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We explore a generating function trick which allows us to keep track of infinitely many statistics using finitely many variables, by recording their individual distributions rather than their joint distributions. Building on previous work…

Using the method of spectral decimation and a modified version of Kirchhoffs Matrix-Tree Theorem, a closed form solution to the number of spanning trees on approximating graphs to a fully symmetric self-similar structure on a finitely…

Symmetric edge polytopes of graphs and root polytopes of semi-balanced digraphs are two classes of lattice polytopes whose $h^*$-polynomials have interesting properties and generalize important graph polynomials. For both classes of…

Embeddings of graphs into distributions of trees that preserve distances in expectation are a cornerstone of many optimization algorithms. Unfortunately, online or dynamic algorithms which use these embeddings seem inherently randomized and…

In many applications, linear models fit the data poorly. This article studies an appealing alternative, the generalized regression model. This model only assumes that there exists an unknown monotonically increasing link function connecting…

Symbolic regression (SR) is the problem of learning a symbolic expression from numerical data. Recently, deep neural models trained on procedurally-generated synthetic datasets showed competitive performance compared to more classical…

Symbolic data analysis (SDA) aggregates large individual-level datasets into a small number of distributional summaries, such as random rectangles or random histograms. The inference is carried out using these summaries in place of the…

Decision Trees (DTs) are commonly used for many machine learning tasks due to their high degree of interpretability. However, learning a DT from data is a difficult optimization problem, as it is non-convex and non-differentiable.…

Estimating the structure of directed acyclic graphs (DAGs, also known as Bayesian networks) is a challenging problem since the search space of DAGs is combinatorial and scales superexponentially with the number of nodes. Existing approaches…

The generalized thimble method to treat field theories with sign problems requires repeatedly solving the computationally-expensive holomorphic flow equations. We present a machine learning technique to bypass this problem. The central idea…

In this paper, we extend the dynamical low-rank approximation method to the space of finite signed measures. Under this framework, we derive stochastic low-rank dynamics for stochastic differential equations (SDEs) coming from classical…

The combination of Monte Carlo methods and deep learning has recently led to efficient algorithms for solving partial differential equations (PDEs) in high dimensions. Related learning problems are often stated as variational formulations…

The data arrangement problem on regular trees (DAPT) consists in assigning the vertices of a given graph G to the leaves of a d-regular tree T such that the sum of the pairwise distances of all pairs of leaves in T which correspond to edges…

Adapting a pretrained diffusion model to new objectives at inference time remains an open problem in generative modeling. Existing steering methods suffer from inaccurate value estimation, especially at high noise levels, which biases…

We consider the problem of deterministically factoring a univariate polynomial over a finite field under the assumption of the Extended Riemann Hypothesis (ERH). This work builds upon the line of approach first explored by Gao in $2001$.…

We give an FPTAS and an efficient sampling algorithm for the high-fugacity hard-core model on bounded-degree bipartite expander graphs and the low-temperature ferromagnetic Potts model on bounded-degree expander graphs. The results apply,…

The notions of bounded expansion and nowhere denseness have been applied very successfully in algorithmic graph theory. We study the corresponding notions of directed bounded expansion and nowhere crownfulness on directed graphs. We show…

Sampling-based algorithms solve the path planning problem by generating random samples in the search-space and incrementally growing a connectivity graph or a tree. Conventionally, the sampling strategy used in these algorithms is biased…

We present a general abstract framework for combinatorial Dyson-Schwinger equations, in which combinatorial identities are lifted to explicit bijections of sets, and more generally equivalences of groupoids. Key features of combinatorial…

A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions…