Quantifying Distributional Model Risk via Optimal Transport
نویسندگان
چکیده
منابع مشابه
Geodesic Shape Retrieval via Optimal Mass Transport
This paper presents a new method for 2-D and 3-D shape retrieval based on geodesic signatures. These signatures are high dimensional statistical distributions computed by extracting several features from the set of geodesic distance maps to each point. The resulting high dimensional distributions are matched to perform retrieval using a fast approximate Wasserstein metric. This allows to propos...
متن کاملConvex Clustering via Optimal Mass Transport
We consider approximating distributions within the framework of optimal mass transport and specialize to the problem of clustering data sets. Distances between distributions are measured in the Wasserstein metric. The main problem we consider is that of approximating sample distributions by ones with sparse support. This provides a new viewpoint to clustering. We propose different relaxations o...
متن کاملNatural gradient via optimal transport I
We study a natural Wasserstein gradient flow on manifolds of probability distributions with discrete sample spaces. We derive the Riemannian structure for the probability simplex from the dynamical formulation of the Wasserstein distance on a weighted graph. We pull back the geometric structure to the parameter space of any given probability model, which allows us to define a natural gradient f...
متن کاملMechanism Design via Optimal Transport Citation
Optimal mechanisms have been provided in quite general multi-item settings [4], as long as each bidder’s type distribution is given explicitly by listing every type in the support along with its associated probability. In the implicit setting, e.g. when the bidders have additive valuations with independent and/or continuous values for the items, these results do not apply, and it was recently s...
متن کاملOptimal transport over nonlinear systems via infinitesimal generators on graphs
We present a set-oriented graph-based framework for continuous-time optimal transport over nonlinear dynamical systems. Our approach allows us to recover provably optimal control laws for steering a given initial distribution in phase space to a final distribution in prescribed finite time for the case of nonlinear control-affine systems. The action of the controlled vector fields is approximat...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Operations Research
سال: 2019
ISSN: 0364-765X,1526-5471
DOI: 10.1287/moor.2018.0936