Related papers: Sum-of-Squares Polynomial Flow
Bayesian posterior inference is prevalent in various machine learning problems. Variational inference provides one way to approximate the posterior distribution, however its expressive power is limited and so is the accuracy of resulting…
This work introduces a novel nonparametric density index defined on graphs, the Sum-over-Forests (SoF) density index. It is based on a clear and intuitive idea: high-density regions in a graph are characterized by the fact that they contain…
Random feature maps are ubiquitous in modern statistical machine learning, where they generalize random projections by means of powerful, yet often difficult to analyze nonlinear operators. In this paper, we leverage the "concentration"…
We investigate here sums of triangular numbers $f(x):=\sum_i b_i T_{x_i}$ where $T_n$ is the $n$-th triangular number. We show that for a set of positive integers $S$ there is a finite subset $S_0$ such that $f$ represents $S$ if and only…
We explicitly describe the possible pairs of triangle and square densities for r-regular finite simple graphs. We also prove that every r-regular unimodular random graph can be approximated by r-regular finite graphs with respect to these…
By assuming some widely-believed arithmetic conjectures, we show that the task of accepting a number that is representable as a sum of $d\geq2$ squares subjected to given congruence conditions is NP-complete. On the other hand, we develop…
We present a generative learning framework for probabilistic sampling based on an extension of the Probabilistic Learning on Manifolds (PLoM) approach, which is designed to generate statistically consistent realizations of a random vector…
The trinomial transform of a sequence is a generalization of the well-known binomial transform, replacing binomial coefficients with trinomial coefficients. We examine Pascal-like triangles under trinomial transform, focusing on the ternary…
Chaotic dynamical systems such as turbulent flows are characterized by an exponential divergence of infinitesimal perturbations to initial conditions. Therefore, conventional adjoint/tangent sensitivity analysis methods that are successful…
Score-based generative models, which transform noise into data by learning to reverse a diffusion process, have become a cornerstone of modern generative AI. This paper contributes to establishing theoretical guarantees for the probability…
Optimizing over the cone of nonnegative polynomials, and its dual counterpart, optimizing over the space of moments that admit a representing measure, are fundamental problems that appear in many different applications from engineering and…
The Sum-of-Squares (SoS) hierarchy is a semi-definite programming meta-algorithm that captures state-of-the-art polynomial time guarantees for many optimization problems such as Max-$k$-CSPs and Tensor PCA. On the flip side, a SoS lower…
This paper introduces a new probabilistic architecture called Sum-Product Graphical Model (SPGM). SPGMs combine traits from Sum-Product Networks (SPNs) and Graphical Models (GMs): Like SPNs, SPGMs always enable tractable inference using a…
Gaussian splatting has recently gained traction as a compelling map representation for SLAM systems, enabling dense and photo-realistic scene modeling. However, its application to monocular SLAM remains challenging due to the lack of…
Optical flow, semantic segmentation, and surface normals represent different information modalities, yet together they bring better cues for scene understanding problems. In this paper, we study the influence between the three modalities:…
In this paper, we propose Continuous Graph Flow, a generative continuous flow based method that aims to model complex distributions of graph-structured data. Once learned, the model can be applied to an arbitrary graph, defining a…
This study enhances a crowd density estimation algorithm originally designed for image-based analysis by adapting it for video-based scenarios. The proposed method integrates a denoising probabilistic model that utilizes diffusion processes…
1) We introduce random discrete Morse theory as a computational scheme to measure the complicatedness of a triangulation. The idea is to try to quantify the frequence of discrete Morse matchings with a certain number of critical cells. Our…
A normalizing flow models a complex probability density as an invertible transformation of a simple base density. Flows based on either coupling or autoregressive transforms both offer exact density evaluation and sampling, but rely on the…
We develop numerical multiscale methods for viscous boundary layer flow. The goal is to derive effective boundary conditions, or wall laws, through high resolution simulations localized to the boundary coupled to a coarser simulation in the…