Related papers: Loop Calculus for Non-Binary Alphabets using Conce…
We propose a new numerical scheme designed for a wide class of structured population models based on the idea of operator splitting and particle approximations. This scheme is related to the Escalator Boxcar Train (EBT) method commonly used…
The performance of bit-interleaved coded modulation (BICM) with bit shaping (i.e., non-equiprobable bit probabilities in the underlying binary code) is studied. For the Gaussian channel, the rates achievable with BICM and bit shaping are…
This paper presents numerical values for auxiliary integrals and coefficients of the beta function in the three-loop approximation for a four-dimensional model with a quartic interaction, using a special type of regularization function. The…
We describe a novel approach to statistical learning from particles tracked while moving in a random environment. The problem consists in inferring properties of the environment from recorded snapshots. We consider here the case of a fluid…
We discuss a generic model of Bayesian inference with binary variables defined on edges of a planar graph. The Loop Calculus approach of [1, 2] is used to evaluate the resulting series expansion for the partition function. We show that, for…
Approximate Bayesian computation (ABC) has become an essential tool for the analysis of complex stochastic models when the likelihood function is numerically unavailable. However, the well-established statistical method of empirical…
The Bethe Ansatz is a method for constructing exact eigenstates of quantum-integrable spin chains. Recently, deterministic quantum algorithms, referred to as "algebraic Bethe circuits", have been developed to prepare Bethe states for the…
Belief Propagation (BP) is one of the most popular methods for inference in probabilistic graphical models. BP is guaranteed to return the correct answer for tree structures, but can be incorrect or non-convergent for loopy graphical…
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…
Two prominent challenges in explainability research involve 1) the nuanced evaluation of explanations and 2) the modeling of missing information through baseline representations. The existing literature introduces diverse evaluation…
In this paper we present an efficiently scaling quantum algorithm which finds the size of the maximum common edge subgraph for a pair of arbitrary graphs and thus provides a meaningful measure of graph similarity. The algorithm makes use of…
The eigenfunctions and eigenvalues of the master-equation for zero range process with totally asymmetric dynamics on a ring are found exactly using the Bethe ansatz weighted with the stationary weights of particle configurations. The Bethe…
In this work we present a new procedure to compute optical spectra including excitonic effects and approximated quasiparticle corrections with reduced computational effort. The excitonic effects on optical spectra are included by solving…
A sharp explicit estimate is proved for the difference $e^\beta-\alpha$ when $\alpha$ and $\beta$ are nonzero algebraic numbers.
Given $0<\alpha<1$, the Beatty sequence of density $\alpha$ is the sequence $B_{\alpha}=(\lfloor n/\alpha\rfloor)_{n\in\mathbb{N}}$. Beatty's theorem states that if $\alpha,\beta$ are irrational numbers with $\alpha+\beta=1$, then the…
We consider the application of approximate Bayesian Computation (ABC) in the context of medical imaging data. We consider the parameter estimation of compartmental models in PET imaging analysis, and provide a simple ABC algorithm for its…
We study the complexity of approximating the partition function of the $q$-state Potts model and the closely related Tutte polynomial for complex values of the underlying parameters. Apart from the classical connections with quantum…
We first propose algorithms for checking language equivalence of finite automata over a large alphabet. We use symbolic automata, where the transition function is compactly represented using a (multi-terminal) binary decision diagrams…
Several algorithms with an approximation guarantee of $O(\log n)$ are known for the Set Cover problem, where $n$ is the number of elements. We study a generalization of the Set Cover problem, called the Partition Set Cover problem. Here,…
Partition functions for non-interacting particles are known to be symmetric functions. It is shown that powerful group-theoretical techniques can be used not only to derive these relationships, but also to significantly simplify calculation…