This paper compares statistical experiments in discounted problems, ranging from the simplest ones where the state is fixed and the flow of information exogenous to more complex ones, where the decision-maker controls the flow of information or the state changes over time.
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This study proposes a unified theory and statistical learning approach for traffic conflict detection, addressing the long-existing call for a consistent and comprehensive methodology to evaluate the collision risk emerged in road user interactions. The proposed theory assumes a context-dependent probabilistic collision risk and frames conflict detection as estimating the risk by statistical learning from observed proximities and contextual variables. Three primary tasks are integrated: representing interaction context from selected observables, inferring proximity distributions in different contexts, and applying extreme value theory to relate conflict intensity with conflict probability. As a result, this methodology is adaptable to various road users and interaction scenarios, enhancing its applicability without the need for pre-labelled conflict data. Demonstration experiments are executed using real-world trajectory data, with the unified metric trained on lane-changing interactions on German highways and applied to near-crash events from the 100-Car Naturalistic Driving Study in the U.S. The experiments demonstrate the methodology's ability to provide effective collision warnings, generalise across different datasets and traffic environments, cover a broad range of conflicts, and deliver a long-tailed distribution of conflict intensity. This study contributes to traffic safety by offering a consistent and explainable methodology for conflict detection applicable across various scenarios. Its societal implications include enhanced safety evaluations of traffic infrastructures, more effective collision warning systems for autonomous and driving assistance systems, and a deeper understanding of road user behaviour in different traffic conditions, contributing to a potential reduction in accident rates and improving overall traffic safety.
The current prevalence of conspiracy theories on the internet is a significant issue, tackled by many computational approaches. However, these approaches fail to recognize the relevance of distinguishing between texts which contain a conspiracy theory and texts which are simply critical and oppose mainstream narratives. Furthermore, little attention is usually paid to the role of inter-group conflict in oppositional narratives. We contribute by proposing a novel topic-agnostic annotation scheme that differentiates between conspiracies and critical texts, and that defines span-level categories of inter-group conflict. We also contribute with the multilingual XAI-DisInfodemics corpus (English and Spanish), which contains a high-quality annotation of Telegram messages related to COVID-19 (5,000 messages per language). We also demonstrate the feasibility of an NLP-based automatization by performing a range of experiments that yield strong baseline solutions. Finally, we perform an analysis which demonstrates that the promotion of intergroup conflict and the presence of violence and anger are key aspects to distinguish between the two types of oppositional narratives, i.e., conspiracy vs. critical.
This paper presents an integrated perspective on robustness in regression. Specifically, we examine the relationship between traditional outlier-resistant robust estimation and robust optimization, which focuses on parameter estimation resistant to imaginary dataset-perturbations. While both are commonly regarded as robust methods, these concepts demonstrate a bias-variance trade-off, indicating that they follow roughly converse strategies.
This paper proposes a novel method to estimate parameters in a logistic regression model. After obtaining the estimators, their asymptotic properties are rigorously investigated.
Deep learning models can exhibit what appears to be a sudden ability to solve a new problem as training time, training data, or model size increases, a phenomenon known as emergence. In this paper, we present a framework where each new ability (a skill) is represented as a basis function. We solve a simple multi-linear model in this skill-basis, finding analytic expressions for the emergence of new skills, as well as for scaling laws of the loss with training time, data size, model size, and optimal compute ($C$). We compare our detailed calculations to direct simulations of a two-layer neural network trained on multitask sparse parity, where the tasks in the dataset are distributed according to a power-law. Our simple model captures, using a single fit parameter, the sigmoidal emergence of multiple new skills as training time, data size or model size increases in the neural network.
Generalised quantifiers, which include Henkin's branching quantifiers, have been introduced by Mostowski and Lindstr\"om and developed as a substantial topic application of logic, especially model theory, to linguistics with work by Barwise, Cooper, Keenan. In this paper, we mainly study the proof theory of some non-standard quantifiers as second order formulae . Our first example is the usual pair of first order quantifiers (for all / there exists) when individuals are viewed as individual concepts handled by second order deductive rules. Our second example is the study of a second order translation of the simplest branching quantifier: ``A member of each team and a member of each board of directors know each other", for which we propose a second order treatment.
This paper introduces a comprehensive framework to adjust a discrete test statistic for improving its hypothesis testing procedure. The adjustment minimizes the Wasserstein distance to a null-approximating continuous distribution, tackling some fundamental challenges inherent in combining statistical significances derived from discrete distributions. The related theory justifies Lancaster's mid-p and mean-value chi-squared statistics for Fisher's combination as special cases. However, in order to counter the conservative nature of Lancaster's testing procedures, we propose an updated null-approximating distribution. It is achieved by further minimizing the Wasserstein distance to the adjusted statistics within a proper distribution family. Specifically, in the context of Fisher's combination, we propose an optimal gamma distribution as a substitute for the traditionally used chi-squared distribution. This new approach yields an asymptotically consistent test that significantly improves type I error control and enhances statistical power.
The rapid pace of development in quantum computing technology has sparked a proliferation of benchmarks for assessing the performance of quantum computing hardware and software. Good benchmarks empower scientists, engineers, programmers, and users to understand a computing system's power, but bad benchmarks can misdirect research and inhibit progress. In this Perspective, we survey the science of quantum computer benchmarking. We discuss the role of benchmarks and benchmarking, and how good benchmarks can drive and measure progress towards the long-term goal of useful quantum computations, i.e., "quantum utility". We explain how different kinds of benchmark quantify the performance of different parts of a quantum computer, we survey existing benchmarks, critically discuss recent trends in benchmarking, and highlight important open research questions in this field.
Sufficient dimension reduction has received much interest over the past 30 years. Most existing approaches focus on statistical models linking the response to the covariate through a regression equation, and as such are not adapted to binary classification problems. We address the question of dimension reduction for binary classification by fitting a localized nearest-neighbor logistic model with $\ell_1$-penalty in order to estimate the gradient of the conditional probability of interest. Our theoretical analysis shows that the pointwise convergence rate of the gradient estimator is optimal under very mild conditions. The dimension reduction subspace is estimated using an outer product of such gradient estimates at several points in the covariate space. Our implementation uses cross-validation on the misclassification rate to estimate the dimension of this subspace. We find that the proposed approach outperforms existing competitors in synthetic and real data applications.
This paper does not describe a working system. Instead, it presents a single idea about representation which allows advances made by several different groups to be combined into an imaginary system called GLOM. The advances include transformers, neural fields, contrastive representation learning, distillation and capsules. GLOM answers the question: How can a neural network with a fixed architecture parse an image into a part-whole hierarchy which has a different structure for each image? The idea is simply to use islands of identical vectors to represent the nodes in the parse tree. If GLOM can be made to work, it should significantly improve the interpretability of the representations produced by transformer-like systems when applied to vision or language
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