Related papers: Generalized Persistence Algorithm for Decomposing …
This work presents generalized low-rank signal decompositions with the aid of switching techniques and adaptive algorithms, which do not require eigen-decompositions, for space-time adaptive processing. A generalized scheme is proposed to…
A general class of polynomial remainder codes is considered. Such codes are very flexible in rate and length and include Reed-Solomon codes as a special case. As an extension of previous work, two joint error-and-erasure decoding approaches…
We present an algorithm for marginalising changepoints in time-series models that assume a fixed number of unknown changepoints. Our algorithm is differentiable with respect to its inputs, which are the values of latent random variables…
We define two notions. The first one is a $rank\ compression\ system$ $\xi$ for a finite poset $\mathbf{P}$ that assigns each interval subposet $I$ to an order-preserving map $\xi_I \colon I^{\xi} \to \mathbf{P}$ satisfying some conditions,…
We develop fast spectral algorithms for tensor decomposition that match the robustness guarantees of the best known polynomial-time algorithms for this problem based on the sum-of-squares (SOS) semidefinite programming hierarchy. Our…
By general case we mean methods able to process simplicial sets and chain complexes not of finite type. A filtration of the object to be studied is the heart of both subjects persistent homology and spectral sequences. In this paper we…
We describe a space-efficient algorithm for solving a generalization of the subset sum problem in a finite group G, using a Pollard-rho approach. Given an element z and a sequence of elements S, our algorithm attempts to find a subsequence…
Motivated by a connection with the factorization of multivariate polynomials, we study integral convex polytopes and their integral decompositions in the sense of the Minkowski sum. We first show that deciding decomposability of integral…
Most of machine learning deals with vector parameters. Ideally we would like to take higher order information into account and make use of matrix or even tensor parameters. However the resulting algorithms are usually inefficient. Here we…
Optimization, a key tool in machine learning and statistics, relies on regularization to reduce overfitting. Traditional regularization methods control a norm of the solution to ensure its smoothness. Recently, topological methods have…
Primary decomposition is a very important tool of commutative algebra and geometry. In this paper we generalized some of the existing algorithms of primary decomposition developed by Eisenbud et al. (cf. [EHV]) for free modules and also…
This paper focuses on minimizing a smooth function combined with a nonsmooth regularization term on a compact Riemannian submanifold embedded in the Euclidean space under a decentralized setting. Typically, there are two types of approaches…
We propose a functorial framework for persistent homology based on finite topological spaces and their associated posets. Starting from a finite metric space, we associate a filtration of finite topologies whose structure maps are…
Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization, $\ell_1$ norm regularized optimization, and $\ell_0$ norm regularized…
We study a catching-up algorithm for a class of differential inclusions driven by maximal monotone operators with continuous perturbations. Using a decomposition of the monotone operator into the closed convex hull of its single-valued part…
In this paper we investigate the intrinsic sequential time complexity of universal elimination procedures for arbitrary continuous data structures encoding input and output objects of elimination theory (i.e. polynomial equation systems)…
We introduce a new algorithm for numerical composition of privacy random variables, useful for computing the accurate differential privacy parameters for composition of mechanisms. Our algorithm achieves a running time and memory usage of…
Persistent homology is a fundamental tool in topological data analysis; however, it lacks methods to quantify the fragility or fineness of cycles, anticipate their formation or disappearance, or evaluate their stability beyond persistence.…
In this paper we present a new approach to computing homology (with field coefficients) and persistent homology. We use concepts from discrete Morse theory, to provide an algorithm which can be expressed solely in terms of simple graph…
Recent work has shown that memory modules are crucial for the generalization ability of neural networks on learning simple algorithms. However, we still have little understanding of the working mechanism of memory modules. To alleviate this…