Related papers: Approximate inference on planar graphs using Loop …
We study the approximation complexity of the partition function of the eight-vertex model on general 4-regular graphs. For the first time, we relate the approximability of the eight-vertex model to the complexity of approximately counting…
In this paper we introduce a notion of spectral approximation for directed graphs. While there are many potential ways one might define approximation for directed graphs, most of them are too strong to allow sparse approximations in…
We give an $\alpha(1+\epsilon)$-approximation algorithm for solving covering LPs, assuming the presence of a $(1/\alpha)$-approximation algorithm for a certain optimization problem. Our algorithm is based on a simple modification of the…
Probabilistic inferences distill knowledge from graphs to aid human make important decisions. Due to the inherent uncertainty in the model and the complexity of the knowledge, it is desirable to help the end-users understand the inference…
We propose a general framework using spike-and-slab prior distributions to aid with the development of high-dimensional Bayesian inference. Our framework allows inference with a general quasi-likelihood function. We show that highly…
Approximate Bayesian Computation (ABC) is a useful class of methods for Bayesian inference when the likelihood function is computationally intractable. In practice, the basic ABC algorithm may be inefficient in the presence of discrepancy…
The computational cost for inference and prediction of statistical models based on Gaussian processes with Mat\'ern covariance functions scales cubicly with the number of observations, limiting their applicability to large data sets. The…
A wide range of numerical methods exists for computing polynomial approximations of solutions of ordinary differential equations based on Chebyshev series expansions or Chebyshev interpolation polynomials. We consider the application of…
Probabilistic inference in pairwise Markov Random Fields (MRFs), i.e. computing the partition function or computing a MAP estimate of the variables, is a foundational problem in probabilistic graphical models. Semidefinite programming…
Solving point-wise feature correspondence in visual data is a fundamental problem in computer vision. A powerful model that addresses this challenge is to formulate it as graph matching, which entails solving a Quadratic Assignment Problem…
We present a polynomial-time Markov chain Monte Carlo algorithm for estimating the partition function of the antiferromagnetic Ising model on any line graph. The analysis of the algorithm exploits the "winding" technology devised by…
We consider the problem of signal estimation in generalized linear models defined via rotationally invariant design matrices. Since these matrices can have an arbitrary spectral distribution, this model is well suited for capturing complex…
Let $Y=\{f(x,y)=0\}$ be the germ of an irreducible plane curve. We present an algorithm to obtain polynomials, whose valuations coincide with the semigroup generators of $Y$. These polynomials are obtained sequentially, adding terms to the…
MAP is the problem of finding a most probable instantiation of a set of nvariables in a Bayesian network, given some evidence. MAP appears to be a significantly harder problem than the related problems of computing the probability of…
In this paper, we have proved four theorems on the degree of approximation of continuous functions by matrix means of their Fourier series which is expressed in terms of the modulus of continuity and a non-negative mediate function.
This study investigated typical performance of approximation algorithms known as belief propagation, greedy algorithm, and linear-programming relaxation for maximum coverage problems on sparse biregular random graphs. After using the cavity…
Belief propagation (BP) is a powerful tool to solve distributed inference problems, though it is limited by short cycles in the corresponding factor graph. Such cycles may lead to incorrect solutions or oscillatory behavior. Only for…
Theoretical attempts proposed so far to describe ordinary percolation processes on real-world networks rely on the locally tree-like ansatz. Such an approximation, however, holds only to a limited extent, as real graphs are often…
We describe a simple method for making inference on a functional of a multivariate distribution. The method is based on a copula representation of the multivariate distribution and it is based on the properties of an Approximate Bayesian…
The most popular method for computing the matrix logarithm is a combination of the inverse scaling and squaring method in conjunction with a Pad\'e approximation, sometimes accompanied by the Schur decomposition. The main computational…