Related papers: A Geometric Form for the Extended Patience Sorting…
Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little…
A hypergraph is a generalization of a graph, in which a hyperedge can connect multiple vertices, modeling complex relationships involving multiple vertices simultaneously. Hypergraph pattern matching, which is to find all isomorphic…
We introduce randomized algorithms to Clifford's Geometric Algebra, generalizing randomized linear algebra to hypercomplex vector spaces. This novel approach has many implications in machine learning, including training neural networks to…
We present a stochastic descent algorithm for unconstrained optimization that is particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained optimization and…
In this paper, we propose a useful replacement for quicksort-style utility functions. The replacement is called Symmetry Partition Sort, which has essentially the same principle as Proportion Extend Sort. The maximal difference between them…
There is a growing demand for performing larger-scale Bayesian inference tasks, arising from greater data availability and higher-dimensional model parameter spaces. In this work we present parallelization strategies for the methodology of…
We introduce the use of hierarchical clustering for relaxed, deterministic coordination and control of multiple robots. Traditionally an unsupervised learning method, hierarchical clustering offers a formalism for identifying and…
This is the first paper in a series on intrinsic Donaldson-Thomas theory, where we develop a new framework for enumerative geometry that allows the generalization of constructions and results from linear moduli stacks to general non-linear…
Mix-up training approaches have proven to be effective in improving the generalization ability of Deep Neural Networks. Over the years, the research community expands mix-up methods into two directions, with extensive efforts to improve…
We propose a new approach to conjugation-invariant random permutations. Namely, we explain how to construct uniform permutations in given conjugacy classes from certain point processes in the plane. This enables the use of geometric tools…
The success of machine learning methods heavily relies on having an appropriate representation for data at hand. Traditionally, machine learning approaches relied on user-defined heuristics to extract features encoding structural…
We initiate the study of subpolytopes of the permutahedron that arise as the convex hulls of stack-sorting on permutations. We primarily focus on $Ln1$ permutations, i.e., permutations of length $n$ whose penultimate and last entries are…
We develop a novel, fundamental and surprisingly simple randomized iterative method for solving consistent linear systems. Our method has six different but equivalent interpretations: sketch-and-project, constrain-and-approximate, random…
Differentiable sorting algorithms allow training with sorting and ranking supervision, where only the ordering or ranking of samples is known. Various methods have been proposed to address this challenge, ranging from optimal…
Combinatorial aspects of multivariate diagonal invariants of the symmetric group are studied. As a consequence it is proved the existence of a multivariate extension of the classical Robinson-Schensted correspondence. Further byproduct are…
Commonly-used clustering algorithms usually find ellipsoidal, spherical or other regular-structured clusters, but are more challenged when the underlying groups lack formal structure or definition. Syncytial clustering is the name that we…
In this paper, we propose a stochastic search algorithm for solving general optimization problems with little structure. The algorithm iteratively finds high quality solutions by randomly sampling candidate solutions from a parameterized…
Mixtures of Gaussian (or normal) distributions arise in a variety of application areas. Many heuristics have been proposed for the task of finding the component Gaussians given samples from the mixture, such as the EM algorithm, a…
We consider the problem of learning a Gaussian graphical model in the case where the observations come from two dependent groups sharing the same variables. We focus on a family of coloured Gaussian graphical models specifically suited for…
Sorting has been one of the most challenging studied problems in different scientific researches. Although many techniques and algorithms have been proposed on the theory of having efficient parallel sorting implementation, however…