex data.
problem Nonlinear relationships in grouped data.
method Replaced linear function with neural networks.
result Improved performance on synthetic and real-world data.
Integrates neural encoders into GLMMs for multimodal data analysis.
problem Scalable Bayesian inference for GLMMs assumes low-dimensional tabular predictors and does not handle high-dimensional modalities.
method Jointly learns modality-specific neural encoders with GLMM objective, performs variance-corrected stochastic-gradient MCMC.
result Preserves interpretable fixed and random effects while scaling to large longitudinal datasets.
New method for accurate Bayesian inference in GLMMs for large-scale data.
problem Challenges in scalable Bayesian inference for GLMMs due to intractable marginal likelihood and high computational cost.
method Stochastic gradient Markov Chain Monte Carlo (SGMCMC) algorithm using Fisher's identity for gradient estimation.
result Accurate posterior inference in large-sample settings with properly calibrated uncertainty.
We propose a Markov chain model for credit rating changes. We do not use any distributional assumptions on the asset values of the rated companies but directly model the rating transitions process. The parameters of the model are estimated by a maximum likelihood approach using historical rating transitions and heurist…
Boosting meta-trees improve decision tree performance.
problem Overfitting in decision trees.
method Boosting approach to construct multiple meta-trees.
result Ensembles of meta-trees prevent overfitting.
The paper studies geometric properties of quasi-trees and tree approximations.
problem Geometric properties and tree approximations of quasi-trees.
method Construction of a tree approximating quasi-trees, proving quasi-isometric properties.
result Every quasi-tree is (1,C)-quasi-isometric to a simplicial tree. Efficiently updates posterior tree distributions over meta-trees.
problem Updating posterior distributions over meta-trees efficiently.
method Batch updating method for posterior tree distributions.
result More efficient batch updating method.
This paper describes experiments, on two domains, to investigate the effect of averaging over predictions of multiple decision trees, instead of using a single tree. Other authors have pointed out theoretical and commonsense reasons for preferring the multiple tree approach. Ideally, we would like to consider predictio…
We introduce a novel incremental decision tree learning algorithm, Hoeffding Anytime Tree, that is statistically more efficient than the current state-of-the-art, Hoeffding Tree. We demonstrate that an implementation of Hoeffding Anytime Tree---"Extremely Fast Decision Tree", a minor modification to the MOA implementat…
We introduce block-tree graphs as a framework for deriving efficient algorithms on graphical models. We define block-tree graphs as a tree-structured graph where each node is a cluster of nodes such that the clusters in the graph are disjoint. This differs from junction-trees, where two clusters connected by an edge al…
This paper introduces TNTK to study infinite soft tree ensembles.
problem Understanding the behavior of infinite soft tree ensembles.
method Introduced Tree Neural Tangent Kernel (TNTK) to analyze infinite soft tree ensembles.
result Identified several non-trivial properties of infinite soft tree ensembles.
Paper analyzes soft tree ensembles using NTK, finding only leaf count matters.
problem Understanding impact of various tree architectures in ensemble learning.
method Formulated and analyzed Neural Tangent Kernel (NTK) for soft tree ensembles.
result Only the number of leaves at each depth is relevant for tree architecture in ensemble learning.
Researchers improve tree model recovery from noisy data.
problem Learning tree structured models from corrupted data.
method Linear latent tree models and continuous corruption model.
result Chow-Liu algorithm consistently learns tree from noisy data.
Optimal survival trees ensemble reduces tree count and improves predictive performance.
problem Improving predictive performance in survival analysis.
method Grows a forest of optimal survival trees by ranking and selecting the best trees based on out-of-bag error.
result Reduces the number of trees in the ensemble while improving predictive performance.
Width trees link link invariants and bridge number.
problem Understanding link invariants through geometric structures.
method Associate width trees to links and use their geometric properties to bound link invariants.
result Width trees uniquely realize certain link invariants under specific conditions.
Paper studies ensemble probabilistic regression trees for smooth approximations.
problem Smooth approximations of regression functions.
method Ensemble versions of probabilistic regression trees.
result Ensemble probabilistic regression trees are consistent and perform well.
The task of translating between programming languages differs from the challenge of translating natural languages in that programming languages are designed with a far more rigid set of structural and grammatical rules. Previous work has used a tree-to-tree encoder/decoder model to take advantage of the inherent tree s…
Recently proposed budding tree is a decision tree algorithm in which every node is part internal node and part leaf. This allows representing every decision tree in a continuous parameter space, and therefore a budding tree can be jointly trained with backpropagation, like a neural network. Even though this continuity …
Characterizes fundamental groups of disjointly tree-graded spaces.
problem Understanding fundamental groups of complex geometric structures.
method Defines and analyzes disjointly tree-graded spaces, characterizing their fundamental groups.
result Fundamental groups of disjointly tree-graded spaces embed into inverse limits of free products of fundamental groups of pieces.
SBT model uses randomized sharding and sub-models to improve Bayesian Additive Regression Trees.
problem Improving efficiency and accuracy of Bayesian Additive Regression Trees.
method Randomized sharding, sub-models, intersection tree structure, optimal design.
result Theoretical optimal weights and worst-case complexity of SBT model.
Decision Machines embeds decision trees into vector spaces for improved optimization.
problem Overfitting and difficulty in finding optimal decision tree structure.
method Embedding Boolean tests into a binary vector space and representing tree structure as matrices.
result Optimized decision trees with enhanced predictive power.
Trees and their products compared to octahedron.
problem Comparing trees and their products to octahedron.
method Product comparison of trees to octahedron.
result Trees and their products meet octahedron comparison.
Tree Index evaluates cluster quality by creating decision trees from data.
problem Evaluating the quality of cluster results from various techniques.
method Tree Index creates a decision tree from clustered data, combining entropy and depth of leaves.
result Tree Index discriminates between sensible and non-sensible clusters on brain dataset.
TES-AE uses tree grammars to speed up autoencoding for tree data.
problem Challenges in autoencoding tree data due to its non-vectorial and discrete nature.
method TES-AE combines reservoir computing with tree grammars for faster training.
result TES-AE outperforms D-VAE in speed and accuracy for tree data.
Flexible tree ensemble learning framework supports arbitrary loss functions and multi-task learning.
problem Limited modeling capabilities of existing tree ensemble learning toolkits.
method Differentiable tree ensembles with tensor-based formulation for efficient training.
result Our framework leads to 100x more compact and 23% more expressive tree ensembles.
Kauri is a novel unsupervised binary tree for clustering that outperforms existing methods.
problem Learning a tree end-to-end for clustering without labels is an open challenge.
method Greedy maximization of the kernel KMeans objective without centroids.
result Kauri often outperforms existing unsupervised clustering methods, especially with non-linear kernels.
We introduce the concept of community trees that summarizes topological structures within a network. A community tree is a tree structure representing clique communities from the clique percolation method (CPM). The community tree also generates a persistent diagram. Community trees and persistent diagrams reveal topol…
HATT improves online decision tree ensembles by using a more eager splitting strategy.
problem Improving the efficiency of online decision tree ensembles.
method Replacing Hoeffding Tree's split strategy with HATT, which uses the Hoeffding Test for candidate splits.
result HATT outperforms Hoeffding Tree in online bagging and boosting ensembles, as shown by significant performance improvements in various testbenches.
Optimal Survival Trees improve accuracy in medical data analysis.
problem Analyzing censored outcomes in medical data.
method Mixed-integer optimization and local search techniques.
result Improves accuracy in large datasets compared to existing methods.
A novel tree algorithm improves time series forecasting accuracy.
problem Improving accuracy in non-linear time series forecasting.
method Developed a hierarchical TAR model as a regression tree that trains globally across series, introducing a forecasting-specific tree algorithm with cross-series learning.
result Significantly higher accuracy than state-of-the-art tree-based algorithms and benchmarks across four metrics.
Tree ensembles such as random forests and boosted trees are accurate but difficult to understand, debug and deploy. In this work, we provide the inTrees (interpretable trees) framework that extracts, measures, prunes and selects rules from a tree ensemble, and calculates frequent variable interactions. An rule-based le…
We introduce a method for creating a special type of tree, called a tree position, from a weighted graph. Leaves of the tree correspond to vertices of the original graph, and the tree edges contain information which can be used to partition these vertices. By repeatedly applying reducing operations to the tree position…
dtControl uses decision trees to represent controllers efficiently and explainably.
problem Representing controllers concisely and explainably.
method dtControl uses decision tree learning algorithms to represent controllers. Novel techniques for determinizing controllers are introduced.
result Novel techniques for determinizing controllers during decision tree construction are extremely efficient, yielding small decision trees.
Uniformly branching trees are equivalent to certain metric spaces.
problem Characterizing metric spaces equivalent to uniformly branching trees.
method Proving equivalence between trivalent quasiconformal trees and uniformly branching trees.
result Any two uniformly branching trees are quasisymmetrically equivalent.
ForestPrune optimizes tree ensemble pruning for compactness and speed.
problem Large tree ensembles in predictive models consume excessive memory and reduce interpretability.
method Developed a specialized optimization algorithm to efficiently prune tree ensembles by depth layers.
result ForestPrune produces compact, high-performing models that outperform existing post-processing methods.
PhyloVAE learns tree topologies without supervision.
problem Learning accurate tree representations from evolutionary data.
method Unsupervised learning via variational autoencoders with efficient tree generation.
result PhyloVAE generates high-resolution tree topologies efficiently.
Latent tree models are graphical models defined on trees, in which only a subset of variables is observed. They were first discussed by Judea Pearl as tree-decomposable distributions to generalise star-decomposable distributions such as the latent class model. Latent tree models, or their submodels, are widely used in:…
A single slow-growing tree matches Random Forest's performance.
problem Matching Random Forest's performance with a single tree.
method SGT uses a learning rate to tame CART's greedy algorithm, improving on greedy ML algorithms.
result SGT and tree ensembles like Booging, BT, and RF improve performance.
Trinary decision tree improves handling of missing data in machine learning.
problem Improving accuracy in decision tree algorithms when dealing with missing data.
method Introduces Trinary decision tree, which does not assume missing values contain information about the response.
result Trinary decision tree outperforms other algorithms in Missing Completely at Random settings, especially when data is only missing out-of-sample.
P-Trees improve investment performance by optimizing the efficient frontier.
problem Optimizing investment performance in complex financial markets.
method Introducing P-Trees, a new tree-based model for analyzing panel data.
result P-Trees significantly advance the efficient frontier and outperform existing models.
A cluster tree provides a highly-interpretable summary of a density function by representing the hierarchy of its high-density clusters. It is estimated using the empirical tree, which is the cluster tree constructed from a density estimator. This paper addresses the basic question of quantifying our uncertainty by ass…
New tree splitting criteria improve probabilistic predictions.
problem Improving tree-based nonparametric predictive distributions.
method Using proper scoring rules for tree splitting criteria.
result Trees with new splitting criteria produce better predictive distributions.
Study of Ricci flow on trees, focusing on edge weights and curvatures.
problem Understanding the evolution of metrics on trees under Ricci flow.
method Continuous-time Ricci flow based on Lin-Lu-Yau Ollivier Ricci curvature.
result Ricci flow converges to zero curvature on edge weights of positive normalized values in caterpillar trees.
Develops a new method to recover large latent tree models efficiently.
problem Inference of large latent tree structures from terminal node observations.
method Spectral Top-Down Recovery (STDR) using Fiedler vector partitioning.
result Proves statistical consistency and sample complexity for accurate tree recovery.
Multistage Defer Trees improve model accuracy while maintaining interpretability.
problem Balancing model accuracy and interpretability, especially in noisy domains.
method A sequence of sparse decision trees that defer predictions to the next tree or a black box.
result Matches the performance of complex tree-based ensembles while using only one or a few sparse trees.