# Gradient flow of the stochastic relaxation on a generic exponential family

## Abstract

We study the natural gradient flow of the expected value E{sub p} [f] of an objective function f for p in an exponential family. We parameterize the exponential family with the expectation parameters and we show that the dynamical system associated to the natural gradient flow can be extended outside the marginal polytope.

- Authors:

- Collegio Carlo Alberto, Via Real Collegio 30, 10024 Moncalieri, Italy and Shinshu University, 4-17-1 Wakasato, Nagano 380-8553 (Japan)
- Collegio Carlo Alberto, Via Real Collegio 30, 10024 Moncalieri (Italy)

- Publication Date:

- OSTI Identifier:
- 22390868

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: AIP Conference Proceedings; Journal Volume: 1641; Journal Issue: 1; Conference: MAXENT 2014: Conference on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Clos Luce, Amboise (France), 21-26 Sep 2014; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EXPECTATION VALUE; FUNCTIONS; PARAMETRIC ANALYSIS; RELAXATION; STOCHASTIC PROCESSES

### Citation Formats

```
Malagò, Luigi, E-mail: malago@shinshu-u.ac.jp, and Pistone, Giovanni, E-mail: giovanni.pistone@carloalberto.org.
```*Gradient flow of the stochastic relaxation on a generic exponential family*. United States: N. p., 2015.
Web. doi:10.1063/1.4905998.

```
Malagò, Luigi, E-mail: malago@shinshu-u.ac.jp, & Pistone, Giovanni, E-mail: giovanni.pistone@carloalberto.org.
```*Gradient flow of the stochastic relaxation on a generic exponential family*. United States. doi:10.1063/1.4905998.

```
Malagò, Luigi, E-mail: malago@shinshu-u.ac.jp, and Pistone, Giovanni, E-mail: giovanni.pistone@carloalberto.org. Tue .
"Gradient flow of the stochastic relaxation on a generic exponential family". United States.
doi:10.1063/1.4905998.
```

```
@article{osti_22390868,
```

title = {Gradient flow of the stochastic relaxation on a generic exponential family},

author = {Malagò, Luigi, E-mail: malago@shinshu-u.ac.jp and Pistone, Giovanni, E-mail: giovanni.pistone@carloalberto.org},

abstractNote = {We study the natural gradient flow of the expected value E{sub p} [f] of an objective function f for p in an exponential family. We parameterize the exponential family with the expectation parameters and we show that the dynamical system associated to the natural gradient flow can be extended outside the marginal polytope.},

doi = {10.1063/1.4905998},

journal = {AIP Conference Proceedings},

number = 1,

volume = 1641,

place = {United States},

year = {Tue Jan 13 00:00:00 EST 2015},

month = {Tue Jan 13 00:00:00 EST 2015}

}

DOI: 10.1063/1.4905998

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