Decision trees (DTs) and their random forest (RF) extensions are workhorses of classification and regression in Euclidean spaces. However, algorithms for learning in non-Euclidean spaces are still limited. We extend DT and RF algorithms to product manifolds: Cartesian products of several hyperbolic, hyperspherical, or Euclidean components. Such manifolds handle heterogeneous curvature while still factorizing neatly into simpler components, making them compelling embedding spaces for complex datasets. Our novel angular reformulation of DTs respects the geometry of the product manifold, yielding splits that are geodesically convex, maximum-margin, and composable. In the special cases of single-component manifolds, our method simplifies to its Euclidean or hyperbolic counterparts, or introduces hyperspherical DT algorithms, depending on the curvature. We benchmark our method on various classification, regression, and link prediction tasks on synthetic data, graph embeddings, mixed-curvature variational autoencoder latent spaces, and empirical data. Compared to six other classifiers, product DTs and RFs ranked first on 21 of 22 single-manifold benchmarks and 18 of 35 product manifold benchmarks, and placed in the top 2 on 53 of 57 benchmarks overall. This highlights the value of product DTs and RFs as straightforward yet powerful new tools for data analysis in product manifolds. Code for our paper is available at https://github.com/pchlenski/embedders.

Random Forests are widely recognized for establishing efficacy in classification and regression tasks, standing out in various domains such as medical diagnosis, finance, and personalized recommendations. These domains, however, are inherently sensitive to privacy concerns, as personal and confidential data are involved. With increasing demand for the right to be forgotten, particularly under regulations such as GDPR and CCPA, the ability to perform machine unlearning has become crucial for Random Forests. However, insufficient attention was paid to this topic, and existing approaches face difficulties in being applied to real-world scenarios. Addressing this gap, we propose the DynFrs framework designed to enable efficient machine unlearning in Random Forests while preserving predictive accuracy. Dynfrs leverages subsampling method Occ(q) and a lazy tag strategy Lzy, and is still adaptable to any Random Forest variant. In essence, Occ(q) ensures that each sample in the training set occurs only in a proportion of trees so that the impact of deleting samples is limited, and Lzy delays the reconstruction of a tree node until necessary, thereby avoiding unnecessary modifications on tree structures. In experiments, applying Dynfrs on Extremely Randomized Trees yields substantial improvements, achieving orders of magnitude faster unlearning performance and better predictive accuracy than existing machine unlearning methods for Random Forests.

The Random Forest (RF) algorithm can be applied to a broad spectrum of problems, including time series prediction. However, neither the classical IID (Independent and Identically distributed) bootstrap nor block bootstrapping strategies (as implemented in rangerts) completely account for the nature of the Data Generating Process (DGP) while resampling the observations. We propose the combination of RF with a residual bootstrapping technique where we replace the IID bootstrap with the AR-Sieve Bootstrap (ARSB), which assumes the DGP to be an autoregressive process. To assess the new model's predictive performance, we conduct a simulation study using synthetic data generated from different types of DGPs. It turns out that ARSB provides more variation amongst the trees in the forest. Moreover, RF with ARSB shows greater accuracy compared to RF with other bootstrap strategies. However, these improvements are achieved at some efficiency costs.

We present Timber, the first white-box poisoning attack targeting decision trees. Timber is based on a greedy attack strategy leveraging sub-tree retraining to efficiently estimate the damage performed by poisoning a given training instance. The attack relies on a tree annotation procedure which enables sorting training instances so that they are processed in increasing order of computational cost of sub-tree retraining. This sorting yields a variant of Timber supporting an early stopping criterion designed to make poisoning attacks more efficient and feasible on larger datasets. We also discuss an extension of Timber to traditional random forest models, which is useful because decision trees are normally combined into ensembles to improve their predictive power. Our experimental evaluation on public datasets shows that our attacks outperform existing baselines in terms of effectiveness, efficiency or both. Moreover, we show that two representative defenses can mitigate the effect of our attacks, but fail at effectively thwarting them.

Random forests have become popular for clinical risk prediction modelling. In a case study on predicting ovarian malignancy, we observed training c-statistics close to 1. Although this suggests overfitting, performance was competitive on test data. We aimed to understand the behaviour of random forests by (1) visualizing data space in three real world case studies and (2) a simulation study. For the case studies, risk estimates were visualised using heatmaps in a 2-dimensional subspace. The simulation study included 48 logistic data generating mechanisms (DGM), varying the predictor distribution, the number of predictors, the correlation between predictors, the true c-statistic and the strength of true predictors. For each DGM, 1000 training datasets of size 200 or 4000 were simulated and RF models trained with minimum node size 2 or 20 using ranger package, resulting in 192 scenarios in total. The visualizations suggested that the model learned spikes of probability around events in the training set. A cluster of events created a bigger peak, isolated events local peaks. In the simulation study, median training c-statistics were between 0.97 and 1 unless there were 4 or 16 binary predictors with minimum node size 20. Median test c-statistics were higher with higher events per variable, higher minimum node size, and binary predictors. Median training slopes were always above 1, and were not correlated with median test slopes across scenarios (correlation -0.11). Median test slopes were higher with higher true c-statistic, higher minimum node size, and higher sample size. Random forests learn local probability peaks that often yield near perfect training c-statistics without strongly affecting c-statistics on test data. When the aim is probability estimation, the simulation results go against the common recommendation to use fully grown trees in random forest models.

Class imbalance in binary classification tasks remains a significant challenge in machine learning, often resulting in poor performance on minority classes. This study comprehensively evaluates three widely-used strategies for handling class imbalance: Synthetic Minority Over-sampling Technique (SMOTE), Class Weights tuning, and Decision Threshold Calibration. We compare these methods against a baseline scenario of no-intervention across 15 diverse machine learning models and 30 datasets from various domains, conducting a total of 9,000 experiments. Performance was primarily assessed using the F1-score, although our study also tracked results on additional 9 metrics including F2-score, precision, recall, Brier-score, PR-AUC, and AUC. Our results indicate that all three strategies generally outperform the baseline, with Decision Threshold Calibration emerging as the most consistently effective technique. However, we observed substantial variability in the best-performing method across datasets, highlighting the importance of testing multiple approaches for specific problems. This study provides valuable insights for practitioners dealing with imbalanced datasets and emphasizes the need for dataset-specific analysis in evaluating class imbalance handling techniques.

Originally proposed for handling time series data, Auto-regressive Decision Trees (ARDTs) have not yet been explored for language modeling. This paper delves into both the theoretical and practical applications of ARDTs in this new context. We theoretically demonstrate that ARDTs can compute complex functions, such as simulating automata, Turing machines, and sparse circuits, by leveraging "chain-of-thought" computations. Our analysis provides bounds on the size, depth, and computational efficiency of ARDTs, highlighting their surprising computational power. Empirically, we train ARDTs on simple language generation tasks, showing that they can learn to generate coherent and grammatically correct text on par with a smaller Transformer model. Additionally, we show that ARDTs can be used on top of transformer representations to solve complex reasoning tasks. This research reveals the unique computational abilities of ARDTs, aiming to broaden the architectural diversity in language model development.

In materials science, data-driven methods accelerate material discovery and optimization while reducing costs and improving success rates. Symbolic regression is a key to extracting material descriptors from large datasets, in particular the Sure Independence Screening and Sparsifying Operator (SISSO) method. While SISSO needs to store the entire expression space to impose heavy memory demands, it limits the performance in complex problems. To address this issue, we propose a RF-SISSO algorithm by combining Random Forests (RF) with SISSO. In this algorithm, the Random Forest algorithm is used for prescreening, capturing non-linear relationships and improving feature selection, which may enhance the quality of the input data and boost the accuracy and efficiency on regression and classification tasks. For a testing on the SISSO's verification problem for 299 materials, RF-SISSO demonstrates its robust performance and high accuracy. RF-SISSO can maintain the testing accuracy above 0.9 across all four training sample sizes and significantly enhancing regression efficiency, especially in training subsets with smaller sample sizes. For the training subset with 45 samples, the efficiency of RF-SISSO was 265 times higher than that of original SISSO. As collecting large datasets would be both costly and time-consuming in the practical experiments, it is thus believed that RF-SISSO may benefit scientific researches by offering a high predicting accuracy with limited data efficiently.

Large language models (LLMs) provide powerful means to leverage prior knowledge for predictive modeling when data is limited. In this work, we demonstrate how LLMs can use their compressed world knowledge to generate intrinsically interpretable machine learning models, i.e., decision trees, without any training data. We find that these zero-shot decision trees can surpass data-driven trees on some small-sized tabular datasets and that embeddings derived from these trees perform on par with data-driven tree-based embeddings on average. Our knowledge-driven decision tree induction and embedding approaches therefore serve as strong new baselines for data-driven machine learning methods in the low-data regime.

We connect the problem of properly PAC learning decision trees to the parameterized Nearest Codeword Problem ($k$-NCP). Despite significant effort by the respective communities, algorithmic progress on both problems has been stuck: the fastest known algorithm for the former runs in quasipolynomial time (Ehrenfeucht and Haussler 1989) and the best known approximation ratio for the latter is $O(n/\log n)$ (Berman and Karpinsky 2002; Alon, Panigrahy, and Yekhanin 2009). Research on both problems has thus far proceeded independently with no known connections. We show that $\textit{any}$ improvement of Ehrenfeucht and Haussler's algorithm will yield $O(\log n)$-approximation algorithms for $k$-NCP, an exponential improvement of the current state of the art. This can be interpreted either as a new avenue for designing algorithms for $k$-NCP, or as one for establishing the optimality of Ehrenfeucht and Haussler's algorithm. Furthermore, our reduction along with existing inapproximability results for $k$-NCP already rule out polynomial-time algorithms for properly learning decision trees. A notable aspect of our hardness results is that they hold even in the setting of $\textit{weak}$ learning whereas prior ones were limited to the setting of strong learning.