Related papers: Reconstruction on Trees and Low-Degree Polynomials

Poly-trees are singly connected causal networks in which variables may arise from multiple causes. This paper develops a method of recovering ply-trees from empirically measured probability distributions of pairs of variables. The method…

We derive tractable criteria for the consistency of Bayesian tree reconstruction procedures, which constitute a central class of algorithms for inferring common ancestry among DNA sequence samples in phylogenetics. Our results encompass…

In generative models with obscured likelihood, Approximate Bayesian Computation (ABC) is often the tool of last resort for inference. However, ABC demands many prior parameter trials to keep only a small fraction that passes an acceptance…

We consider the phylogenetic tree reconstruction problem with insertions and deletions (indels). Phylogenetic algorithms proceed under a model where sequences evolve down the model tree, and given sequences at the leaves, the problem is to…

Since their inception in the 1980's, regression trees have been one of the more widely used non-parametric prediction methods. Tree-structured methods yield a histogram reconstruction of the regression surface, where the bins correspond to…

Tensor network contraction is a fundamental computational challenge underlying quantum many-body physics, statistical mechanics, and machine learning. Belief propagation (BP) provides an efficient approximate solution, but introduces…

In the \emph{trace reconstruction problem}, an unknown source string $x \in \{0,1\}^n$ is transmitted through a probabilistic \emph{deletion channel} which independently deletes each bit with some fixed probability $\delta$ and concatenates…

A number of problems in statistical physics and computer science can be expressed as the computation of marginal probabilities over a Markov random field. Belief propagation, an iterative message-passing algorithm, computes exactly such…

Reconstructing the tree of life from molecular sequences is a fundamental problem in computational biology. Modern data sets often contain a large number of genes, which can complicate the reconstruction problem due to the fact that…

Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and nonconvex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction…

For a graph $G$, the parameter treedepth measures the minimum depth among all forests $F$, called elimination forests, such that $G$ is a subgraph of the ancestor-descendant closure of $F$. We introduce a logic, called neighborhood operator…

Inferring probabilistic networks from data is a notoriously difficult task. Under various goodness-of-fit measures, finding an optimal network is NP-hard, even if restricted to polytrees of bounded in-degree. Polynomial-time algorithms are…

We present a linear programming based algorithm for computing a spanning tree $T$ of a set $P$ of $n$ points in $\Re^d$, such that its crossing number is $O(\min(t \log n, n^{1-1/d}))$, where $t$ the minimum crossing number of any spanning…

Phylogenetic invariants are certain polynomials in the joint probability distribution of a Markov model on a phylogenetic tree. Such polynomials are of theoretical interest in the field of algebraic statistics and they are also of practical…

A standard way of justifying that a certain probabilistic property holds in a system is to provide a witnessing subsystem (also called critical subsystem) for the property. Computing minimal witnessing subsystems is NP-hard already for…

We consider two core algorithmic problems for probabilistic verification: the maximal end-component decomposition and the almost-sure reachability set computation for Markov decision processes (MDPs). For MDPs with treewidth $k$, we present…

We consider the well-studied problem of finding a spanning tree with minimum average distance between vertex pairs (called a MAD tree). This is a classic network design problem which is known to be NP-hard. While approximation algorithms…

We consider the problem of graph matching, or learning vertex correspondence, between two correlated stochastic block models (SBMs). The graph matching problem arises in various fields, including computer vision, natural language processing…

In many natural average-case problems, there are or there are believed to be critical values in the parameter space where the structure of the space of solutions changes in a fundamental way. These phase transitions are often believed to…

In this effort we propose a novel approach for reconstructing multivariate functions from training data, by identifying both a suitable network architecture and an initialization using polynomial-based approximations. Training deep neural…