The purpose of this paper is to rigorously quantify the statistical and learning-theoretic properties of adversarial training models for classification. Equivalently, we establish the statistical properties of empirical optimal partial transport. Precisely, first we provide two types of central limit theorems (CLT): CLT centered at the expected empirical value, and CLT centered at the population one with smoothing. These results are based on the uniqueness of optimal potential for various equivalent optimal transport formulations, and the empirical process theory argument. For the binary setting, we indeed prove the uniqueness of optimal potential by leveraging the connection between optimal partial transport and the derived multi-marginal optimal transport formula. As byproducts, we also obtain the stability of a saddle point of the adversarial training model, and the sample complexity and concentration probability of the generalization error.
Distributionally robust optimization (DRO) studies parameter estimation under uncertainty in the underlying probability distribution and has emerged as a principled framework for analyzing robustness and generalization. In particular, Wasserstein DRO, with distributional uncertainty induced by the Wasserstein distance,...
Elis Stefansson, David Vävinggren, Antônio H. Ribeiro· 0 citations
A penalized DRO formulation in which the adversary may choose any distribution but incurs a Wasserstein penalty for deviating from the empirical distribution is studied, showing that the adversary's problem can be reformulated as an optimization problem over transport maps that push empirical samples to adversarial one...
Alireza Abdollahpoorrostam, Ehsan Sharifian, Buse Sen et al.· 0 citations
We consider a general model for high-dimensional empirical risk minimization whereby the data xi are d-dimensional Gaussian vectors, the model is parametrized by Θ∈Rd×k and the loss depends on the data via the projection ΘTxi. This setting covers as special cases classical statistics methods (e.g., multinomial regressi...
Kiana Asgari, Andrea Montanari, Basil Saeed· Annals of Statistics· 0 citations
Online learning is an attractive framework in many domains because it permits well-defined learning even when data are dependent or chosen adversarially. This generality, however, comes at a steep price, introducing significant statistical and computational barriers. Recently, smoothed online learning has emerged as a...
S. Voitovych, Adam Block, Alexander Rakhlin et al.· 0 citations
The optimal transport (OT) map provides a geometric transformation for aligning probability distributions and has become a useful tool in machine learning. However, existing estimators of the OT map still exhibit a gap between sharp statistical guarantees and practical parametric estimation based on stable training obj...
Kunwoong Kim, Insung Kong, Yongdai Kim· 0 citations
The central limit theorem and consistency of the fully transcript-based sandwich covariance and intrinsic Wald region under local differential privacy are proved and the predicted decrease in estimation error and near-nominal coverage under moderate privacy is supported.
Adaptive AI agents can help make BIM data more machine-readable by navigating IFC models, interpreting inconsistent information, and mapping it to defined standards. In this blog, Alok Rawat shares findings from a real-world pilot in construction workflows. The post Adaptive AI Agents in Construction Workflows appeared first on GPT-Lab.
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