Related papers: Lower bounds for testing graphical models: colorin…
In this paper we investigate the computational complexity of learning the graph structure underlying a discrete undirected graphical model from i.i.d. samples. We first observe that the notoriously difficult problem of learning parities…
This paper studies structure detection problems in high temperature ferromagnetic (positive interaction only) Ising models. The goal is to distinguish whether the underlying graph is empty, i.e., the model consists of independent Rademacher…
This paper explores the information-theoretic limitations of graph property testing in zero-field Ising models. Instead of learning the entire graph structure, sometimes testing a basic graph property such as connectivity, cycle presence or…
The ferromagnetic Ising model is a model of a magnetic material and a central topic in statistical physics. It also plays a starring role in the algorithmic study of approximate counting: approximating the partition function of the…
We consider testing for the parameters of Ferromagnetic Ising models. While testing for the presence of possibly sparse magnetizations, we provide a general lower bound of minimax separation rates which yields sharp results in high…
In the multicoloring problem, also known as ($a$:$b$)-coloring or $b$-fold coloring, we are given a graph G and a set of $a$ colors, and the task is to assign a subset of $b$ colors to each vertex of G so that adjacent vertices receive…
We consider the problem of sampling from the Ising model when the underlying interaction matrix has eigenvalues lying within an interval of length $\gamma$. Recent work in this setting has shown various algorithmic results that apply…
Approximating the partition function of the ferromagnetic Ising model with general external fields is known to be #BIS-hard in the worst case, even for bounded-degree graphs, and it is widely believed that no polynomial-time approximation…
We present novel information-theoretic limits on detecting sparse changes in Ising models, a problem that arises in many applications where network changes can occur due to some external stimuli. We show that the sample complexity for…
We consider the problem of learning the structure of ferromagnetic Ising models Markov on sparse Erdos-Renyi random graph. We propose simple local algorithms and analyze their performance in the regime of correlation decay. We prove that an…
We study classical Ising spin-$\frac{1}{2}$ models on the 2D square lattice with ferromagnetic or antiferromagnetic nearest-neighbor interactions, under the effect of a pure imaginary magnetic field. The complex Boltzmann weights of spin…
The isolation lemma of Mulmuley et al \cite{MVV87} is an important tool in the design of randomized algorithms and has played an important role in several nontrivial complexity upper bounds. On the other hand, polynomial identity testing is…
Learning the unknown causal parameters of a linear structural causal model is a fundamental task in causal analysis. The task, known as the problem of identification, asks to estimate the parameters of the model from a combination of…
Recent results establish for 2-spin antiferromagnetic systems that the computational complexity of approximating the partition function on graphs of maximum degree D undergoes a phase transition that coincides with the uniqueness phase…
As powerful as machine learning (ML) techniques are in solving problems involving data with large dimensionality, explaining the results from the fitted parameters remains a challenging task of utmost importance, especially in physics…
Property Testing is a formal framework to study the computational power and complexity of sampling from combinatorial objects. A central goal in standard graph property testing is to understand which graph properties are testable with…
In (Kabanets, Impagliazzo, 2004) it is shown how to decide the circuit polynomial identity testing problem (CPIT) in deterministic subexponential time, assuming hardness of some explicit multilinear polynomial family for arithmetical…
Maximal independent set (MIS), maximal matching (MM), and $(\Delta+1)$-coloring in graphs of maximum degree $\Delta$ are among the most prominent algorithmic graph theory problems. They are all solvable by a simple linear-time greedy…
Two graphs $G$ and $H$ are homomorphism indistinguishable over a graph class $\mathcal{F}$ if they admit the same number of homomorphisms from every graph $F \in \mathcal{F}$. Many graph isomorphism relaxations such as (quantum) isomorphism…
A remarkable connection has been established for antiferromagnetic 2-spin systems, including the Ising and hard-core models, showing that the computational complexity of approximating the partition function for graphs with maximum degree D…