New Generalizations of the Bethe Approximation via Asymptotic Expansion
نویسندگان
چکیده
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., low-density parity-check codes, compressed sensing, etc. Recently, Vontobel gives a novel characterization of the Bethe approximation using graph cover. In this paper, a new approximation based on the Bethe approximation is proposed. The new approximation is derived from Vontobel’s characterization using graph cover, and expressed by using the edge zeta function, which is related with the Hessian of the Bethe free energy as shown by Watanabe and Fukumizu. On some conditions, it is proved that the new approximation is asymptotically better than the Bethe approximation.
منابع مشابه
New Understanding of the Bethe Approximation and the Replica Method
In this thesis, new generalizations of the Bethe approximation and new understanding of the replica method are proposed. The Bethe approximation is an efficient approximation for graphical models, which gives an asymptotically accurate estimate of the partition function for many graphical models. The Bethe approximation explains the well-known message passing algorithm, belief propagation, whic...
متن کاملNumerical method for singularly perturbed fourth order ordinary differential equations of convection-diffusion type
In this paper, we have proposed a numerical method for singularly perturbed fourth order ordinary differential equations of convection-diffusion type. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference method. In order to get a numerical solution for the derivative of the solution, the given interval is divided in...
متن کاملEffect of dimensionality on the percolation thresholds of various d-dimensional lattices
We show analytically that the [0,1], [1,1], and [2,1] Padé approximants of the mean cluster number S(p) for site and bond percolation on general d-dimensional lattices are upper bounds on this quantity in any Euclidean dimension d , where p is the occupation probability. These results lead to certain lower bounds on the percolation threshold pc that become progressively tighter as d increases a...
متن کاملFull asymptotic expansion for Polya structures
In order to obtain the full asymptotic expansion for Pólya trees, i.e. rooted unlabelled and non-plane trees, Flajolet and Sedgewick observed that their specification could be seen as a slight disturbance of the functional equation satisfied by the Cayley tree function. Such an approach highlights the complicated formal expressions with some combinatorial explanation. They initiated this proces...
متن کاملLoop series expansion with propagation diagrams
Abstract. The Bethe approximation is a successful method for approximating partition functions of probabilistic models associated with a graph. Recently, Chertkov and Chernyak derived an interesting formula called “Loop Series Expansion”, which is an expansion of the partition function. The main term of the series is the Bethe approximation while other terms are labelled by subgraphs called gen...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1210.2592 شماره
صفحات -
تاریخ انتشار 2012