5 research outputs found
On Perfect Bases in Finite Abelian Groups
Let be a finite abelian group and be a positive integer. A subset
of is called a {\em perfect -basis of } if each element of can be
written uniquely as the sum of at most (not-necessarily-distinct) elements
of ; similarly, we say that is a {\em perfect restricted -basis of
} if each element of can be written uniquely as the sum of at most
distinct elements of . We prove that perfect -bases exist only in the
trivial cases of or . The situation is different with restricted
addition where perfection is more frequent; here we treat the case of and
prove that has a perfect restricted -basis if, and only if, it is
isomorphic to , , , ,
, or .Comment: To appear in Involv
2D-Shapley: A Framework for Fragmented Data Valuation
Data valuation -- quantifying the contribution of individual data sources to
certain predictive behaviors of a model -- is of great importance to enhancing
the transparency of machine learning and designing incentive systems for data
sharing. Existing work has focused on evaluating data sources with the shared
feature or sample space. How to valuate fragmented data sources of which each
only contains partial features and samples remains an open question. We start
by presenting a method to calculate the counterfactual of removing a fragment
from the aggregated data matrix. Based on the counterfactual calculation, we
further propose 2D-Shapley, a theoretical framework for fragmented data
valuation that uniquely satisfies some appealing axioms in the fragmented data
context. 2D-Shapley empowers a range of new use cases, such as selecting useful
data fragments, providing interpretation for sample-wise data values, and
fine-grained data issue diagnosis.Comment: ICML 202
Augment Your Past
The project focuses on the past by providing the historical facts and photos of the Gettysburg College Campus from 1890s to 1920s. It allows the audience to compare the present Gettysburg College Campus with the past by using an augmented reality mobile application developed in Unity. The project hopes to interest the College community to learn more about the College history using modern approaches of conveying the past
Learning to Refit for Convex Learning Problems
Machine learning (ML) models need to be frequently retrained on changing
datasets in a wide variety of application scenarios, including data valuation
and uncertainty quantification. To efficiently retrain the model, linear
approximation methods such as influence function have been proposed to estimate
the impact of data changes on model parameters. However, these methods become
inaccurate for large dataset changes. In this work, we focus on convex learning
problems and propose a general framework to learn to estimate optimized model
parameters for different training sets using neural networks. We propose to
enforce the predicted model parameters to obey optimality conditions and
maintain utility through regularization techniques, which significantly improve
generalization. Moreover, we rigorously characterize the expressive power of
neural networks to approximate the optimizer of convex problems. Empirical
results demonstrate the advantage of the proposed method in accurate and
efficient model parameter estimation compared to the state-of-the-art