Flows, Scaling, and Entropy Revisited: a Unified Perspective via Optimizing Joint Distributions
In this short expository note, we describe a unified algorithmic perspective on several classical problems which have traditionally been studied in different communities. This perspective views the main characters -- the problems of Optimal Transport, Minimum Mean Cycle, Matrix Scaling, and Matrix B...
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| creator | Altschuler, Jason M |
| description | In this short expository note, we describe a unified algorithmic perspective
on several classical problems which have traditionally been studied in
different communities. This perspective views the main characters -- the
problems of Optimal Transport, Minimum Mean Cycle, Matrix Scaling, and Matrix
Balancing -- through the same lens of optimization problems over joint
probability distributions P(x,y) with constrained marginals. While this is how
Optimal Transport is typically introduced, this lens is markedly less
conventional for the other three problems. This perspective leads to a simple
and unified framework spanning problem formulation, algorithm development, and
runtime analysis. |
| doi_str_mv | 10.48550/arxiv.2210.16456 |
| format | Article |
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on several classical problems which have traditionally been studied in
different communities. This perspective views the main characters -- the
problems of Optimal Transport, Minimum Mean Cycle, Matrix Scaling, and Matrix
Balancing -- through the same lens of optimization problems over joint
probability distributions P(x,y) with constrained marginals. While this is how
Optimal Transport is typically introduced, this lens is markedly less
conventional for the other three problems. This perspective leads to a simple
and unified framework spanning problem formulation, algorithm development, and
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on several classical problems which have traditionally been studied in
different communities. This perspective views the main characters -- the
problems of Optimal Transport, Minimum Mean Cycle, Matrix Scaling, and Matrix
Balancing -- through the same lens of optimization problems over joint
probability distributions P(x,y) with constrained marginals. While this is how
Optimal Transport is typically introduced, this lens is markedly less
conventional for the other three problems. This perspective leads to a simple
and unified framework spanning problem formulation, algorithm development, and
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on several classical problems which have traditionally been studied in
different communities. This perspective views the main characters -- the
problems of Optimal Transport, Minimum Mean Cycle, Matrix Scaling, and Matrix
Balancing -- through the same lens of optimization problems over joint
probability distributions P(x,y) with constrained marginals. While this is how
Optimal Transport is typically introduced, this lens is markedly less
conventional for the other three problems. This perspective leads to a simple
and unified framework spanning problem formulation, algorithm development, and
runtime analysis.</abstract><doi>10.48550/arxiv.2210.16456</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Data Structures and Algorithms Mathematics - Optimization and Control |
| title | Flows, Scaling, and Entropy Revisited: a Unified Perspective via Optimizing Joint Distributions |
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