CONTINUOUS EXPONENTIAL FAMILIES: AN EQUATING TOOL

SMML estimators for exponential families with continuous sufficient statistics

The minimum message length principle is an information theoretic criterion that links data compression with statistical inference. This paper studies the strict minimum message length (SMML) estimator for d-dimensional exponential families with continuous sufficient statistics, for all d. The partition of an SMML estimator is shown to consist of convex polytopes (i.e. convex polygons when d = 2...

Exponential families

Optimally approximating exponential families

This article studies exponential families E on finite sets such that the information divergence D(P E) of an arbitrary probability distribution from E is bounded by some constant D > 0. A particular class of low-dimensional exponential families that have low values of D can be obtained from partitions of the state space. The main results concern optimality properties of these partition exponent...

Asymptotics of Exponential Families

if we use the convention that additive terms that do not contain the parameter may be dropped from log likelihoods (because they do not affect any likelihood-based statistical inferences). Thus we have another definition of exponential families: a statistical model is an exponential family of distributions if there exists a statistic Y and a parameter θ such that the log likelihood has the form...

Satisfiability with Exponential Families

Fix a set S ⊆ {0, 1}∗ of exponential size, e.g. |S ∩ {0, 1}n| ∈ Ω(αn), α > 1. The S-SAT problem asks whether a propositional formula F over variables v1, . . . , vn has a satisfying assignment (v1, . . . , vn) ∈ {0, 1}n ∩S. Our interest is in determining the complexity of S-SAT. We prove that S-SAT is NP-complete for all context-free sets S. Furthermore, we show that if S-SAT is in P for some e...