RFX (Random Forests X), where X stands for compression or quantization, presents a production-ready implementation of Breiman and Cutler's Random Forest classification methodology in Python. RFX v1.0 provides complete classification: out-of-bag error estimation, overall and local importance measures, proximity matrices with QLORA compression, case-wise analysis, and interactive visualization (rfviz)--all with CPU and GPU acceleration. Regression, unsupervised learning, CLIQUE importance, and RF-GAP proximity are planned for v2.0. This work introduces four solutions addressing the proximity matrix memory bottleneck limiting Random Forest analysis to ~60,000 samples: (1) QLORA (Quantized Low-Rank Adaptation) compression for GPU proximity matrices, reducing memory from 80GB to 6.4MB for 100k samples (12,500x compression with INT8 quantization) while maintaining 99% geometric structure preservation, (2) CPU TriBlock proximity--combining upper-triangle storage with block-sparse thresholding--achieving 2.7x memory reduction with lossless quality, (3) SM-aware GPU batch sizing achieving 95% GPU utilization, and (4) GPU-accelerated 3D MDS visualization computing embeddings directly from low-rank factors using power iteration. Validation across four implementation modes (GPU/CPU x case-wise/non-case-wise) demonstrates correct implementation. GPU achieves 1.4x speedup over CPU for overall importance with 500+ trees. Proximity computation scales from 1,000 to 200,000+ samples (requiring GPU QLORA), with CPU TriBlock filling the gap for medium-scale datasets (10K-50K samples). RFX v1.0 eliminates the proximity memory bottleneck, enabling proximity-based Random Forest analysis on datasets orders of magnitude larger than previously feasible. Open-source production-ready classification following Breiman and Cutler's original methodology.

Discovering subgroups with the maximum average treatment effect is crucial for targeted decision making in domains such as precision medicine, public policy, and education. While most prior work is formulated in the potential outcome framework, the corresponding structural causal model (SCM) for this task has been largely overlooked. In practice, two approaches dominate. The first estimates pointwise conditional treatment effects and then fits a tree on those estimates, effectively turning subgroup estimation into the harder problem of accurate pointwise estimation. The second constructs decision trees or rule sets with ad-hoc 'causal' heuristics, typically without rigorous justification for why a given heuristic may be used or whether such heuristics are necessary at all. We address these issues by studying the problem directly under the SCM framework. Under the assumption of a partition-based model, we show that optimal subgroup discovery reduces to recovering the data-generating models and hence a standard supervised learning problem (regression or classification). This allows us to adopt any partition-based methods to learn the subgroup from data. We instantiate the approach with CART, arguably one of the most widely used tree-based methods, to learn the subgroup with maximum treatment effect. Finally, on a large collection of synthetic and semi-synthetic datasets, we compare our method against a wide range of baselines and find that our approach, which avoids such causal heuristics, more accurately identifies subgroups with maximum treatment effect. Our source code is available at https://github.com/ylincen/causal-subgroup.

Decision trees are popular in survival analysis for their interpretability and ability to model complex relationships. Survival trees, which predict the timing of singular events using censored historical data, are typically built through heuristic approaches. Recently, there has been growing interest in globally optimized trees, where the overall tree is trained by minimizing the error function over all its parameters. We propose a new soft survival tree model (SST), with a soft splitting rule at each branch node, trained via a nonlinear optimization formulation amenable to decomposition. Since SSTs provide for every input vector a specific survival function associated to a single leaf node, they satisfy the conditional computation property and inherit the related benefits. SST and the training formulation combine flexibility with interpretability: any smooth survival function (parametric, semiparametric, or nonparametric) estimated through maximum likelihood can be used, and each leaf node of an SST yields a cluster of distinct survival functions which are associated to the data points routed to it. Numerical experiments on 15 well-known datasets show that SSTs, with parametric and spline-based semiparametric survival functions, trained using an adaptation of the node-based decomposition algorithm proposed by Consolo et al. (2024) for soft regression trees, outperform three benchmark survival trees in terms of four widely-used discrimination and calibration measures. SSTs can also be extended to consider group fairness.

Decision trees and random forests are well established models that not only offer good predictive performance, but also provide rich feature importance information. While practitioners often employ variable importance methods that rely on this impurity-based information, these methods remain poorly characterized from a theoretical perspective. We provide novel insights into the performance of these methods by deriving finite sample performance guarantees in a high-dimensional setting under various modeling assumptions. We further demonstrate the effectiveness of these impurity-based methods via an extensive set of simulations.

Deep distributed decision trees and tree ensembles have grown in importance due to the need to model increasingly large datasets. However, PLANET, the standard distributed tree learning algorithm implemented in systems such as \xgboost and Spark MLlib, scales poorly as data dimensionality and tree depths grow. We present Yggdrasil, a new distributed tree learning method that outperforms existing methods by up to 24x. Unlike PLANET, Yggdrasil is based on vertical partitioning of the data (i.e., partitioning by feature), along with a set of optimized data structures to reduce the CPU and communication costs of training. Yggdrasil (1) trains directly on compressed data for compressible features and labels; (2) introduces efficient data structures for training on uncompressed data; and (3) minimizes communication between nodes by using sparse bitvectors. Moreover, while PLANET approximates split points through feature binning, Yggdrasil does not require binning, and we analytically characterize the impact of this approximation. We evaluate Yggdrasil against the MNIST 8M dataset and a high-dimensional dataset at Yahoo; for both, Yggdrasil is faster by up to an order of magnitude.

Decision tree (and its extensions such as Gradient Boosting Decision Trees and Random Forest) is a widely used machine learning algorithm, due to its practical effectiveness and model interpretability. With the emergence of big data, there is an increasing need to parallelize the training process of decision tree. However, most existing attempts along this line suffer from high communication costs. In this paper, we propose a new algorithm, called \emph{Parallel Voting Decision Tree (PV-Tree)}, to tackle this challenge. After partitioning the training data onto a number of (e.g., $M$) machines, this algorithm performs both local voting and global voting in each iteration.

Gradient Boosting Decision Tree (GBDT) is a popular machine learning algorithm, and has quite a few effective implementations such as XGBoost and pGBRT. Although many engineering optimizations have been adopted in these implementations, the efficiency and scalability are still unsatisfactory when the feature dimension is high and data size is large. A major reason is that for each feature, they need to scan all the data instances to estimate the information gain of all possible split points, which is very time consuming.

While practitioners often employ variable importance methods that rely on this impurity-based information, these methods remain poorly characterized from a theoretical perspective.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/