Randomized Transport Plans via Hierarchical Fully Probabilistic Design
An optimal randomized strategy for design of balanced, normalized mass transport plans is developed. It replaces -- but specializes to -- the deterministic, regularized optimal transport (OT) strategy, which yields only a certainty-equivalent plan. The incompletely specified -- and therefore uncertain -- transport plan is acknowledged to be a random process. Therefore, hierarchical fully probabilistic design (HFPD) is adopted, yielding an optimal hyperprior supported on the set of possible transport plans, and consistent with prior mean constraints on the marginals of the uncertain plan. This Bayesian resetting of the design problem for transport plans -- which we call HFPD-OT -- confers new opportunities. These include (i) a strategy for the generation of a random sample of joint transport plans; (ii) randomized marginal contracts for individual source-target pairs; and (iii) consistent measures of uncertainty in the plan and its contracts. An application in fair market matching is outlined, in which HFPD-OT enables the recruitment of a more diverse subset of contracts -- than is possible in classical OT -- into the delivery of an expected plan.
Code (0)
등록된 구현이 없습니다.
Tasks
FairnessMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Probabilistic contingent planning based on HTN for high-quality plans
Deterministic planning assumes that the planning evolves along a fully predictable path, and therefore it loses the practical value in most real projections. A more realistic view is that planning ought to take into cons…
String Diagram of Optimal Transports
We present a novel hierarchical framework for optimal transport (OT) using string diagrams, namely string diagrams of optimal transports. This framework reduces complex hierarchical OT problems to standard OT problems, a…
On Transportation of Mini-batches: A Hierarchical Approach
Mini-batch optimal transport (m-OT) has been successfully used in practical applications that involve probability measures with a very high number of supports. The m-OT solves several smaller optimal transport problems a…
Domain AdaptationKR$^3$: An Architecture for Knowledge Representation and Reasoning in Robotics
This paper describes an architecture that combines the complementary strengths of declarative programming and probabilistic graphical models to enable robots to represent, reason with, and learn from, qualitative and qua…
Variational Hetero-Encoder Randomized GANs for Joint Image-Text Modeling
For bidirectional joint image-text modeling, we develop variational hetero-encoder (VHE) randomized generative adversarial network (GAN), a versatile deep generative model that integrates a probabilistic text decoder, pr…
DecoderGenerative Adversarial Network