Stein Displacement Field
A displacement field defined within the Stein method framework, in which the Stein operator acts on the displacement field to parameterize the density ratio, unifying statistical and dynamical descriptions of distribution shift and reducing the estimation problem to convex optimization.
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This research proposes a unified estimation framework that parameterizes the density ratio with a displacement field acting on a base distribution, so that density ratio estimation and displacement field estimation are obtained simultaneously through the same convex optimization problem.
This paper's Pull-back algorithm is similar to normalizing flows in that it also adopts a layer-by-layer stacking strategy, but it does not require the transformation to be invertible, nor does it require a closed-form Jacobian determinant; each layer only needs to learn a Stein displacement field, which makes the Pull-back algorithm more flexible in transformation form than traditional normalizing flows.
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This research proposes a unified estimation framework that parameterizes the density ratio with a displacement field acting on a base distribution, so that density ratio estimation and displacement field estimation are obtained simultaneously through the same convex optimization problem.
50%UnverifiedThis paper's Pull-back algorithm is similar to normalizing flows in that it also adopts a layer-by-layer stacking strategy, but it does not require the transformation to be invertible, nor does it require a closed-form Jacobian determinant; each layer only needs to learn a Stein displacement field, which makes the Pull-back algorithm more flexible in transformation form than traditional normalizing flows.
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