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Saturday 18 October

Statistics Applications

A hierarchical Bayesian approach for population-based structural health monitoring in ship hull structures

Structural health monitoring (SHM) strategies involve the processing of structural response data to indirectly assess an asset's condition. These strategies can be enhanced for a group of structures, especially when they are similar, since mutual underlying physics are expected to exist. The concept behind population-based SHM exploits the sharing of data among individuals, so that data-rich members can support data-scarce ones. One approach to population-level modeling is the hierarchical Bayesian method, where the model is structured hierarchically in terms of its parameters, and correlation among learning tasks is enabled by conditioning on shared latent variables. This work investigates the application of a hierarchical Bayesian model to infer expected distributions of deflection amplitudes at both the population and domain levels, with the aim of detecting excessive initial deflections in a population of plate elements. Although these damages are typically localized, they can trigger unexpected events, if not properly monitored. The work is conducted in a numerical setting using a Finite Element model to generate strain response data, which serve as the monitoring data. Bayesian inference was conducted using Markov Chain Monte Carlo (MCMC), with a surrogate model employed to calculate the likelihood function. The hierarchical approach was compared to an independent model for a plate component with few data. The results revealed that, under data sparsity conditions, the hierarchical model can offer more robust results in terms of uncertainty, which is essential for decision-making tasks.
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All authors Georgios Aravanis, Nicholas Silionis, Jacopo Bardiani, Marco Giglio, Konstantinos Anyfantis, Claudio Sbarufatti

Statistical Methodology

Estimate Time-Varying Exposure Effects via Ensemble Learning-based Marginal Structural Model with Application to Adolescent Cognitive Development Study

Evaluating the effects of time-varying exposures is essential for longitudinal studies. The effect estimation becomes increasingly challenging when dealing with hundreds of time-dependent confounders. We propose a Marginal Structure Ensemble Learning Model (MASE) to provide a marginal structure model (MSM)-based robust estimator under the longitudinal setting. The proposed model integrates multiple machine learning algorithms to model propensity scores and a sequence of conditional outcome means such that it becomes less sensitive to model mis-specification due to any single algorithm and allows many confounders with potential non-linear confounding effects to reduce the risk of inconsistent estimation. Extensive simulation analysis demonstrates the superiority of MASE over benchmark methods (e.g., MSM, G-computation, Targeted maximum likelihood), yielding smaller estimation bias and improved inference accuracy. We apply MASE to the adolescent cognitive development study to investigate the time-varying effects of sleep insufficiency on cognitive performance. The results reveal an aggregated negative impact of insufficient sleep on cognitive development among youth.
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Statistics Applications

Synergizing chemical and AI communities for advancing laboratories of the future

The development of automated experimental facilities and the digitization of experimental data have introduced numerous opportunities to radically advance chemical laboratories. As many laboratory tasks involve predicting and understanding previously unknown chemical relationships, machine learning (ML) approaches trained on experimental data can substantially accelerate the conventional design-build-test-learn process. This outlook article aims to help chemists understand and begin to adopt ML predictive models for a variety of laboratory tasks, including experimental design, synthesis optimization, and materials characterization. Furthermore, this article introduces how artificial intelligence (AI) agents based on large language models can help researchers acquire background knowledge in chemical or data science and accelerate various aspects of the discovery process. We present three case studies in distinct areas to illustrate how ML models and AI agents can be leveraged to reduce time-consuming experiments and manual data analysis. Finally, we highlight existing challenges that require continued synergistic effort from both experimental and computational communities to address.
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All authors Saejin Oh, Xinyi Fang, I-Hsin Lin, Paris Dee, Christopher S. Dunham, Stacy M. Copp, Abigail G. Doyle, Javier Read de Alaniz, Mengyang Gu

Statistical Computation · Cross-listed from cs.DC

Communication-Efficient and Memory-Aware Parallel Bootstrapping using MPI

Bootstrapping is a powerful statistical resampling technique for estimating the sampling distribution of an estimator. However, its computational cost becomes prohibitive for large datasets or a high number of resamples. This paper presents a theoretical analysis and design of parallel bootstrapping algorithms using the Message Passing Interface (MPI). We address two key challenges: high communication overhead and memory constraints in distributed environments. We propose two novel strategies: 1) Local Statistic Aggregation, which drastically reduces communication by transmitting sufficient statistics instead of full resampled datasets, and 2) Synchronized Pseudo-Random Number Generation, which enables distributed resampling when the entire dataset cannot be stored on a single process. We develop analytical models for communication and computation complexity, comparing our methods against naive baseline approaches. Our analysis demonstrates that the proposed methods offer significant reductions in communication volume and memory usage, facilitating scalable parallel bootstrapping on large-scale systems.
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Machine Learning (Statistics) · Cross-listed from cs.CV

Differentiable, Bit-shifting, and Scalable Quantization without training neural network from scratch

Quantization of neural networks provides benefits of inference in less compute and memory requirements. Previous work in quantization lack two important aspects which this work provides. First almost all previous work in quantization used a non-differentiable approach and for learning; the derivative is usually set manually in backpropogation which make the learning ability of algorithm questionable, our approach is not just differentiable, we also provide proof of convergence of our approach to the optimal neural network. Second previous work in shift/logrithmic quantization either have avoided activation quantization along with weight quantization or achieved less accuracy. Learning logrithmic quantize values of form $2^n$ requires the quantization function can scale to more than 1 bit quantization which is another benifit of our quantization that it provides $n$ bits quantization as well. Our approach when tested with image classification task using imagenet dataset, resnet18 and weight quantization only achieves less than 1 percent accuracy compared to full precision accuracy while taking only 15 epochs to train using shift bit quantization and achieves comparable to SOTA approaches accuracy in both weight and activation quantization using shift bit quantization in 15 training epochs with slightly higher(only higher cpu instructions) inference cost compared to 1 bit quantization(without logrithmic quantization) and not requiring any higher precision multiplication.
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Friday 17 October

Statistics Applications

How can methods for classifying and clustering trajectories be used for prevention trials? An example in Alzheimer's disease area

Background: Clinical trials are designed to prove the efficacy of an intervention by means of model-based approaches involving parametric hypothesis testing. Issues arise when no effect is observed in the study population. Indeed, an effect may be present in a subgroup and the statistical test cannot detect it. To investigate this possibility, we proposed to change the paradigm to a data-driven approach. We selected exploratory methods to provide another perspective on the data and to identify particular homogeneous subgroups of subjects within which an effect might be detected. In the setting of prevention trials, the endpoint is a trajectory of repeated measures. In the settings of prevention trials, the endpoint is a trajectory of repeated measures, which requires the use of methods that can take data autocorrelation into account. The primary aim of this work was to explore the applicability of different methods for clustering and classifying trajectories. Methods: The Multidomain Alzheimer Preventive Trial (MAPT) was a three-year randomized controlled trial with four parallel arms (NCT00672685). The primary outcome was a composite Z-score combining four cognitive tests. The data were analyzed by quadratic mixed effects model. This study was inconclusive. Exploratory analysis is therefore relevant to investigate the use of data-driven methods for trajectory classification. The methods used were unsupervised: k-means for longitudinal data, Hierarchical Cluster Analysis (HCA), graphic semiology, and supervised analysis with dichotomous classification according to responder status. Results: Using k-means for longitudinal data, three groups were obtained and one of these groups showed cognitive decline over the three years of follow-up. This method could be applied directly to the primary outcome, the composite Z-score with repeated observations over time. With the two others unsupervised methods, we were unable to process longitudinal data directly. It was therefore necessary to choose an indicator of change in trajectories and to consider the rate of change between two measurements. For the HCA method, Ward's aggregation was performed. The Euclidean distance and rates of change were applied for the graphic semiology method. Lastly, as there were no objective criteria to define responder status, we defined our responders based on clinical criteria. Discussion: In the princeps study, the prevention trial was found to be inconclusive, likely due to the heterogeneity of the population, which may have masked a treatment effect later identified in a refined subgroup of high Beta Amyloid subjects. So, we have adopted an alternative unsupervised approach to subject stratification based on their trajectories. We could then identify patterns of similar trajectories of cognitive decline and also highlight the potential problem of a large heterogeneity of the profiles, maybe due to the final endpoint considered.
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All authors Céline Bougel, Sébastien Déjean, Caroline Giulioli, Philippe Saint-Pierre, Nicolas Savy, Sandrine Andrieu

Statistics Applications

Mortality Modeling and Forecasting with the Actuaries Climate Index

Climate change poses increasing challenges for mortality modeling and underscores the need to integrate climate-related variables into mortality forecasting. This study introduces a two-step approach that incorporates climate information from the Actuaries Climate Index (ACI) into mortality models. In the first step, we model region-specific seasonal mortality dynamics using the Lee-Carter model with SARIMA processes, a cosine-sine decomposition, and a cyclic spline-based function. In the second step, residual deviations from the baseline model are explained by ACI components using Generalized Linear Models, Generalized Additive Models, and Extreme Gradient Boosting. To further capture the dependence between mortality and climate, we develop a SARIMA-Copula forecasting approach linking mortality period effects with temperature extremes. Our results show that incorporating ACI components systematically enhances out-of-sample accuracy, underscoring the value of integrating climate-related variables into stochastic mortality modeling. The proposed framework offers actuaries and policymakers a practical tool for anticipating and managing climate-related mortality risks.
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Machine Learning (Statistics) · Cross-listed from cs.LG

Protein Folding with Neural Ordinary Differential Equations

Recent advances in protein structure prediction, such as AlphaFold, have demonstrated the power of deep neural architectures like the Evoformer for capturing complex spatial and evolutionary constraints on protein conformation. However, the depth of the Evoformer, comprising 48 stacked blocks, introduces high computational costs and rigid layerwise discretization. Inspired by Neural Ordinary Differential Equations (Neural ODEs), we propose a continuous-depth formulation of the Evoformer, replacing its 48 discrete blocks with a Neural ODE parameterization that preserves its core attention-based operations. This continuous-time Evoformer achieves constant memory cost (in depth) via the adjoint method, while allowing a principled trade-off between runtime and accuracy through adaptive ODE solvers. Benchmarking on protein structure prediction tasks, we find that the Neural ODE-based Evoformer produces structurally plausible predictions and reliably captures certain secondary structure elements, such as alpha-helices, though it does not fully replicate the accuracy of the original architecture. However, our model achieves this performance using dramatically fewer resources, just 17.5 hours of training on a single GPU, highlighting the promise of continuous-depth models as a lightweight and interpretable alternative for biomolecular modeling. This work opens new directions for efficient and adaptive protein structure prediction frameworks.
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Machine Learning (Statistics) · Cross-listed from cs.LG

One-Bit Quantization for Random Features Models

Recent advances in neural networks have led to significant computational and memory demands, spurring interest in one-bit weight compression to enable efficient inference on resource-constrained devices. However, the theoretical underpinnings of such compression remain poorly understood. We address this gap by analyzing one-bit quantization in the Random Features model, a simplified framework that corresponds to neural networks with random representations. We prove that, asymptotically, quantizing weights of all layers except the last incurs no loss in generalization error, compared to the full precision random features model. Our findings offer theoretical insights into neural network compression. We also demonstrate empirically that one-bit quantization leads to significant inference speed ups for the Random Features models even on a laptop GPU, confirming the practical benefits of our work. Additionally, we provide an asymptotically precise characterization of the generalization error for Random Features with an arbitrary number of layers. To the best of our knowledge, our analysis yields more general results than all previous works in the related literature.
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Statistics Applications

A Compositional Approach to Modelling Cause-specific Mortality with Zero Counts

Understanding and forecasting mortality by cause is an essential branch of actuarial science, with wide-ranging implications for decision-makers in public policy and industry. To accurately capture trends in cause-specific mortality, it is critical to consider dependencies between causes of death and produce forecasts by age and cause coherent with aggregate mortality forecasts. One way to achieve these aims is to model cause-specific deaths using compositional data analysis (CODA), treating the density of deaths by age and cause as a set of dependent, non-negative values that sum to one. A major drawback of standard CODA methods is the challenge of zero values, which frequently occur in cause-of-death mortality modelling. Thus, we propose using a compositional power transformation, the $\alpha$-transformation, to model cause-specific life-table death counts. The $\alpha$-transformation offers a statistically rigorous approach to handling zero value subgroups in CODA compared to ad-hoc techniques: adding an arbitrarily small amount. We illustrate the $\alpha$-transformation on England and Wales, and US death counts by cause from the Human Cause-of-Death database, for cardiovascular-related causes of death. Results demonstrate the $\alpha$-transformation improves forecast accuracy of cause-specific life-table death counts compared with log-ratio-based CODA transformations. The forecasts suggest declines in proportions of deaths from major cardiovascular causes (myocardial infarction and other ischemic heart diseases (IHD)).
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All authors Zhe Michelle Dong, Han Lin Shang, Francis Hui, Aaron Bruhn

Machine Learning (Statistics)

Personalized Collaborative Learning with Affinity-Based Variance Reduction

Multi-agent learning faces a fundamental tension: leveraging distributed collaboration without sacrificing the personalization needed for diverse agents. This tension intensifies when aiming for full personalization while adapting to unknown heterogeneity levels – gaining collaborative speedup when agents are similar, without performance degradation when they are different. Embracing the challenge, we propose personalized collaborative learning (PCL), a novel framework for heterogeneous agents to collaboratively learn personalized solutions with seamless adaptivity. Through carefully designed bias correction and importance correction mechanisms, our method AffPCL robustly handles both environment and objective heterogeneity. We prove that AffPCL reduces sample complexity over independent learning by a factor of $\max\{n^{-1}, \delta\}$, where $n$ is the number of agents and $\delta\in[0,1]$ measures their heterogeneity. This affinity-based acceleration automatically interpolates between the linear speedup of federated learning in homogeneous settings and the baseline of independent learning, without requiring prior knowledge of the system. Our analysis further reveals that an agent may obtain linear speedup even by collaborating with arbitrarily dissimilar agents, unveiling new insights into personalization and collaboration in the high heterogeneity regime.
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Machine Learning (Statistics) · Cross-listed from cs.LG

Benchmarking noisy label detection methods

Label noise is a common problem in real-world datasets, affecting both model training and validation. Clean data are essential for achieving strong performance and ensuring reliable evaluation. While various techniques have been proposed to detect noisy labels (or label errors), there is no clear consensus on optimal approaches. We perform a comprehensive benchmark of detection methods by decomposing them into three fundamental components: gathering strategy (in-sample vs out-of-sample), label disagreement measure, and aggregation method. This decomposition can be applied to many existing detection methods, and enables systematic comparison across diverse approaches. To fairly compare methods, we propose a unified benchmark task: detecting a fraction of training samples equal to the dataset's noise rate. We also introduce a novel metric: the false negative rate at this fixed operating point. Our evaluation spans vision and tabular datasets under both synthetic and real-world noise conditions. We identify that in-sample gathering using average probability aggregation combined with the logit margin as the label disagreement measure achieves the best results across most scenarios. Our findings provide practical guidance for designing new detection methods and selecting techniques for specific applications.
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Machine Learning (Statistics) · Cross-listed from cs.LG

Explore-then-Commit for Nonstationary Linear Bandits with Latent Dynamics

We study a nonstationary bandit problem where rewards depend on both actions and latent states, the latter governed by unknown linear dynamics. Crucially, the state dynamics also depend on the actions, resulting in tension between short-term and long-term rewards. We propose an explore-then-commit algorithm for a finite horizon $T$. During the exploration phase, random Rademacher actions enable estimation of the Markov parameters of the linear dynamics, which characterize the action-reward relationship. In the commit phase, the algorithm uses the estimated parameters to design an optimized action sequence for long-term reward. Our proposed algorithm achieves $\tilde{\mathcal{O}}(T^{2/3})$ regret. Our analysis handles two key challenges: learning from temporally correlated rewards, and designing action sequences with optimal long-term reward. We address the first challenge by providing near-optimal sample complexity and error bounds for system identification using bilinear rewards. We address the second challenge by proving an equivalence with indefinite quadratic optimization over a hypercube, a known NP-hard problem. We provide a sub-optimality guarantee for this problem, enabling our regret upper bound. Lastly, we propose a semidefinite relaxation with Goemans-Williamson rounding as a practical approach.
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All authors Sunmook Choi, Yahya Sattar, Yassir Jedra, Maryam Fazel, Sarah Dean

Machine Learning (Statistics) · Cross-listed from cs.LG

Expressive Reward Synthesis with the Runtime Monitoring Language

A key challenge in reinforcement learning (RL) is reward (mis)specification, whereby imprecisely defined reward functions can result in unintended, possibly harmful, behaviours. Indeed, reward functions in RL are typically treated as black-box mappings from state-action pairs to scalar values. While effective in many settings, this approach provides no information about why rewards are given, which can hinder learning and interpretability. Reward Machines address this issue by representing reward functions as finite state automata, enabling the specification of structured, non-Markovian reward functions. However, their expressivity is typically bounded by regular languages, leaving them unable to capture more complex behaviours such as counting or parametrised conditions. In this work, we build on the Runtime Monitoring Language (RML) to develop a novel class of language-based Reward Machines. By leveraging the built-in memory of RML, our approach can specify reward functions for non-regular, non-Markovian tasks. We demonstrate the expressiveness of our approach through experiments, highlighting additional advantages in flexible event-handling and task specification over existing Reward Machine-based methods.
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Statistics Applications

Estimating Time-Varying Epidemic Severity Rates with Adaptive Deconvolution

Several key metrics in public health convey the probability that a primary event will lead to a more serious secondary event in the future.Several key metrics in public health convey the probability that a primary event will lead to a more serious secondary event in the future. These "severity rates" can change over the course of an epidemic in response to shifting conditions like new therapeutics, variants, or public health interventions. In practice, time-varying parameters such as the case-fatality rate are typically estimated from aggregate count data. Prior work has demonstrated that commonly-used ratio-based estimators can be highly biased, motivating the development of new methods. In this paper, we develop an adaptive deconvolution approach based on approximating a Poisson-binomial model for secondary events, and we regularize the maximum likelihood solution in this model with a trend filtering penalty to produce smooth but locally adaptive estimates of severity rates over time. This enables us to compute severity rates both retrospectively and in real time. Experiments based on COVID-19 death and hospitalization data show that our deconvolution estimator is generally more accurate than the standard ratio-based methods, and displays reasonable robustness to model misspecification.
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All authors Jeremy Goldwasser, Addison J. Hu, Alyssa Bilinski, Daniel J. McDonald, Ryan J. Tibshirani

Statistics Applications

COWs and their Hybrids: A Statistical View of Custom Orthogonal Weights

A recurring challenge in high energy physics is inference of the signal component from a distribution for which observations are assumed to be a mixture of signal and background events. A standard assumption is that there exists information encoded in a discriminant variable that is effective at separating signal and background. This can be used to assign a signal weight to each event, with these weights used in subsequent analyses of one or more control variables of interest. The custom orthogonal weights (COWs) approach of Dembinski, et al.(2022), a generalization of the sPlot approach of Barlow (1987) and Pivk and Le Diberder (2005), is tailored to address this objective. The problem, and this method, present interesting and novel statistical issues. Here we formalize the assumptions needed and the statistical properties, while also considering extensions and alternative approaches.
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Statistical Methodology

Extending Prediction-Powered Inference through Conformal Prediction

Prediction-powered inference is a recent methodology for the safe use of black-box ML models to impute missing data, strengthening inference of statistical parameters. However, many applications require strong properties besides valid inference, such as privacy, robustness or validity under continuous distribution shifts; deriving prediction-powered methods with such guarantees is generally an arduous process, and has to be done case by case. In this paper, we resolve this issue by connecting prediction-powered inference with conformal prediction: by performing imputation through a calibrated conformal set-predictor, we attain validity while achieving additional guarantees in a natural manner. We instantiate our procedure for the inference of means, Z- and M-estimation, as well as e-values and e-value-based procedures. Furthermore, in the case of e-values, ours is the first general prediction-powered procedure that operates off-line. We demonstrate these advantages by applying our method on private and time-series data. Both tasks are nontrivial within the standard prediction-powered framework but become natural under our method.
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All authors Daniel Csillag, Pedro Dall'Antonia, Claudio José Struchiner, Guilherme Tegoni Goedert

Machine Learning (Statistics) · Cross-listed from cs.LG

Still Competitive: Revisiting Recurrent Models for Irregular Time Series Prediction

Modeling irregularly sampled multivariate time series is a persistent challenge in domains like healthcare and sensor networks. While recent works have explored a variety of complex learning architectures to solve the prediction problems for irregularly sampled time series, it remains unclear what the true benefits of some of these architectures are, and whether clever modifications of simpler and more efficient RNN-based algorithms are still competitive, i.e. they are on par with or even superior to these methods. In this work, we propose and study GRUwE: Gated Recurrent Unit with Exponential basis functions, that builds upon RNN-based architectures for observations made at irregular times. GRUwE supports both regression-based and event-based predictions in continuous time. GRUwE works by maintaining a Markov state representation of the time series that updates with the arrival of irregular observations. The Markov state update relies on two reset mechanisms: (i) observation-triggered reset to account for the new observation, and (ii) time-triggered reset that relies on learnable exponential decays, to support the predictions in continuous time. Our empirical evaluations across several real-world benchmarks on next-observation and next-event prediction tasks demonstrate that GRUwE can indeed achieve competitive or superior performance compared to the recent state-of-the-art (SOTA) methods. Thanks to its simplicity, GRUwE offers compelling advantages: it is easy to implement, requires minimal hyper-parameter tuning efforts, and significantly reduces the computational overhead in the online deployment.
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Machine Learning (Statistics) · Cross-listed from cs.LG

Zeroth-Order Sharpness-Aware Learning with Exponential Tilting

Classic zeroth-order optimization approaches typically optimize for a smoothed version of the original function, i.e., the expected objective under randomly perturbed model parameters. This can be interpreted as encouraging the loss values in the perturbation set to be small on average. Popular sharpness-aware minimization (SAM) objectives, however, typically focus on the largest loss within the neighborhood to arrive at flat minima more effectively. In this work, we connect zeroth-order optimization (and its corresponding objectives) with SAM approaches explicitly, through an exponential tilting objective that provides a smooth transition between the average- and the max-loss formulations. We explore new zeroth-order algorithms to solve a soft SAM objective parameterized by a tilting parameter $t$. We provide precise characterizations of the sharpness notions of the tilted SAM framework. Practically, our approach can be used as a gradient-free and memory-efficient alternative to SAM variants, and it achieves better generalization compared to vanilla zeroth-order baselines on a wide range of downstream tasks, including classification, multiple choice QA, and language generation.
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Statistics Applications

The Cultural Mapping and Pattern Analysis (CMAP) Visualization Toolkit: Open Source Text Analysis for Qualitative and Computational Social Science

The CMAP (cultural mapping and pattern analysis) visualization toolkit introduced in this paper is an open-source suite for analyzing and visualizing text data - from qualitative fieldnotes and in-depth interview transcripts to historical documents and web-scaped data like message board posts or blogs. The toolkit is designed for scholars integrating pattern analysis, data visualization, and explanation in qualitative and/or computational social science (CSS). Despite the existence of off-the-shelf commercial qualitative data analysis software, there is a dearth of highly scalable open source options that can work with large data sets, and allow advanced statistical and language modeling. The foundation of the toolkit is a pragmatic approach that aligns research tools with social science project goals- empirical explanation, theory-guided measurement, comparative design, or evidence-based recommendations- guided by the principle that research paradigm and questions should determine methods. Consequently, the CMAP visualization toolkit offers a range of possibilities through the adjustment of relatively small number of parameters, and allows integration with other python tools.
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Machine Learning (Statistics) · Cross-listed from cs.LG

Expert Merging in Sparse Mixture of Experts with Nash Bargaining

Existing expert merging strategies for Sparse Mixture of Experts (SMoE) typically rely on input-dependent or input-independent averaging of expert parameters, but often lack a principled weighting mechanism. In this work, we reinterpret expert merging through the lens of game theory, revealing cooperative and competitive dynamics among experts. Based on this perspective, we introduce Nash Merging of Experts (NAMEx), a novel framework that incorporates Nash Bargaining into the merging process, enabling more balanced and efficient collaboration among experts. Additionally, we incorporate complex momentum into NAMEx to accelerate expert propagation with theoretical guarantees for convergence. Extensive experiments across language modelling, text classification, image classification, and zero-shot robustness under data corruption show that NAMEx consistently outperforms competing methods while integrating seamlessly with popular MoE architectures. Finally, we demonstrate NAMEx's scalability by applying it to large-scale systems, including Qwen1.5-MoE (14B) and DeepSeek-MoE (16B), where it proves effective in both zero-shot and fine-tuning settings. The code is publicly available at: https://github.com/anh147/NAMEx.
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All authors Dung V. Nguyen, Anh T. Nguyen, Minh H. Nguyen, Luc Q. Nguyen, Shiqi Jiang, Ethan Fetaya, Linh Duy Tran, Gal Chechik, Tan M. Nguyen

Machine Learning (Statistics) · Cross-listed from cs.LG

A Minimal-Assumption Analysis of Q-Learning with Time-Varying Policies

In this work, we present the first finite-time analysis of Q-learning with time-varying learning policies (i.e., on-policy sampling) for discounted Markov decision processes under minimal assumptions, requiring only the existence of a policy that induces an irreducible Markov chain over the state space. We establish a last-iterate convergence rate for $\mathbb{E}[\|Q_k - Q^*\|_\infty^2]$, implying a sample complexity of order $\mathcal{O}(1/\xi^2)$ for achieving $\mathbb{E}[\|Q_k - Q^*\|_\infty]\le \xi$. This matches the rate of off-policy Q-learning, but with worse dependence on exploration-related parameters. We also derive a finite-time rate for $\mathbb{E}[\|Q^{\pi_k} - Q^*\|_\infty^2]$, where $\pi_k$ is the learning policy at iteration $k$, highlighting the exploration-exploitation trade-off in on-policy Q-learning. While exploration is weaker than in off-policy methods, on-policy learning enjoys an exploitation advantage as the learning policy converges to an optimal one. Numerical results support our theory. Technically, rapidly time-varying learning policies induce time-inhomogeneous Markovian noise, creating significant analytical challenges under minimal exploration. To address this, we develop a Poisson-equation-based decomposition of the Markovian noise under a lazy transition matrix, separating it into a martingale-difference term and residual terms. The residuals are controlled via sensitivity analysis of the Poisson equation solution with respect to both the Q-function estimate and the learning policy. These techniques may extend to other RL algorithms with time-varying policies, such as single-timescale actor-critic methods and learning-in-games algorithms.
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Statistical Computation · Cross-listed from q-bio.QM

BASIN: Bayesian mAtrix variate normal model with Spatial and sparsIty priors in Non-negative deconvolution

Spatial transcriptomics allows researchers to visualize and analyze gene expression within the precise location of tissues or cells. It provides spatially resolved gene expression data but often lacks cellular resolution, necessitating cell type deconvolution to infer cellular composition at each spatial location. In this paper we propose BASIN for cell type deconvolution, which models deconvolution as a nonnegative matrix factorization (NMF) problem incorporating graph Laplacian prior. Rather than find a deterministic optima like other recent methods, we propose a matrix variate Bayesian NMF method with nonnegativity and sparsity priors, in which the variables are maintained in their matrix form to derive a more efficient matrix normal posterior. BASIN employs a Gibbs sampler to approximate the posterior distribution of cell type proportions and other parameters, offering a distribution of possible solutions, enhancing robustness and providing inherent uncertainty quantification. The performance of BASIN is evaluated on different spatial transcriptomics datasets and outperforms other deconvolution methods in terms of accuracy and efficiency. The results also show the effect of the incorporated priors and reflect a truncated matrix normal distribution as we expect.
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All authors Jiasen Zhang, Xi Qiao, Liangliang Zhang, Weihong Guo

Machine Learning (Statistics)

Learning density ratios in causal inference using Bregman-Riesz regression

The ratio of two probability density functions is a fundamental quantity that appears in many areas of statistics and machine learning, including causal inference, reinforcement learning, covariate shift, outlier detection, independence testing, importance sampling, and diffusion modeling. Naively estimating the numerator and denominator densities separately using, e.g., kernel density estimators, can lead to unstable performance and suffer from the curse of dimensionality as the number of covariates increases. For this reason, several methods have been developed for estimating the density ratio directly based on (a) Bregman divergences or (b) recasting the density ratio as the odds in a probabilistic classification model that predicts whether an observation is sampled from the numerator or denominator distribution. Additionally, the density ratio can be viewed as the Riesz representer of a continuous linear map, making it amenable to estimation via (c) minimization of the so-called Riesz loss, which was developed to learn the Riesz representer in the Riesz regression procedure in causal inference. In this paper we show that all three of these methods can be unified in a common framework, which we call Bregman–Riesz regression. We further show how data augmentation techniques can be used to apply density ratio learning methods to causal problems, where the numerator distribution typically represents an unobserved intervention. We show through simulations how the choice of Bregman divergence and data augmentation strategy can affect the performance of the resulting density ratio learner. A Python package is provided for researchers to apply Bregman–Riesz regression in practice using gradient boosting, neural networks, and kernel methods.
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Machine Learning (Statistics) · Cross-listed from cs.CR

The Hidden Cost of Modeling P(X): Vulnerability to Membership Inference Attacks in Generative Text Classifiers

Membership Inference Attacks (MIAs) pose a critical privacy threat by enabling adversaries to determine whether a specific sample was included in a model's training dataset. Despite extensive research on MIAs, systematic comparisons between generative and discriminative classifiers remain limited. This work addresses this gap by first providing theoretical motivation for why generative classifiers exhibit heightened susceptibility to MIAs, then validating these insights through comprehensive empirical evaluation. Our study encompasses discriminative, generative, and pseudo-generative text classifiers across varying training data volumes, evaluated on nine benchmark datasets. Employing a diverse array of MIA strategies, we consistently demonstrate that fully generative classifiers which explicitly model the joint likelihood $P(X,Y)$ are most vulnerable to membership leakage. Furthermore, we observe that the canonical inference approach commonly used in generative classifiers significantly amplifies this privacy risk. These findings reveal a fundamental utility-privacy trade-off inherent in classifier design, underscoring the critical need for caution when deploying generative classifiers in privacy-sensitive applications. Our results motivate future research directions in developing privacy-preserving generative classifiers that can maintain utility while mitigating membership inference vulnerabilities.
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All authors Owais Makroo, Siva Rajesh Kasa, Sumegh Roychowdhury, Karan Gupta, Nikhil Pattisapu, Santhosh Kasa, Sumit Negi

Machine Learning (Statistics) · Cross-listed from cs.LG

Narrowing Action Choices with AI Improves Human Sequential Decisions

Recent work has shown that, in classification tasks, it is possible to design decision support systems that do not require human experts to understand when to cede agency to a classifier or when to exercise their own agency to achieve complementarity$\unicode{x2014}$experts using these systems make more accurate predictions than those made by the experts or the classifier alone. The key principle underpinning these systems reduces to adaptively controlling the level of human agency, by design. Can we use the same principle to achieve complementarity in sequential decision making tasks? In this paper, we answer this question affirmatively. We develop a decision support system that uses a pre-trained AI agent to narrow down the set of actions a human can take to a subset, and then asks the human to take an action from this action set. Along the way, we also introduce a bandit algorithm that leverages the smoothness properties of the action sets provided by our system to efficiently optimize the level of human agency. To evaluate our decision support system, we conduct a large-scale human subject study ($n = 1{,}600$) where participants play a wildfire mitigation game. We find that participants who play the game supported by our system outperform those who play on their own by $\sim$$30$% and the AI agent used by our system by $>$$2$%, even though the AI agent largely outperforms participants playing without support. We have made available the data gathered in our human subject study as well as an open source implementation of our system at https://github.com/Networks-Learning/narrowing-action-choices .
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All authors Eleni Straitouri, Stratis Tsirtsis, Ander Artola Velasco, Manuel Gomez-Rodriguez

Statistics Applications · Cross-listed from cs.LG

FSRF: Factorization-guided Semantic Recovery for Incomplete Multimodal Sentiment Analysis

In recent years, Multimodal Sentiment Analysis (MSA) has become a research hotspot that aims to utilize multimodal data for human sentiment understanding. Previous MSA studies have mainly focused on performing interaction and fusion on complete multimodal data, ignoring the problem of missing modalities in real-world applications due to occlusion, personal privacy constraints, and device malfunctions, resulting in low generalizability. To this end, we propose a Factorization-guided Semantic Recovery Framework (FSRF) to mitigate the modality missing problem in the MSA task. Specifically, we propose a de-redundant homo-heterogeneous factorization module that factorizes modality into modality-homogeneous, modality-heterogeneous, and noisy representations and design elaborate constraint paradigms for representation learning. Furthermore, we design a distribution-aligned self-distillation module that fully recovers the missing semantics by utilizing bidirectional knowledge transfer. Comprehensive experiments on two datasets indicate that FSRF has a significant performance advantage over previous methods with uncertain missing modalities.
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All authors Ziyang Liu, Pengjunfei Chu, Shuming Dong, Chen Zhang, Mingcheng Li, Jin Wang

Statistical Methodology · Cross-listed from cs.LG

Beyond Accuracy: Are Time Series Foundation Models Well-Calibrated?

The recent development of foundation models for time series data has generated considerable interest in using such models across a variety of applications. Although foundation models achieve state-of-the-art predictive performance, their calibration properties remain relatively underexplored, despite the fact that calibration can be critical for many practical applications. In this paper, we investigate the calibration-related properties of five recent time series foundation models and two competitive baselines. We perform a series of systematic evaluations assessing model calibration (i.e., over- or under-confidence), effects of varying prediction heads, and calibration under long-term autoregressive forecasting. We find that time series foundation models are consistently better calibrated than baseline models and tend not to be either systematically over- or under-confident, in contrast to the overconfidence often seen in other deep learning models.
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All authors Coen Adler, Yuxin Chang, Felix Draxler, Samar Abdi, Padhraic Smyth

Machine Learning (Statistics) · Cross-listed from cs.LG

Learning Correlated Reward Models: Statistical Barriers and Opportunities

Random Utility Models (RUMs) are a classical framework for modeling user preferences and play a key role in reward modeling for Reinforcement Learning from Human Feedback (RLHF). However, a crucial shortcoming of many of these techniques is the Independence of Irrelevant Alternatives (IIA) assumption, which collapses all human preferences to a universal underlying utility function, yielding a coarse approximation of the range of human preferences. On the other hand, statistical and computational guarantees for models avoiding this assumption are scarce. In this paper, we investigate the statistical and computational challenges of learning a correlated probit model, a fundamental RUM that avoids the IIA assumption. First, we establish that the classical data collection paradigm of pairwise preference data is fundamentally insufficient to learn correlational information, explaining the lack of statistical and computational guarantees in this setting. Next, we demonstrate that best-of-three preference data provably overcomes these shortcomings, and devise a statistically and computationally efficient estimator with near-optimal performance. These results highlight the benefits of higher-order preference data in learning correlated utilities, allowing for more fine-grained modeling of human preferences. Finally, we validate these theoretical guarantees on several real-world datasets, demonstrating improved personalization of human preferences.
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All authors Yeshwanth Cherapanamjeri, Constantinos Daskalakis, Gabriele Farina, Sobhan Mohammadpour

Machine Learning (Statistics)

Adaptive Conformal Inference through the Lens of Blackwell Approachability

This article considers an online version of conformal inference, called adaptive conformal inference [ACI] and introduced by Gibbs and Candès (2021): prediction sets are issued sequentially, after observing features and before the outcomes are revealed. These sets are evaluated both in terms of validity (the fraction of rounds where the outcome was lying in the prediction set) and efficiency (the average lengths of the prediction sets). The two criteria point to different directions (validity favors larger sets). We also target a wide range of scenarios, with exchangeable data and arbitrary data (lack of any stochastic guarantees) as two extremes. A series of existing strategies for ACI typically guarantee that empirical coverage converges to the desired level for arbitrary sequences, but they generally lack simultaneous efficiency guarantees. To provide a unified study, we first formulate ACI as a repeated two-player game with finite action sets and vector-valued payoffs encoding validity and efficiency. Building on this reformulation, we introduce a strategy based on Blackwell approachability and on its opportunistic extension by Bernstein et al. (2014) that ensures validity while adapting the efficiency of the prediction intervals to the underlying degree of stochasticity of the opponent player. The resulting guarantee is "best of many worlds": it recovers the relevant efficiency guarantees in exchangeable and adversarial settings, and provides guarantees in intermediate settings that arise in typical applications such as the forecasting of time series.
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