Related papers: The Bethe Free Energy Allows to Compute the Condit…
The loop series provides a formal way to write down corrections to the Bethe entropy (and/or free energy) of graphical models. We provide methods to rigorously control such expansions for low-density parity-check codes used over a highly…
We prove that the Bethe expression for the conditional input-output entropy of cycle LDPC codes on binary symmetric channels above the MAP threshold is exact in the large block length limit. The analysis relies on methods from statistical…
Given a locally consistent set of reduced density matrices, we construct approximate density matrices which are globally consistent with the local density matrices we started from when the trial density matrix has a tree structure. We…
We address the problem of the joint sequence detection in partial-response (PR) channels and decoding of low-density parity-check (LDPC) codes. We model the PR channel and the LDPC code as a combined inference problem. We present for the…
We present a combinatorial characterization of the Bethe entropy function of a factor graph, such a characterization being in contrast to the original, analytical, definition of this function. We achieve this combinatorial characterization…
In this paper we consider regular low-density parity-check codes over a binary-symmetric channel in the decoding regime. We prove that up to a certain noise threshold the bit-error probability of the bit-sampling decoder converges in mean…
The ground state energy of integrable asymptotically free theories can be conjecturally computed by using the Bethe ansatz, once the theory has been coupled to an external potential through a conserved charge. This leads to a precise…
We explore a recently introduced quantum thermodynamic entropy $S^Q_{univ}$ of a pure state of a composite system-environment computational "universe" with a simple system $\mathcal{S}$ coupled to a constant temperature bath $\mathcal{E}$.…
The minimum error entropy (MEE) criterion has been successfully used in fields such as parameter estimation, system identification and the supervised machine learning. There is in general no explicit expression for the optimal MEE estimate…
We formulate a unified definition of the statistical effective temperature (SET) for finite-dimensional classical and quantum systems using dimension-dependent indices of purity derived from the eigenvalue spectrum. This spectral approach…
In graphical models, factor graphs, and more generally energy-based models, the interactions between variables are encoded by a graph, a hypergraph, or, in the most general case, a partially ordered set (poset). Inference on such…
It is well known that an arbitrary graphical model of statistical inference defined on a tree, i.e. on a graph without loops, is solved exactly and efficiently by an iterative Belief Propagation (BP) algorithm convergent to unique minimum…
The Bethe free energy approximation provides an effective way for relaxing NP-hard problems of probabilistic inference. However, its accuracy depends on the model parameters and particularly degrades if a phase transition in the model…
We study a quantity called discrete layered entropy, which approximates the Shannon entropy within a logarithmic gap. Compared to the Shannon entropy, the discrete layered entropy is piecewise linear, approximates the expected length of the…
The Bethe approximation, discovered in statistical physics, gives an efficient algorithm called belief propagation (BP) for approximating a partition function. BP empirically gives an accurate approximation for many problems, e.g.,…
We describe a non-perturbative method for computing the energy band structures of one-dimensional models with general point potentials sitting at equally spaced sites. This is done thanks to a Bethe ansatz approach and the method is…
We consider the interacting Bose gas in the thermodynamic limit in a large box in $\R^d$ at positive temperature $1/\beta\in(0,\infty)$ with particle density $\sim\rho\in(0,\infty)$. We follow a path-integral approach and adopt from \cite…
As an application of generalised statistical mechanics, it is studied a possible route toward a consistent generalised information theory in terms of a family of non-extensive, non-parametric entropies $H^\pm_D(P)$. Unlike other proposals…
The decoding error probability of codes is studied as a function of their block length. It is shown that the existence of codes with a polynomially small decoding error probability implies the existence of codes with an exponentially small…
We define and investigate a notion of entropy for quantum error correcting codes. The entropy of a code for a given quantum channel has a number of equivalent realisations, such as through the coefficients associated with the Knill-Laflamme…