Estimating individualized treatment effects under continuous treatments (e.g., medication dosage) is challenging because treatment-response heterogeneity is often entangled with treatment-assignment bias in observational data. This paper proposes H-AdvCE, a Hellinger distance-based representation learning framework for cluster-aware continuous treatment effect estimation. The key idea is to learn a latent representation that preserves outcome-relevant heterogeneity while reducing dependence between the representation and treatment assignment. Theoretically, we derive a new counterfactual generalization error bound based on the Hellinger distance and show that it is tighter than commonly used Kullback–Leibler (KL) divergence-based alternatives. To optimize this objective, we introduce a variational Hellinger regularizer and formulate the learning problem as a min–max adversarial game. Empirically, H-AdvCE achieves strong performance on IHDP, News, and TCGA benchmarks for continuous dose-response estimation. Beyond prediction accuracy, the learned latent space reveals response-aware subgroups with distinct dose-response patterns, demonstrating its potential for clustering-driven interpretation in continuous treatment effect analysis. Our code is available at https://github.com/syzhao117/AdvCE .

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 method, 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.

OBJECTIVE: Estimating readmission risk for intensive care unit (ICU) patients is critical for clinicians to optimize resource allocation and prevent premature discharges. Machine learning models currently applied to this task either lack interpretability or cannot identify patient subgroups with distinctive readmission risks and characteristics. We addressed this gap by introducing a cutting-edge rule-based model, namely truly unordered rule sets (TURS), to reveal heterogeneous readmission risks and subgroup-level patient characteristics. MATERIALS AND METHODS: We trained TURS on all ICU admissions from January 2011 to January 2020 at Leiden University Medical Center. For each subgroup, patient characteristics and the influence of feature variables on readmission risk were analyzed. RESULTS: TURS identified subgroups with heterogeneous feature distributions and feature importance, providing actionable insights for ICU discharge planning. Its predictive performance (area under the receiver operating characteristic curve [ROC-AUC] 70.5%) and model complexity (5 rules, average length 2) surpassed other rule-based models. DISCUSSION: Subgroup analysis highlighted the heterogeneity of patients. First, we compared the conditional probability distribution of each feature variable, conditioned on the fact that a patient was in a certain subgroup, with its unconditional distribution. We identified features deviating from the unconditional distribution, illustrating unique subgroup-specific implications. Furthermore, we demonstrated that features with the highest impact on the readmission risk were distinctive for each subgroup. CONCLUSION: The TURS model provided a concise summary of patient subgroups, aiding ICU discharge decisions and advancing knowledge discovery in the ICU.

We introduce Time-Conditioned Contraction Matching (TCCM), a novel method for semi-supervised anomaly detection in tabular data. TCCM is inspired by flow matching, a recent generative modeling framework that learns velocity fields between probability distributions and has shown strong performance compared to diffusion models and generative adversarial networks. Instead of directly applying flow matching as originally formulated, TCCM builds on its core idea—learning velocity fields between distributions—but simplifies the framework by predicting a time-conditioned contraction vector toward a fixed target (the origin) at each sampled time step. This design offers three key advantages: (1) a lightweight and scalable training objective that removes the need for solving ordinary differential equations during training and inference; (2) an efficient scoring strategy called one time-step deviation, which quantifies deviation from expected contraction behavior in a single forward pass, addressing the inference bottleneck of existing continuous-time models such as DTE (a diffusion-based model with leading anomaly detection accuracy but heavy inference cost); and (3) explainability and provable robustness, as the learned velocity field operates directly in input space, making the anomaly score inherently feature-wise attributable; moreover, the score function is Lipschitz-continuous with respect to the input, providing theoretical guarantees under small perturbations. Extensive experiments on the ADBench benchmark show that TCCM strikes a favorable balance between detection accuracy and inference cost, outperforming state-of-the-art methods—especially on high-dimensional and large-scale datasets. The source code is provided at https://github.com/ZhongLIFR/TCCM-NIPS.

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.

Abstract Unsupervised discretization is a crucial step in many knowledge discovery tasks. The state-of-the-art method for one-dimensional data infers locally adaptive histograms using the minimum description length (MDL) principle, but the multi-dimensional case is far less studied: current methods consider the dimensions one at a time (if not independently), which result in discretizations based on rectangular cells of adaptive size. Unfortunately, this approach is unable to adequately characterize dependencies among dimensions and/or results in discretizations consisting of more cells (or bins) than is desirable. To address this problem, we propose an expressive model class that allows for far more flexible partitions of two-dimensional data. We extend the state of the art for the one-dimensional case to obtain a model selection problem based on the normalized maximum likelihood, a form of refined MDL. As the flexibility of our model class comes at the cost of a vast search space, we introduce a heuristic algorithm, named PALM, whichpartitions each dimensionalternately and thenmerges neighboring regions, all using the MDL principle. Experiments on synthetic data show that PALM (1) accurately reveals ground truth partitions that are within the model class (i.e., the search space), given a large enough sample size; (2) approximates well a wide range of partitions outside the model class; (3) converges, in contrast to the state-of-the-art multivariate discretization method IPD. Finally, we apply our algorithm to three spatial datasets, and we demonstrate that, compared to kernel density estimation (KDE), our algorithm not only reveals more detailed density changes, but also fits unseen data better, as measured by the log-likelihood.

information for discrete-continuous mixtures using multi-dimensional adaptive histograms.