TY - JOUR

T1 - Inverse spin glass and related maximum entropy problems

AU - Castellana, Michele

AU - Bialek, William

N1 - Publisher Copyright:
© 2014 American Physical Society.

PY - 2014/9/12

Y1 - 2014/9/12

N2 - If we have a system of binary variables and we measure the pairwise correlations among these variables, then the least structured or maximum entropy model for their joint distribution is an Ising model with pairwise interactions among the spins. Here we consider inhomogeneous systems in which we constrain, for example, not the full matrix of correlations, but only the distribution from which these correlations are drawn. In this sense, what we have constructed is an inverse spin glass: rather than choosing coupling constants at random from a distribution and calculating correlations, we choose the correlations from a distribution and infer the coupling constants. We argue that such models generate a block structure in the space of couplings, which provides an explicit solution of the inverse problem. This allows us to generate a phase diagram in the space of (measurable) moments of the distribution of correlations. We expect that these ideas will be most useful in building models for systems that are nonequilibrium statistical mechanics problems, such as networks of real neurons.

AB - If we have a system of binary variables and we measure the pairwise correlations among these variables, then the least structured or maximum entropy model for their joint distribution is an Ising model with pairwise interactions among the spins. Here we consider inhomogeneous systems in which we constrain, for example, not the full matrix of correlations, but only the distribution from which these correlations are drawn. In this sense, what we have constructed is an inverse spin glass: rather than choosing coupling constants at random from a distribution and calculating correlations, we choose the correlations from a distribution and infer the coupling constants. We argue that such models generate a block structure in the space of couplings, which provides an explicit solution of the inverse problem. This allows us to generate a phase diagram in the space of (measurable) moments of the distribution of correlations. We expect that these ideas will be most useful in building models for systems that are nonequilibrium statistical mechanics problems, such as networks of real neurons.

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U2 - 10.1103/PhysRevLett.113.117204

DO - 10.1103/PhysRevLett.113.117204

M3 - Article

C2 - 25260004

AN - SCOPUS:84925064215

VL - 113

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 11

M1 - 117204

ER -