Data-driven optimization aims to translate a machine learning model into decision-making by optimizing decisions on estimated costs. Such a pipeline can be conducted by fitting a distributional model which is then plugged into the target optimization problem. While this fitting can utilize traditional methods such as maximum likelihood, a more recent approach uses estimation-optimization integration that minimizes decision error instead of estimation error. Although intuitive, the statistical benefit of the latter approach is not well understood yet is important to guide the prescriptive usage of machine learning. In this paper, we dissect the performance comparisons between these approaches in terms of the amount of model misspecification. In particular, we show how the integrated approach offers a ``universal double benefit'' on the top two dominating terms of regret when the underlying model is misspecified, while the traditional approach can be advantageous when the model is nearly well-specified. Our comparison is powered by finite-sample tail regret bounds that are derived via new higher-order expansions of regrets and the leveraging of a recent Berry-Esseen theorem.

This paper investigates the critical role of hyperparameters in predictive multiplicity, where different machine learning models trained on the same dataset yield divergent predictions for identical inputs. These inconsistencies can seriously impact high-stakes decisions such as credit assessments, hiring, and medical diagnoses. Focusing on six widely used models for tabular data - Elastic Net, Decision Tree, k-Nearest Neighbor, Support Vector Machine, Random Forests, and Extreme Gradient Boosting - we explore how hyperparameter tuning influences predictive multiplicity, as expressed by the distribution of prediction discrepancies across benchmark datasets. Key hyperparameters such as lambda in Elastic Net, gamma in Support Vector Machines, and alpha in Extreme Gradient Boosting play a crucial role in shaping predictive multiplicity, often compromising the stability of predictions within specific algorithms. Our experiments on 21 benchmark datasets reveal that tuning these hyperparameters leads to notable performance improvements but also increases prediction discrepancies, with Extreme Gradient Boosting exhibiting the highest discrepancy and substantial prediction instability. This highlights the trade-off between performance optimization and prediction consistency, raising concerns about the risk of arbitrary predictions. These findings provide insight into how hyperparameter optimization leads to predictive multiplicity. While predictive multiplicity allows prioritizing domain-specific objectives such as fairness and reduces reliance on a single model, it also complicates decision-making, potentially leading to arbitrary or unjustified outcomes.

Investigating critical phenomena or phase transitions is of high interest in physics and chemistry, for which Monte Carlo (MC) simulations, a crucial tool for numerically analyzing macroscopic properties of given systems, are often hindered by an emerging divergence of correlation length -- known as scale invariance at criticality (SIC) in the renormalization group theory. SIC causes the system to behave the same at any length scale, from which many existing sampling methods suffer: long-range correlations cause critical slowing down in Markov chain Monte Carlo (MCMC), and require intractably large receptive fields for generative samplers. In this paper, we propose a Renormalization-informed Generative Critical Sampler (RiGCS) -- a novel sampler specialized for near-critical systems, where SIC is leveraged as an advantage rather than a nuisance. Specifically, RiGCS builds on MultiLevel Monte Carlo (MLMC) with Heat Bath (HB) algorithms, which perform ancestral sampling from low-resolution to high-resolution lattice configurations with site-wise-independent conditional HB sampling. Although MLMC-HB is highly efficient under exact SIC, it suffers from a low acceptance rate under slight SIC violation. Notably, SIC violation always occurs in finite-size systems, and may induce long-range and higher-order interactions in the renormalized distributions, which are not considered by independent HB samplers. RiGCS enhances MLMC-HB by replacing a part of the conditional HB sampler with generative models that capture those residual interactions and improve the sampling efficiency. Our experiments show that the effective sample size of RiGCS is a few orders of magnitude higher than state-of-the-art generative model baselines in sampling configurations for 128x128 two-dimensional Ising systems.

The rapid development and large body of literature on machine learning interatomic potentials (MLIPs) can make it difficult to know how to proceed for researchers who are not experts but wish to use these tools. The spirit of this review is to help such researchers by serving as a practical, accessible guide to the state-of-the-art in MLIPs. This review paper covers a broad range of topics related to MLIPs, including (i) central aspects of how and why MLIPs are enablers of many exciting advancements in molecular modeling, (ii) the main underpinnings of different types of MLIPs, including their basic structure and formalism, (iii) the potentially transformative impact of universal MLIPs for both organic and inorganic systems, including an overview of the most recent advances, capabilities, downsides, and potential applications of this nascent class of MLIPs, (iv) a practical guide for estimating and understanding the execution speed of MLIPs, including guidance for users based on hardware availability, type of MLIP used, and prospective simulation size and time, (v) a manual for what MLIP a user should choose for a given application by considering hardware resources, speed requirements, energy and force accuracy requirements, as well as guidance for choosing pre-trained potentials or fitting a new potential from scratch, (vi) discussion around MLIP infrastructure, including sources of training data, pre-trained potentials, and hardware resources for training, (vii) summary of some key limitations of present MLIPs and current approaches to mitigate such limitations, including methods of including long-range interactions, handling magnetic systems, and treatment of excited states, and finally (viii) we finish with some more speculative thoughts on what the future holds for the development and application of MLIPs over the next 3-10+ years.

Heterogeneous tabular data poses unique challenges in generative modelling due to its fundamentally different underlying data structure compared to homogeneous modalities, such as images and text. Although previous research has sought to adapt the successes of generative modelling in homogeneous modalities to the tabular domain, defining an effective generator for tabular data remains an open problem. One major reason is that the evaluation criteria inherited from other modalities often fail to adequately assess whether tabular generative models effectively capture or utilise the unique structural information encoded in tabular data. In this paper, we carefully examine the limitations of the prevailing evaluation framework and introduce $\textbf{TabStruct}$, a novel evaluation benchmark that positions structural fidelity as a core evaluation dimension. Specifically, TabStruct evaluates the alignment of causal structures in real and synthetic data, providing a direct measure of how effectively tabular generative models learn the structure of tabular data. Through extensive experiments using generators from eight categories on seven datasets with expert-validated causal graphical structures, we show that structural fidelity offers a task-independent, domain-agnostic evaluation dimension. Our findings highlight the importance of tabular data structure and offer practical guidance for developing more effective and robust tabular generative models. Code is available at https://github.com/SilenceX12138/TabStruct.

Current Semi-supervised Learning (SSL) adopts the pseudo-labeling strategy and further filters pseudo-labels based on confidence thresholds. However, this mechanism has notable drawbacks: 1) setting the reasonable threshold is an open problem which significantly influences the selection of the high-quality pseudo-labels; and 2) deep models often exhibit the over-confidence phenomenon which makes the confidence value an unreliable indicator for assessing the quality of pseudo-labels due to the scarcity of labeled data. In this paper, we propose an Uncertainty-aware Ensemble Structure (UES) to assess the utility of pseudo-labels for unlabeled samples. We further model the utility of pseudo-labels as long-tailed weights to avoid the open problem of setting the threshold. Concretely, the advantage of the long-tailed weights ensures that even unreliable pseudo-labels still contribute to enhancing the model's robustness. Besides, UES is lightweight and architecture-agnostic, easily extending to various computer vision tasks, including classification and regression. Experimental results demonstrate that combining the proposed method with DualPose leads to a 3.47% improvement in Percentage of Correct Keypoints (PCK) on the Sniffing dataset with 100 data points (30 labeled), a 7.29\% improvement in PCK on the FLIC dataset with 100 data points (50 labeled), and a 3.91% improvement in PCK on the LSP dataset with 200 data points (100 labeled). Furthermore, when combined with FixMatch, the proposed method achieves a 0.2% accuracy improvement on the CIFAR-10 dataset with 40 labeled data points and a 0.26% accuracy improvement on the CIFAR-100 dataset with 400 labeled data points.

Self-Consistent Equation-guided Neural Networks for Censored Time-to-Event Data Sehwan Kim 1, Rui Wang 1,2, and Wenbin Lu 3 1 Department of Population Medicine, Harvard Pilgrim Health Care Institute and Harvard Medical School, Boston, MA 2 Department of Biostatistics, Harvard School of Public Health, Boston, MA 3 Department of Statistics, North Carolina State University, Raleigh, NC March 13, 2025 Abstract In survival analysis, estimating the conditional survival function given predictors is often of interest. There is a growing trend in the development of deep learning methods for analyzing censored time-to-event data, especially when dealing with high-dimensional predictors that are complexly interrelated. Many existing deep learning approaches for estimating the conditional survival functions extend the Cox regression models by replacing the linear function of predictor effects by a shallow feed-forward neural network while maintaining the proportional hazards assumption. Their implementation can be computationally intensive due to the use of the full dataset at each iteration because the use of batch data may distort the at-risk set of the partial likelihood function. To overcome these limitations, we propose a novel deep learning approach to non-parametric estimation of the conditional survival functions using the generative adversarial networks leveraging self-consistent equations. The proposed method is model-free and does not require any parametric assumptions on the structure of the conditional survival function. We establish the convergence rate of our proposed estimator of the conditional survival function. In addition, we evaluate the performance of the proposed method through simulation studies and demonstrate its application on a real-world dataset. 1 Introduction Censored time-to-event data are widely encountered in various fields where understanding the timing of events, such as failure rates or disease progression, is critical, but the exact event times Correspondence author: Wenbin Lu, email: wlu4@ncsu.edu 1 arXiv:2503.09097v1 For example, estimating survival probability based on covariate information is essential for risk prediction, which plays a key role in developing and evaluating personalized medicine. The Kaplan-Meier (KM) estimator (Kaplan and Meier, 1958), Cox proportional hazards model (Cox, 1972), and random survival forests (Ishwaran et al., 2008) are commonly-used methods for estimating survival functions. The KM estimator is a non-parametric method suitable for population-level analyses. However, its utility is limited when the objective is to estimate conditional survival probabilities at the individual level. The Cox proportional hazards model offers a semi-parametric approach for estimating conditional survival functions, accommodating the incorporation of covariates.

A novel formulation of the clustering problem is introduced in which the task is expressed as an estimation problem, where the object to be estimated is a function which maps a point to its distribution of cluster membership. Unlike existing approaches which implicitly estimate such a function, like Gaussian Mixture Models (GMMs), the proposed approach bypasses any explicit modelling assumptions and exploits the flexible estimation potential of nonparametric smoothing. An intuitive approach for selecting the tuning parameters governing estimation is provided, which allows the proposed method to automatically determine both an appropriate level of flexibility and also the number of clusters to extract from a given data set. Experiments on a large collection of publicly available data sets are used to document the strong performance of the proposed approach, in comparison with relevant benchmarks from the literature. R code to implement the proposed approach is available from https://github.com/DavidHofmeyr/ I. Introduction Cluster analysis refers to the task of partitioning a set of data into groups (or clusters) in such a way that points within the same cluster tend to be more similar than points in different clusters.

This paper proposes a single-qudit quantum neural network for multiclass classification, by using the enhanced representational capacity of high-dimensional qudit states. Our design employs an $d$-dimensional unitary operator, where $d$ corresponds to the number of classes, constructed using the Cayley transform of a skew-symmetric matrix, to efficiently encode and process class information. This architecture enables a direct mapping between class labels and quantum measurement outcomes, reducing circuit depth and computational overhead. To optimize network parameters, we introduce a hybrid training approach that combines an extended activation function -- derived from a truncated multivariable Taylor series expansion -- with support vector machine optimization for weight determination. We evaluate our model on the MNIST and EMNIST datasets, demonstrating competitive accuracy while maintaining a compact single-qudit quantum circuit. Our findings highlight the potential of qudit-based QNNs as scalable alternatives to classical deep learning models, particularly for multiclass classification. However, practical implementation remains constrained by current quantum hardware limitations. This research advances quantum machine learning by demonstrating the feasibility of higher-dimensional quantum systems for efficient learning tasks.

Patient-ventilator asynchrony (PVA) is a common and critical issue during mechanical ventilation, affecting up to 85% of patients. PVA can result in clinical complications such as discomfort, sleep disruption, and potentially more severe conditions like ventilator-induced lung injury and diaphragm dysfunction. Traditional PVA management, which relies on manual adjustments by healthcare providers, is often inadequate due to delays and errors. While various computational methods, including rule-based, statistical, and deep learning approaches, have been developed to detect PVA events, they face challenges related to dataset imbalances and lack of interpretability. In this work, we propose a shapelet-based approach SHIP for PVA detection, utilizing shapelets -- discriminative subsequences in time-series data -- to enhance detection accuracy and interpretability. Our method addresses dataset imbalances through shapelet-based data augmentation and constructs a shapelet pool to transform the dataset for more effective classification. The combined shapelet and statistical features are then used in a classifier to identify PVA events. Experimental results on medical datasets show that SHIP significantly improves PVA detection while providing interpretable insights into model decisions.