Search

Data trading is increasingly gaining attention. However, the inherent replicability and privacy concerns of data make it challenging to directly apply traditional trading theories to data markets. This paper compares data trading markets with traditional ones, focusing particularly on how the replicability and privacy of data impact data markets. We discuss how data's replicability fundamentally alters the concept of opportunity cost in traditional microeconomics within the context of data markets. Additionally, we explore how to leverage this change to maximize benefits without compromising data privacy. This paper outlines the constraints for data circulation within the privacy domain chain and presents a model that maximizes data's value under these constraints. Specific application scenarios are provided, and experiments demonstrate the solvability of this model.

The error propagation among estimated parameters reflects the correlation among the parameters. We study the capability of machine learning of "learning" the correlation of estimated parameters. We show that machine learning can recover the relation between the uncertainties of different parameters, especially, as predicted by the error propagation formula. Gravitational lensing can be used to probe both astrophysics and cosmology. As a practical application, we show that the machine learning is able to intelligently find the error propagation among the gravitational lens parameters (effective lens mass $M_{L}$ and Einstein radius $\theta_{E}$) in accordance with the theoretical formula for the singular isothermal ellipse (SIE) lens model. The relation of errors of lens mass and Einstein radius, (e.g. the ratio of standard deviations $\mathcal{F}=\sigma_{\hat{ M_{L}}}/ \sigma_{\hat{\theta_{E}}}$) predicted by the deep convolution neural network are consistent with the error propagation formula of SIE lens model. As a proof-of-principle test, a toy model of linear relation with Gaussian noise is presented. We found that the predictions obtained by machine learning indeed indicate the information about the law of error propagation and the distribution of noise. Error propagation plays a crucial role in identifying the physical relation among parameters, rather than a coincidence relation, therefore we anticipate our case study on the error propagation of machine learning predictions could extend to other physical systems on searching the correlation among parameters.

The expenses involved in training state-of-the-art deep hashing retrieval models have witnessed an increase due to the adoption of more sophisticated models and large-scale datasets. Dataset Distillation (DD) or Dataset Condensation(DC) focuses on generating smaller synthetic dataset that retains the original information. Nevertheless, existing DD methods face challenges in maintaining a trade-off between accuracy and efficiency. And the state-of-the-art dataset distillation methods can not expand to all deep hashing retrieval methods. In this paper, we propose an efficient condensation framework that addresses these limitations by matching the feature-embedding between synthetic set and real set. Furthermore, we enhance the diversity of features by incorporating the strategies of early-stage augmented models and multi-formation. Extensive experiments provide compelling evidence of the remarkable superiority of our approach, both in terms of performance and efficiency, compared to state-of-the-art baseline methods.

Data valuation using Shapley value has emerged as a prevalent research domain in machine learning applications. However, it is a challenge to address the role of order in data cooperation as most research lacks such discussion. To tackle this problem, this paper studies the definition of the partial ordinal Shapley value by group theory in abstract algebra. Besides, since the calculation of the partial ordinal Shapley value requires exponential time, this paper also gives three algorithms for approximating the results. The Truncated Monte Carlo algorithm is derived from the classic Shapley value approximation algorithm. The Classification Monte Carlo algorithm and the Classification Truncated Monte Carlo algorithm are based on the fact that the data points in the same class provide similar information, then we can accelerate the calculation by leaving out some data points in each class., Comment: 9 pages