# FisMat2017 - Submission - View

**Abstract's title**: How simple are simple spin models?

**Affiliation**: Abdus Salam ICTP

**Affiliation Address**: Strada Costiera 11, 34151, Trieste

**Country**: Italy

Information theory provides a sharp definition of the complexity of statistical models.

Simple models are those with a small stochastic complexity, which is computed in terms of the susceptibility

matrix (Fisher Information). We study the stochastic complexity of spin models (in the exponential family)

with interactions of arbitrary order.

Invariance with respect to bijections within the space of operators allows us to classify models in complexity

classes. This invariance also shows that simplicity is not related to the order of the interactions,

but rather to their mutual arrangement. Models where statistical dependencies are localized on

non-overlapping groups of few variables (and that afford predictions on independencies that are

easy to falsify) are simple. On the contrary, fully connected pairwise models, which are often used

in statistical learning, are highly complex because of their extended set of interactions.

Since the stochastic complexity is a penalty term in Bayesian model selection, our results suggests that

models that should be privileged in statistical learning for high dimensional datasets are not the ones that

are currently used.