Patterns of wins and losses in pairwise contests, such as occur in sports and games, consumer research and paired comparison studies, and human and animal social hierarchies, are commonly analyzed using probabilistic models that allow one to quantify the strength of competitors or predict the outcome of future contests. Here we generalize this approach to incorporate two additional features: an element of randomness or luck that leads to upset wins, and a "depth of competition" variable that measures the complexity of a game or hierarchy. Fitting the resulting model to a large collection of data sets we estimate depth and luck in a range of games, sports, and social situations. In general, we find that social competition tends to be "deep," meaning it has a pronounced hierarchy with many distinct levels, but also that there is often a nonzero chance of an upset victory, meaning that dominance challenges can be won even by significant underdogs. Competition in sports and games, by contrast, tends to be shallow and in most cases there is little evidence of upset wins, beyond those already implied by the shallowness of the hierarchy.
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The Shapley value equals a player's contribution to the potential of a game. The potential is a most natural one-number summary of a game, which can be computed as the expected accumulated worth of a random partition of the players. This computation integrates the coalition formation of all players and readily extends to games with externalities. We investigate those potential functions for games with externalities that can be computed this way. It turns out that the potential that corresponds to the MPW solution introduced by Macho-Stadler et al. (2007, J. Econ. Theory 135, 339-356), is unique in the following sense. It is obtained as a the expected accumulated worth of a random partition, it generalizes the potential for games without externalities, and it induces a solution that satisfies the null player property even in the presence of externalities.
A central challenge in the verification of quantum computers is benchmarking their performance as a whole and demonstrating their computational capabilities. In this work, we find a universal model of quantum computation, Bell sampling, that can be used for both of those tasks and thus provides an ideal stepping stone towards fault-tolerance. In Bell sampling, we measure two copies of a state prepared by a quantum circuit in the transversal Bell basis. We show that the Bell samples are classically intractable to produce and at the same time constitute what we call a circuit shadow: from the Bell samples we can efficiently extract information about the quantum circuit preparing the state, as well as diagnose circuit errors. In addition to known properties that can be efficiently extracted from Bell samples, we give two new and efficient protocols, a test for the depth of the circuit and an algorithm to estimate a lower bound to the number of T gates in the circuit. With some additional measurements, our algorithm learns a full description of states prepared by circuits with low T-count.
We revisit a self-supervised method that segments unlabelled speech into word-like segments. We start from the two-stage duration-penalised dynamic programming method that performs zero-resource segmentation without learning an explicit lexicon. In the first acoustic unit discovery stage, we replace contrastive predictive coding features with HuBERT. After word segmentation in the second stage, we get an acoustic word embedding for each segment by averaging HuBERT features. These embeddings are clustered using K-means to get a lexicon. The result is good full-coverage segmentation with a lexicon that achieves state-of-the-art performance on the ZeroSpeech benchmarks.
In the digital era, the prevalence of depressive symptoms expressed on social media has raised serious concerns, necessitating advanced methodologies for timely detection. This paper addresses the challenge of interpretable depression detection by proposing a novel methodology that effectively combines Large Language Models (LLMs) with eXplainable Artificial Intelligence (XAI) and conversational agents like ChatGPT. In our methodology, explanations are achieved by integrating BERTweet, a Twitter-specific variant of BERT, into a novel self-explanatory model, namely BERT-XDD, capable of providing both classification and explanations via masked attention. The interpretability is further enhanced using ChatGPT to transform technical explanations into human-readable commentaries. By introducing an effective and modular approach for interpretable depression detection, our methodology can contribute to the development of socially responsible digital platforms, fostering early intervention and support for mental health challenges under the guidance of qualified healthcare professionals.
In this paper we extend the equal division and the equal surplus division values for transferable utility cooperative games to the more general setup of transferable utility cooperative games with level structures. In the case of the equal surplus division value we propose three possible extensions, one of which has already been described in the literature. We provide axiomatic characterizations of the values considered, apply them to a particular cost sharing problem and compare them in the framework of such an application.
In this paper we extend the equal division and the equal surplus division values for transferable utility cooperative games to the more general setup of transferable utility cooperative games with a priori unions. In the case of the equal surplus division value we propose three possible extensions. We provide axiomatic characterizations of the new values. Furthermore, we apply the proposed modifications to a particular cost sharing problem and compare the numerical results with those obtained with the original values.
In the regression framework, the empirical measure based on the responses resulting from the nearest neighbors, among the covariates, to a given point $x$ is introduced and studied as a central statistical quantity. First, the associated empirical process is shown to satisfy a uniform central limit theorem under a local bracketing entropy condition on the underlying class of functions reflecting the localizing nature of the nearest neighbor algorithm. Second a uniform non-asymptotic bound is established under a well-known condition, often referred to as Vapnik-Chervonenkis, on the uniform entropy numbers. The covariance of the Gaussian limit obtained in the uniform central limit theorem is simply equal to the conditional covariance operator given the covariate value. This suggests the possibility of using standard formulas to estimate the variance by using only the nearest neighbors instead of the full data. This is illustrated on two problems: the estimation of the conditional cumulative distribution function and local linear regression.
We propose a local modification of the standard subdiffusion model by introducing the initial Fickian diffusion, which results in a multiscale diffusion model. The developed model resolves the incompatibility between the nonlocal operators in subdiffusion and the local initial conditions and thus eliminates the initial singularity of the solutions of the subdiffusion, while retaining its heavy tail behavior away from the initial time. The well-posedness of the model and high-order regularity estimates of its solutions are analyzed by resolvent estimates, based on which the numerical discretization and analysis are performed. Numerical experiments are carried out to substantiate the theoretical findings.
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
Breast cancer remains a global challenge, causing over 1 million deaths globally in 2018. To achieve earlier breast cancer detection, screening x-ray mammography is recommended by health organizations worldwide and has been estimated to decrease breast cancer mortality by 20-40%. Nevertheless, significant false positive and false negative rates, as well as high interpretation costs, leave opportunities for improving quality and access. To address these limitations, there has been much recent interest in applying deep learning to mammography; however, obtaining large amounts of annotated data poses a challenge for training deep learning models for this purpose, as does ensuring generalization beyond the populations represented in the training dataset. Here, we present an annotation-efficient deep learning approach that 1) achieves state-of-the-art performance in mammogram classification, 2) successfully extends to digital breast tomosynthesis (DBT; "3D mammography"), 3) detects cancers in clinically-negative prior mammograms of cancer patients, 4) generalizes well to a population with low screening rates, and 5) outperforms five-out-of-five full-time breast imaging specialists by improving absolute sensitivity by an average of 14%. Our results demonstrate promise towards software that can improve the accuracy of and access to screening mammography worldwide.
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