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arXiv:2402.09698v4 Announce Type: replace-cross Abstract: In sequential anytime-valid inference, any admissible procedure must be based on e-processes: generalizations of test martingales that quantify the accumulated evidence against a composite null hypothesis at any stopping time. This paper proposes a method for combining e-processes constructed in different filtrations but for the same null. Although e-processes in the same filtration can be combined effortlessly (by averaging), e-processes in different filtrations cannot because their validity in a coarser filtration does not translate to a finer filtration. This issue arises in sequential tests of randomness and independence, as well as in the evaluation of sequential forecasters. We establish that a class of functions called adjusters can lift arbitrary e-processes across filtrations. The result yields a generally applicable "adjust-then-combine" procedure, which we demonstrate on the problem of testing randomness in real-world financial data. Furthermore, we prove a characterization theorem for adjusters that formalizes a sense in which using adjusters is necessary. There are two major implications. First, if we have a powerful e-process in a coarsened filtration, then we readily have a powerful e-process in the original filtration. Second, when we coarsen the filtration to construct an e-process, there is a logarithmic cost to recovering validity in the original filtration.

arXiv:2307.15691v3 Announce Type: replace Abstract: ODTLearn is an open-source Python package that provides methods for learning optimal decision trees for high-stakes predictive and prescriptive tasks based on the mixed-integer optimization (MIO) framework proposed in (Aghaei et al., 2021) and several of its extensions. The current version of the package provides implementations for learning optimal classification trees, optimal fair classification trees, optimal classification trees robust to distribution shifts, and optimal prescriptive trees from observational data. We have designed the package to be easy to maintain and extend as new optimal decision tree problem classes, reformulation strategies, and solution algorithms are introduced. To this end, the package follows object-oriented design principles and supports both commercial (Gurobi) and open source (COIN-OR branch and cut) solvers. The package documentation and an extensive user guide can be found at https://d3m-research-group.github.io/odtlearn/. Additionally, users can view the package source code and submit feature requests and bug reports by visiting https://github.com/D3M-Research-Group/odtlearn.

arXiv:2507.14507v2 Announce Type: replace Abstract: Diffusion models, initially developed for image synthesis, demonstrate remarkable generative capabilities. Recently, their application has expanded to time series forecasting (TSF), yielding promising results. Existing surveys on time series primarily focus on the application of diffusion models to time series tasks or merely provide model-by-model introductions of diffusion-based TSF models, without establishing a systematic taxonomy for existing diffusion-based TSF models. In this survey, we firstly introduce several standard diffusion models and their prevalent variants, explaining their adaptation to TSF tasks. Then, we provide a comprehensive review of diffusion models for TSF, paying special attention to the sources of conditional information and the mechanisms for integrating this conditioning within the models. In analyzing existing approaches using diffusion models for TSF, we provide a systematic categorization and a comprehensive summary of them in this survey. Furthermore, we examine several foundational diffusion models applied to TSF, alongside commonly used datasets and evaluation metrics. Finally, we discuss the progress and limitations of these approaches, as well as potential future research directions for diffusion-based TSF. Overall, this survey offers a comprehensive overview of recent progress and future prospects for diffusion models in TSF, serving as a valuable reference for researchers in the field.

arXiv:2509.00258v1 Announce Type: new Abstract: We develop a probabilistic method for assessing the tail behavior and geometric stability of one-dimensional n i.i.d. samples by tracking how their span contracts when the most extreme points are trimmed. Central to our approach is the diameter-shrinkage ratio, that quantifies the relative reduction in data range as extreme points are successively removed. We derive analytical expressions, including finite-sample corrections, for the expected shrinkage under both the uniform and Gaussian hypotheses, and establish that these curves remain distinct even for moderate number of removal. We construct an elementary decision rule that assigns a sample to whichever theoretical shrinkage profile it most closely follows. This test achieves higher classification accuracy than the classical likelihood-ratio test in small-sample or noisy regimes, while preserving asymptotic consistency for large n. We further integrate our criterion into a clustering pipeline (e.g. DBSCAN), demonstrating its ability to validate one-dimensional clusters without any density estimation or parameter tuning. This work thus provides both theoretical insight and practical tools for robust distributional inference and cluster stability analysis.

arXiv:2509.02528v1 Announce Type: cross Abstract: We study the problem of learning the optimal control policy for fine-tuning a given diffusion process, using general value function approximation. We develop a new class of algorithms by solving a variational inequality problem based on the Hamilton-Jacobi-Bellman (HJB) equations. We prove sharp statistical rates for the learned value function and control policy, depending on the complexity and approximation errors of the function class. In contrast to generic reinforcement learning problems, our approach shows that fine-tuning can be achieved via supervised regression, with faster statistical rate guarantees.

arXiv:2509.00931v1 Announce Type: new Abstract: We present a novel deep generative semi-supervised framework for credit card fraud detection, formulated as time series classification task. As financial transaction data streams grow in scale and complexity, traditional methods often require large labeled datasets, struggle with time series of irregular sampling frequencies and varying sequence lengths. To address these challenges, we extend conditional Generative Adversarial Networks (GANs) for targeted data augmentation, integrate Bayesian inference to obtain predictive distributions and quantify uncertainty, and leverage log-signatures for robust feature encoding of transaction histories. We introduce a novel Wasserstein distance-based loss to align generated and real unlabeled samples while simultaneously maximizing classification accuracy on labeled data. Our approach is evaluated on the BankSim dataset, a widely used simulator for credit card transaction data, under varying proportions of labeled samples, demonstrating consistent improvements over benchmarks in both global statistical and domain-specific metrics. These findings highlight the effectiveness of GAN-driven semi-supervised learning with log-signatures for irregularly sampled time series and emphasize the importance of uncertainty-aware predictions.

arXiv:2505.05857v3 Announce Type: replace-cross Abstract: In the last few decades, Machine Learning (ML) has achieved significant success across domains ranging from healthcare, sustainability, and the social sciences, to criminal justice and finance. But its deployment in increasingly sophisticated, critical, and sensitive areas affecting individuals, the groups they belong to, and society as a whole raises critical concerns around fairness, transparency and robustness, among others. As the complexity and scale of ML systems and of the settings in which they are deployed grow, so does the need for responsible ML methods that address these challenges while providing guaranteed performance in deployment. Mixed-integer optimization (MIO) offers a powerful framework for embedding responsible ML considerations directly into the learning process while maintaining performance. For example, it enables learning of inherently transparent models that can conveniently incorporate fairness or other domain specific constraints. This tutorial paper provides an accessible and comprehensive introduction to this topic discussing both theoretical and practical aspects. It outlines some of the core principles of responsible ML, their importance in applications, and the practical utility of MIO for building ML models that align with these principles. Through examples and mathematical formulations, it illustrates practical strategies and available tools for efficiently solving MIO problems for responsible ML. It concludes with a discussion on current limitations and open research questions, providing suggestions for future work.

arXiv:2509.00538v1 Announce Type: new Abstract: We address the problem of determining the causal direction between two univariate, continuous-valued variables, X and Y, under the assumption of no hidden confounders. In general, it is not possible to make definitive statements about causality without some assumptions on the underlying model. To distinguish between cause and effect, we propose a bivariate causal score based on the Minimum Description Length (MDL) principle, using functions that possess the density property on a compact real interval. We prove the identifiability of these causal scores under specific conditions. These conditions can be easily tested. Gaussianity of the noise in the causal model equations is not assumed, only that the noise is low. The well-studied class of cubic splines possesses the density property on a compact real interval. We propose LCUBE as an instantiation of the MDL-based causal score utilizing cubic regression splines. LCUBE is an identifiable method that is also interpretable, simple, and very fast. It has only one hyperparameter. Empirical evaluations compared to state-of-the-art methods demonstrate that LCUBE achieves superior precision in terms of AUDRC on the real-world Tuebingen cause-effect pairs dataset. It also shows superior average precision across common 10 benchmark datasets and achieves above average precision on 13 datasets.

arXiv:2509.00924v1 Announce Type: new Abstract: At its core, machine learning seeks to train models that reliably generalize beyond noisy observations; however, the theoretical vacuum in which state-of-the-art universal approximation theorems (UATs) operate isolates them from this goal, as they assume noiseless data and allow network parameters to be chosen freely, independent of algorithmic realism. This paper bridges that gap by introducing an architecture-specific randomized training algorithm that constructs a uniform approximator from $N$ noisy training samples on the $d$-dimensional cube $[0,1]^d$. Our trained neural networks attain the minimax-optimal quantity of textit{trainable} (non-random) parameters, subject to logarithmic factors which vanish under the idealized noiseless sampling assumed in classical UATs. Additionally, our trained models replicate key behaviours of real-world neural networks, absent in standard UAT constructions, by: (1) exhibiting sub-linear parametric complexity when fine-tuning on structurally related and favourable out-of-distribution tasks, (2) exactly interpolating the training data, and (3) maintaining reasonable Lipschitz regularity (after the initial clustering attention layer). These properties bring state-of-the-art UATs closer to practical machine learning, shifting the central open question from algorithmic implementability with noisy samples to whether stochastic gradient descent can achieve comparable guarantees.

arXiv:2509.00472v1 Announce Type: new Abstract: We introduce a Partial Functional Dynamic Backdoor Diffusion-based Causal Model (PFD-BDCM), specifically designed for causal inference in the presence of unmeasured confounders with spatial heterogeneity and temporal dependency. The proposed PFD-BDCM framework addresses the restrictions of the existing approaches by uniquely integrating models for complex spatio-temporal dynamics with the analysis of multi-resolution variables. Specifically, the framework systematically mitigates confounding bias by integrating valid backdoor adjustment sets into a diffusion-based sampling mechanism. Moreover, it accounts for the intricate dynamics of unmeasured confounders through the deployment of region-specific structural equations and conditional autoregressive processes, and accommodates variables observed at heterogeneous resolutions via basis expansions for functional data. Our theoretical analysis establishes error bounds for counterfactual estimates of PFD-BDCM, formally linking reconstruction accuracy to counterfactual fidelity under monotonicity assumptions of structural equation and invertibility assumptions of encoding function. Empirical evaluations on synthetic datasets and real-world air pollution data demonstrate PFD-BDCM's superiority over existing methods.