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At least 1,081 records · Page 60Linked to original sources

arXiv2025

Deviation Ratings: A General, Clone-Invariant Rating Method

Many real-world multi-agent or multi-task evaluation scenarios can be naturally modelled as normal-form games due to inherent strategic (adversarial, cooperative, and mixed motive) interactions. These strategic interactions may be agentic (e.g. players trying to win), fundamental (e.g. cost vs quality), or complementary (e.g. niche finding and specialization). In such a formulation, it is the strategies (actions, policies, agents, models, tasks, prompts, etc.) that are rated. However, the rating problem is complicated by redundancy and complexity of N-player strategic interactions. Repeated or similar strategies can distort ratings for those that counter or complement them. Previous work proposed ``clone invariant'' ratings to handle such redundancies, but this was limited to two-player zero-sum (i.e. strictly competitive) interactions. This work introduces the first N-player general-sum clone invariant rating, called deviation ratings, based on coarse correlated equilibria. The rating is explored on several domains including LLMs evaluation.

cs.GT↗

arXiv2025

A Simplified and Numerically Stable Approach to the BG/NBD Churn Prediction model

This study extends the BG/NBD churn probability model, addressing its limitations in industries where customer behaviour is often influenced by seasonal events and possibly high purchase counts. We propose a modified definition of churn, considering a customer to have churned if they make no purchases within M days. Our contribution is twofold: First, we simplify the general equation for the specific case of zero purchases within M days. Second, we derive an alternative expression using numerical techniques to mitigate numerical overflow or underflow issues. This approach provides a more practical and robust method for predicting customer churn in industries with irregular purchase patterns.

stat.OT↗

arXiv2025

Score Matching Riemannian Diffusion Means

Estimating means on Riemannian manifolds is generally computationally expensive because the Riemannian distance function is not known in closed-form for most manifolds. To overcome this, we show that Riemannian diffusion means can be efficiently estimated using score matching with the gradient of Brownian motion transition densities using the same principle as in Riemannian diffusion models. Empirically, we show that this is more efficient than Monte Carlo simulation while retaining accuracy and is also applicable to learned manifolds. Our method, furthermore, extends to computing the Fréchet mean and the logarithmic map for general Riemannian manifolds. We illustrate the applicability of the estimation of diffusion mean by efficiently extending Euclidean algorithms to general Riemannian manifolds with a Riemannian $k$-means algorithm and maximum likelihood Riemannian regression.

stat.OT↗

arXiv2025

Entropy of spatial network with applications to non-extensive statistical mechanics

A new method is proposed for analyzing complexity and studying the information in random geometric networks using Tsallis entropy tool. Tsallis entropy of the ensemble of random geometric networks is calculated based on the components of the random connection model on the point process which is obtained by connecting the points with a probability that depends on their relative positions (10.1016/j.indag.2022.05.002, 2022). According to information theory and conditional discussion, the bounds for Shannon and Tsallis entropies of the ensemble of this random graph are presented. Using this function and Lagrange's formula, the connection function that provides the maximum Tsallis entropy based on general constraints is obtained. Then, a simulation-based example is presented to clarify the application of the proposed method in the study of ad hoc wireless networks. By observing the obtained results, it can be stated that the wireless networks that adhere to the model studied here are almost maximally complex. Also, Tsallis conditional entropy maximizing function is compared with other connection functions using numerical calculations and the optimal value for the maximization of conditional entropies is obtained.

cond-mat.stat-mech↗

arXiv2025

A Statistical Case Against Empirical Human-AI Alignment

Empirical human-AI alignment aims to make AI systems act in line with observed human behavior. While noble in its goals, we argue that empirical alignment can inadvertently introduce statistical biases that warrant caution. This position paper thus advocates against naive empirical alignment, offering prescriptive alignment and a posteriori empirical alignment as alternatives. We substantiate our principled argument by tangible examples like human-centric decoding of language models.

cs.AI↗

arXiv2025

A tutorial on optimal dynamic treatment regimes

A dynamic treatment regime is a sequence of treatment decision rules tailored to an individual's evolving status over time. In precision medicine, much focus has been placed on finding an optimal dynamic treatment regime which, if followed by everyone in the population, would yield the best outcome on average; and extensive investigation has been conducted from both methodological and applications standpoints. The aim of this tutorial is to provide readers who are interested in optimal dynamic treatment regimes with a systematic, detailed but accessible introduction, including the formal definition and formulation of this topic within the framework of causal inference, identification assumptions required to link the causal quantity of interest to the observed data, existing statistical models and estimation methods to learn the optimal regime from data, and application of these methods to both simulated and real data.

stat.OT↗

arXiv2025

A Generalized Theory of Mixup for Structure-Preserving Synthetic Data

Mixup is a widely adopted data augmentation technique known for enhancing the generalization of machine learning models by interpolating between data points. Despite its success and popularity, limited attention has been given to understanding the statistical properties of the synthetic data it generates. In this paper, we delve into the theoretical underpinnings of mixup, specifically its effects on the statistical structure of synthesized data. We demonstrate that while mixup improves model performance, it can distort key statistical properties such as variance, potentially leading to unintended consequences in data synthesis. To address this, we propose a novel mixup method that incorporates a generalized and flexible weighting scheme, better preserving the original data's structure. Through theoretical developments, we provide conditions under which our proposed method maintains the (co)variance and distributional properties of the original dataset. Numerical experiments confirm that the new approach not only preserves the statistical characteristics of the original data but also sustains model performance across repeated synthesis, alleviating concerns of model collapse identified in previous research.

cs.LG↗

arXiv2025

The impact of the storytelling fallacy on real data examples in methodological research

The term "researcher degrees of freedom" (RDF), which was introduced in metascientific literature in the context of the replication crisis in science, refers to the extent of flexibility a scientist has in making decisions related to data analysis. These choices occur at all stages of the data analysis process. In combination with selective reporting, RDF may lead to over-optimistic statements and an increased rate of false positive findings. Even though the concept has been mainly discussed in fields such as epidemiology or psychology, similar problems affect methodological statistical research. Researchers who develop and evaluate statistical methods are left with a multitude of decisions when designing their comparison studies. This leaves room for an over-optimistic representation of the performance of their preferred method(s). The present paper defines and explores a particular RDF that has not been previously identified and discussed. When interpreting the results of real data examples that are most often part of methodological evaluations, authors typically tell a domain-specific "story" that best supports their argumentation in favor of their preferred method. However, there are often plenty of other plausible stories that would support different conclusions. We define the "storytelling fallacy" as the selective use of anecdotal domain-specific knowledge to support the superiority of specific methods in real data examples. While such examples fed by domain knowledge play a vital role in methodological research, if deployed inappropriately they can also harm the validity of conclusions on the investigated methods. The goal of our work is to create awareness for this issue, fuel discussions on the role of real data in generating evidence in methodological research and warn readers of methodological literature against naive interpretations of real data examples.

stat.OT↗

arXiv2025

Bayesian Graph Traversal

This research considers Bayesian decision-analytic approaches toward the traversal of an uncertain graph. Namely, a traveler progresses over a graph in which rewards are gained upon a node's first visit and costs are incurred for every edge traversal. The traveler knows the graph's adjacency matrix and his starting position but does not know the rewards and costs. The traveler is a Bayesian who encodes his beliefs about these values using a Gaussian process prior and who seeks to maximize his expected utility over these beliefs. Adopting a decision-analytic perspective, we develop sequential decision-making solution strategies for this coupled information-collection and network-routing problem. We show that the problem is NP-Hard and derive properties of the optimal walk. These properties provide heuristics for the traveler's problem that balance exploration and exploitation. We provide a practical case study focused on the use of unmanned aerial systems for public safety and empirically study policy performance in myriad Erdos-Renyi settings.

cs.AI↗

arXiv2025

Hard negative sampling in hyperedge prediction

Hypergraph, which allows each hyperedge to encompass an arbitrary number of nodes, is a powerful tool for modeling multi-entity interactions. Hyperedge prediction is a fundamental task that aims to predict future hyperedges or identify existent but unobserved hyperedges based on those observed. In link prediction for simple graphs, most observed links are treated as positive samples, while all unobserved links are considered as negative samples. However, this full-sampling strategy is impractical for hyperedge prediction, due to the number of unobserved hyperedges in a hypergraph significantly exceeds the number of observed ones. Therefore, one has to utilize some negative sampling methods to generate negative samples, ensuring their quantity is comparable to that of positive samples. In current hyperedge prediction, randomly selecting negative samples is a routine practice. But through experimental analysis, we discover a critical limitation of random selecting that the generated negative samples are too easily distinguishable from positive samples. This leads to premature convergence of the model and reduces the accuracy of prediction. To overcome this issue, we propose a novel method to generate negative samples, named as hard negative sampling (HNS). Unlike traditional methods that construct negative hyperedges by selecting node sets from the original hypergraph, HNS directly synthesizes negative samples in the hyperedge embedding space, thereby generating more challenging and informative negative samples. Our results demonstrate that HNS significantly enhances both accuracy and robustness of the prediction. Moreover, as a plug-and-play technique, HNS can be easily applied in the training of various hyperedge prediction models based on representation learning.

cs.SI↗

arXiv2025

How causal perspectives can inform neuroscience data analysis

Over the past two decades, considerable strides have been made in advancing neuroscientific techniques, yet challenges remain in attributing causality to observed associations. This review addresses a fundamental issue in observational neuroscience studies and advocates for incorporating causal inference frameworks into standard practice. We systematically introduce necessary definitions and concepts, emphasizing how causal assumptions underlie statistical analyses even when not explicitly stated. Through a running example on sleep quality and white matter integrity, we illustrate how persistent challenges, including confounding and selection biases, can be conceptualized and addressed using causal frameworks. We demonstrate practical approaches for making assumption violations transparent through hands-on examples: supplementary case studies using multi-site harmonization and head motion exclusion procedures provide step-by-step diagnostic techniques for checking covariate overlap and identifying selection bias through exclusion pattern analysis. We explore how these causal perspectives can inform both experimental design and analytical choices, particularly for observational studies where traditional randomization is infeasible. Together, we believe this framework offers concrete tools for strengthening causal interpretations and inspiring more robust approaches to problems in neuroscience.

q-bio.OT↗

arXiv2025

The Problem of the Priors, or Posteriors?

The problem of the priors is well known: it concerns the challenge of identifying norms that govern one's prior credences. I argue that a key to addressing this problem lies in considering what I call the problem of the posteriors -- the challenge of identifying norms that directly govern one's posterior credences, which backward induce some norms on the priors via the diachronic requirement of conditionalization. This forward-looking approach can be summarized as: Think ahead, work backward. Although this idea can be traced to Freedman (1963), Carnap (1963), and Shimony (1970), I believe that it has not received enough attention. In this paper, I initiate a systematic defense of forward-looking Bayesianism, addressing potential objections from more traditional views (both subjectivist and objectivist). I also develop a specific approach to forward-looking Bayesianism -- one that values the convergence of posterior credences to the truth, and treats it as a fundamental rather than derived norm. This approach, called convergentist Bayesianism, is argued to be crucial for a Bayesian foundation of Ockham's razor in statistics and machine learning.

stat.OT↗

arXiv2025

A quantile-based bivariate distribution

In this paper we present a flexible bivariate distribution specified by a quantile function. The distribution contains as special cases new bivariate exponential, Pareto I, Pareto II, beta, power, log logistic and uniform distributions and also can approximate many other continuous models. Various $L$-moment based properties of the distribution such as covariance, coskewness, cokurtosis, $L$-correlation, etc are discussed. The distribution is used to model two real data sets.

stat.OT↗

arXiv2025

The Hall of Fame Cut in Major League Baseball

I present a simple and transparent standard for career greatness in baseball: any major league player with H > 2500 or HR > 350 or K > 2800 or W > 240 makes my Hall of Fame Cut. Rate statistics are avoided due to small sample issues and to ensure the standard is permanent once achieved. Hits and home runs were chosen to represent the two extremes of batting styles. Strikeouts are chosen as the most fundamental unit of pitching performance whereas wins are included in deference to their historical importance as a benchmark. Most major league batters and pitchers in the elected Hall of Fame also make my Hall of Fame Cut but my quantitative standard shifts attention to several under-appreciated players, such as Johnny Damon and Bartolo Colon, and allows us to celebrate recent and active players without the waiting period (5 years post-retirement) needed for Hall of Fame election. My Hall of Fame Cut is also agnostic to performance enhancement or off-field issues and strongly favors longevity over peak performance.

stat.OT↗

arXiv2025

Resolving Jeffreys-Lindley Paradox

Jeffreys-Lindley paradox is a case where frequentist and Bayesian hypothesis testing methodologies contradict with each other. This has caused confusion among data analysts for selecting a methodology for their statistical inference tasks. Though the paradox goes back to mid 1930's so far there hasn't been a satisfactory resolution given for it. In this paper we show that it arises mainly due to the simple fact that, in the frequentist approach, the difference between the hypothesized parameter value and the observed estimate of the parameter is assessed in terms of the standard error of the estimate, no matter what the actual numerical difference is and how small the standard error is, whereas in the Bayesian methodology it has no effect due to the definition of the Bayes factor in the context, even though such an assessment is present. In fact, the paradox is an instance of conflict between statistical and practical significance and a result of using a sharp null hypothesis to approximate an acceptable small range of values for the parameter. Occurrence of type-I error that is allowed in frequentist methodology plays important role in the paradox. Therefore, the paradox is not a conflict between two inference methodologies but an instance of not agreeing their conclusions

stat.OT↗

arXiv2025

The information mismatch, and how to fix it

We live in unprecedented times in terms of our ability to use evidence to inform medical care. For example, we can perform data-driven post-test probability calculations. However, there is work to do. As has been previously noted, sensitivity and specificity, which play a key role in post-test probability calculations, are defined as unadjusted for patient covariates. In light of this, there have been multiple recommendations that sensitivity and specificity be adjusted for covariates. However, there is less work on the downstream clinical impact of unadjusted sensitivity and specificity. We discuss this here. We argue that unadjusted sensitivity and specificity, when mixed with covariate-dependent pre-test probability scores (which are more easily available nowadays given the multitude of online calculators), can lead to a post-test probability that contains an ``information mismatch.'' We write the equations behind such an information mismatch and discuss the steps that can be taken to fix it.

stat.OT↗

arXiv2025

Coarse-Grained Games: A Framework for Bounded Perception in Game Theory

In everyday life, we frequently make coarse-grained judgments. When we say that Olivia and Noah excel in mathematics, we disregard the specific differences in their mathematical abilities. Similarly, when we claim that a particular automobile manufacturer produces high-quality cars, we overlook the minor variations among individual vehicles. These coarse-grained assessments are distinct from erroneous or deceptive judgments, such as those resulting from student cheating or false advertising by corporations. Despite the prevalence of such judgments, little attention has been given to their underlying mathematical structure. In this paper, we introduce the concept of coarse-graining into game theory, analyzing games where players may perceive different payoffs as identical while preserving the underlying order structure. We call it a Coarse-Grained Game (CGG). This framework allows us to examine the rational inference processes that arise when players equate distinct micro-level payoffs at a macro level, and to explore how Nash equilibria are preserved or altered as a result. Our key findings suggest that CGGs possess several desirable properties that make them suitable for modeling phenomena in the social sciences. This paper demonstrates two such applications: first, in cases of overly minor product updates, consumers may encounter an equilibrium selection problem, resulting in market behavior that is not driven by objective quality differences; second, the lemon market can be analyzed not only through objective information asymmetry but also through asymmetries in perceptual resolution or recognition ability.

econ.TH↗

arXiv2026

Minimum Volume Conformal Sets for Multivariate Regression

Conformal prediction provides a principled framework for constructing predictive sets with finite-sample validity. While much of the focus has been on univariate response variables, existing multivariate methods either impose rigid geometric assumptions or rely on flexible but computationally expensive approaches that do not explicitly optimize prediction set volume. We propose an optimization-driven framework based on a novel loss function that directly learns minimum-volume covering sets while ensuring valid coverage. This formulation naturally induces a new nonconformity score for conformal prediction, which adapts to the residual distribution and covariates. Our approach optimizes over prediction sets defined by arbitrary norm balls, including single and multi-norm formulations. Additionally, by jointly optimizing both the predictive model and predictive uncertainty, we obtain prediction sets that are tight, informative, and computationally efficient, as demonstrated in our experiments on real-world datasets.

stat.ML↗