A new type of distributional regression tree uses soft split rules for better predictive performance.
problem Estimating complete conditional distributions in regression.
method Distributional adaptive soft regression trees using multivariate soft split rules.
result The method outperforms various benchmark methods, especially in complex non-linear interactions.
ASBART accelerates Soft BART for faster Bayesian regression.
problem Slow computation in Soft BART.
method Proposed ASBART, a variant of Soft BART.
result ASBART is about 10 times faster than Soft BART with similar accuracy.
VaSST uses soft symbolic trees for probabilistic symbolic regression.
problem Efficiently recover symbolic expressions from noisy data.
method Variational inference with soft symbolic trees.
result Superior performance in structural recovery and predictive accuracy.
Bayesian GBMs improve predictive uncertainty calibration for tabular data.
problem Lack of well-calibrated predictive uncertainties in gradient boosting machines.
method Variational inference with soft decision trees.
result Variational soft GBMs provide useful uncertainty estimates and maintain good predictive performance.
SBAMDT uses adaptive soft splits to model complex decision boundaries.
problem Limited ability of standard decision trees to capture complex decision boundaries.
method Probabilistic additive decision tree model with adaptive soft multivariate splits.
result Demonstrated improved predictive performance on synthetic and real datasets.
The paper introduces a new model to correct bias in treatment effect estimates due to sample selection.
problem Bias in treatment effect estimates due to sample selection.
method Type 2 Tobit Bayesian Additive Regression Trees (TOBART-2) with Dirichlet Process Mixture distribution and soft trees.
result Corrects bias in treatment effect estimates by accounting for nonlinearities and model uncertainty.
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.
We present an algorithm for learning decision trees using stochastic gradient information as the source of supervision. In contrast to previous approaches to gradient-based tree learning, our method operates in the incremental learning setting rather than the batch learning setting, and does not make use of soft splits…
SoftBart improves BART for high-noise modeling in science.
problem High noise in scientific data.
method Soft BART algorithm for Bayesian additive regression trees.
result Improves predictive performance and facilitates larger model integration.
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.
Dropout is a very effective method in preventing overfitting and has become the go-to regularizer for multi-layer neural networks in recent years. Hierarchical mixture of experts is a hierarchically gated model that defines a soft decision tree where leaves correspond to experts and decision nodes correspond to gating …
Rectified decision trees improve machine learning interpretability and effectiveness.
problem Combining interpretability and effectiveness in machine learning models.
method Knowledge distillation and modified decision tree splitting criteria.
result Soft labels improve model performance and reduce model size.
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 …
We discuss an autoencoder model in which the encoding and decoding functions are implemented by decision trees. We use the soft decision tree where internal nodes realize soft multivariate splits given by a gating function and the overall output is the average of all leaves weighted by the gating values on their path. …
This paper improves deep forest models with soft routing and topology learning.
problem Expensive computational costs and lack of interpretability in deep neural networks.
method Soft routing in probabilistic trees and topology learning for joint optimization.
result Empowered deep forests achieve better performance with reduced model complexity.
In regression tasks the distribution of the data is often too complex to be fitted by a single model. In contrast, partition-based models are developed where data is divided and fitted by local models. These models partition the input space and do not leverage the input-output dependency of multimodal-distributed data,…
Introduces Soft-SVM for binary classification bridging logistic and SVM.
problem Data separability issues in binary classification.
method Soft-SVM regression using convex relaxation of hinge loss with softness and class-separation parameters.
result Soft-SVM performs well in classification and prediction errors.
We comment on the fact that gradient ascent for logistic regression has a connection with the perceptron learning algorithm. Logistic learning is the "soft" variant of perceptron learning.
In this article supervised learning problems are solved using soft rule ensembles. We first review the importance sampling learning ensembles (ISLE) approach that is useful for generating hard rules. The soft rules are then obtained with logistic regression from the corresponding hard rules. In order to deal with the p…
Regression, unlike classification, has lacked a comprehensive and effective approach to deal with cost-sensitive problems by the reuse (and not a re-training) of general regression models. In this paper, a wide variety of cost-sensitive problems in regression (such as bids, asymmetric losses and rejection rules) can be…
Study uses regression and ML for COVID-19 mortality forecasting.
problem Forecasting COVID-19 mortality during the first wave in Spain.
method Cyclical curve log-regression, multivariate time series spatial residual correlation analysis, Bayesian approach, machine learning.
result Empirical analysis shows ML regression models perform better than traditional methods.
How to obtain a model with good interpretability and performance has always been an important research topic. In this paper, we propose rectified decision trees (ReDT), a knowledge distillation based decision trees rectification with high interpretability, small model size, and empirical soundness. Specifically, we ext…
sGBM speeds up gradient boosting by parallelizing and adapting base learners.
problem Infeasibility of parallelizing GBM training and sub-optimal performance in online settings.
method Integrates multiple differentiable base learners, jointly optimizing them with linear speed-up.
result sGBM achieves higher time efficiency and better accuracy than traditional GBM.
New method improves stability of soft FQI for offline RL.
problem Stability issues in soft FQI under function approximation.
method Stationary reweighting to align operator norms.
result Local linear convergence proved under certain 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 Hierarchical Mixture of Experts (HME) is a well-known tree-based model for regression and classification, based on soft probabilistic splits. In its original formulation it was trained by maximum likelihood, and is therefore prone to over-fitting. Furthermore the maximum likelihood framework offers no natural metri…
Hybrid model for online nonlinear prediction using LSTM and soft GBDT.
problem Online nonlinear prediction with manual feature selection and model selection issues.
method End-to-end architecture with LSTM for feature extraction and soft GBDT for regression, jointly optimized.
result Significant performance improvements over conventional methods on real datasets.
Neural Networks and Decision Trees: two popular techniques for supervised learning that are seemingly disconnected in their formulation and optimization method, have recently been combined in a single construct. The connection pivots on assembling an artificial Neural Network with nodes that allow for a gate-like funct…
Deep neural networks have proved to be a very effective way to perform classification tasks. They excel when the input data is high dimensional, the relationship between the input and the output is complicated, and the number of labeled training examples is large. But it is hard to explain why a learned network makes a…
New framework optimizes decisions under uncertainty considering causal and continuous data.
problem Optimizing decisions under uncertain distributions with causal and continuous data structures.
method Developed a framework using Causal Sinkhorn DRO with Soft Regression Forest decision rules.
result Framework provides interpretable and tractable decision rules for optimizing under uncertainty.
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.
A new tree method for tensor data improves regression accuracy.
problem Efficiently modeling tensor data for regression problems.
method Scalar-output regression tree models for scalar-on-tensor problems, and tensor-on-tensor problems using additive tree ensemble approaches.
result The tensor-input tree (TT) method outperforms tensor-input GP models in efficiency and accuracy.
Regression trees learn gradients of differentiable functions.
problem Understanding gradients of differentiable functions using regression trees.
method Developed a method to estimate gradients of differentiable functions using regression trees and exposed quantities from tree learning libraries.
result Gradient estimates from regression trees can be used to improve predictive analysis and solve tasks in uncertainty quantification.
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.
Regression Trees analyze stock returns, revealing market excess return as the most informative factor.
problem Understanding informational content of three factors in stock returns.
method Joint regression tree analysis of daily stock return data for 5 major US corporations.
result The market excess return factor is always the most informative in all cases (solo and joint).
Additive nonparametric regression models provide an attractive tool for variable selection in high dimensions when the relationship between the response and predictors is complex. They offer greater flexibility compared to parametric non-linear regression models and better interpretability and scalability than the non-…
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…
SMART combines decision trees and MARS for better regression modeling.
problem High variance in decision trees for continuous relationships, poor performance in MARS for discontinuities.
method SMART uses a decision tree to identify subsets with distinct continuous relationships, then applies MARS to fit these relationships independently.
result SMART improves regression performance over state-of-the-art methods in capturing discontinuities and continuous relationships.
JSRT improves regression tree performance by incorporating global node information.
problem Regression tree performance relies on local node means, ignoring global node information.
method Proposes JSRT by integrating global mean information from different nodes.
result Demonstrates superior performance and efficiency compared to other regression tree methods.
π-GNN learns soft permutations for graph representations, improving graph classification and regression.
problem Limitations of MPNNs in graph neural networks.
method Proposes π-GNN, which learns a soft permutation matrix for each graph, projecting graphs into a common vector space.
result π-GNN achieves performance competitive with state-of-the-art models on graph classification and regression tasks.
Unified approach for interpretable regression with flexible modeling.
problem Combining predictive adaptivity with interpretability in heterogeneous data.
method Combining random Fourier features, spectral feature map, principal component analysis, Gaussian mixture model, and cluster-specific generalized additive models.
result Consistently improves upon classical and black-box models across benchmark datasets.
New trees-based models handle correlated data better.
problem Standard trees-based models ignore correlation structure.
method Explicitly accounts for correlation structure in splitting criterion, stopping rules, and fitted values.
result New approach superior to standard models in simulations and real data.
GP-BART improves BART's predictive performance by incorporating Gaussian process priors.
problem Lack of smoothness and explicit covariance structure in BART.
method GP-BART extends BART with Gaussian process priors for tree predictions.
result GP-BART outperforms traditional models in various applications.
Active learning improves soft sensor development by suggesting informative labels.
problem Expensive labeling of process variables in industrial settings.
method Adapted active learning strategies for online data streams and used semi-supervised autoencoders.
result Improved predictive performance of soft sensors using active learning and autoencoders.
Paper compares hard and soft EM for BN learning from incomplete data.
problem Learning BNs from incomplete data using EM algorithms.
method Investigates the impact of imputation vs. belief propagation in hard and soft EM.
result A decision tree can guide practitioners in choosing the best EM algorithm.
Enhances time-series regression trees with latent factors for robust financial analysis.
problem Handling predictors with measurement error, trends, seasonality, and missing data.
method Integrates latent stationary factors extracted via state-space methods into time-series regression trees.
result Factor-augmented trees provide a reliable approach for macro-finance problems, exemplified by the lead-lag effect between equity volatility and the business cycle.
We study the convergence of the predictive surface of regression trees and forests. To support our analysis we introduce a notion of adaptive concentration for regression trees. This approach breaks tree training into a model selection phase in which we pick the tree splits, followed by a model fitting phase where we f…
There is growing evidence that converting targets to soft targets in supervised learning can provide considerable gains in performance. Much of this work has considered classification, converting hard zero-one values to soft labels---such as by adding label noise, incorporating label ambiguity or using distillation. In…