Probabilistic Optimal Transport based on Collective Graphical Models
- URL: http://arxiv.org/abs/2006.08866v1
- Date: Tue, 16 Jun 2020 02:03:34 GMT
- Title: Probabilistic Optimal Transport based on Collective Graphical Models
- Authors: Yasunori Akagi, Yusuke Tanaka, Tomoharu Iwata, Takeshi Kurashima,
Hiroyuki Toda
- Abstract summary: Optimal Transport (OT) is a powerful tool for measuring the similarity between probability distributions and histograms.
We propose a new framework in which OT is considered as a maximum a posteriori (MAP) solution of a probabilistic generative model.
- Score: 38.49457447599772
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Optimal Transport (OT) is being widely used in various fields such as machine
learning and computer vision, as it is a powerful tool for measuring the
similarity between probability distributions and histograms. In previous
studies, OT has been defined as the minimum cost to transport probability mass
from one probability distribution to another. In this study, we propose a new
framework in which OT is considered as a maximum a posteriori (MAP) solution of
a probabilistic generative model. With the proposed framework, we show that OT
with entropic regularization is equivalent to maximizing a posterior
probability of a probabilistic model called Collective Graphical Model (CGM),
which describes aggregated statistics of multiple samples generated from a
graphical model. Interpreting OT as a MAP solution of a CGM has the following
two advantages: (i) We can calculate the discrepancy between noisy histograms
by modeling noise distributions. Since various distributions can be used for
noise modeling, it is possible to select the noise distribution flexibly to
suit the situation. (ii) We can construct a new method for interpolation
between histograms, which is an important application of OT. The proposed
method allows for intuitive modeling based on the probabilistic
interpretations, and a simple and efficient estimation algorithm is available.
Experiments using synthetic and real-world spatio-temporal population datasets
show the effectiveness of the proposed interpolation method.
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