Related papers: Iterative Scaling Algorithm for Channels
Probabilistic ideas and tools have recently begun to permeate into several fields where they had traditionally not played a major role, including fields such as numerical linear algebra and optimization. One of the key ways in which these…
Clustering is often used for discovering structure in data. Clustering systems differ in the objective function used to evaluate clustering quality and the control strategy used to search the space of clusterings. Ideally, the search…
In the context of next generation radio telescopes, like the Square Kilometre Array, the efficient processing of large-scale datasets is extremely important. Convex optimisation tasks under the compressive sensing framework have recently…
In this paper, we argue that iterative computation with diffusion models offers a powerful paradigm for not only generation but also visual perception tasks. We unify tasks such as depth estimation, optical flow, and amodal segmentation…
Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination,…
We propose and study a multi-scale approach to vector quantization. We develop an algorithm, dubbed reconstruction trees, inspired by decision trees. Here the objective is parsimonious reconstruction of unsupervised data, rather than…
Dimensionality reduction (DR) on the manifold includes effective methods which project the data from an implicit relational space onto a vectorial space. Regardless of the achievements in this area, these algorithms suffer from the lack of…
Most machine learning algorithms, such as classification or regression, treat the individual data point as the object of interest. Here we consider extending machine learning algorithms to operate on groups of data points. We suggest…
The impressive practical performance of neural networks is often attributed to their ability to learn low-dimensional data representations and hierarchical structure directly from data. In this work, we argue that these two phenomena are…
Common clustering algorithms require multiple scans of all the data to achieve convergence, and this is prohibitive when large databases, with data arriving in streams, must be processed. Some algorithms to extend the popular K-means method…
Clustering samples according to an effective metric and/or vector space representation is a challenging unsupervised learning task with a wide spectrum of applications. Among several clustering algorithms, k-means and its kernelized version…
This paper describes a new QR factorization algorithm which is especially designed for massively parallel platforms combining parallel distributed multi-core nodes. These platforms make the present and the foreseeable future of…
This paper presents an approach for side channel cryptanalysis with iterative approximate Bayesian inference, based on sequential decoding methods. Reliability information about subkey hypotheses is generated in the form of likelihoods, and…
The deletion channel is the simplest point-to-point communication channel that models lack of synchronization. Despite significant effort, little is known about its capacity, and even less about optimal coding schemes. In this paper we…
We consider the problem of constructing quantum operations or channels, if they exist, that transform a given set of quantum states $\{\rho_1, \dots, \rho_k\}$ to another such set $\{\hat\rho_1, \dots, \hat\rho_k\}$. In other words, we must…
The adaptive multi-channel method is applied to derive probability distributions from data samples. Moreover, an explicit algorithm is introduced, for which both the channel weights and the channels themselves are adaptive, and which can be…
We derive an analytical calculation formula for the channel capacity of a classical channel without any iteration while its existing algorithms require iterations and the number of iteration depends on the required precision level. Hence,…
We propose a new method with $\mathcal{L}_2$ distance that maps one $N$-dimensional distribution to another, taking into account available information about correspondences. We solve the high-dimensional problem in 1D space using an…
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…
For linear systems $Ax=b$ we develop iterative algorithms based on a sketch-and-project approach. By using judicious choices for the sketch, such as the history of residuals, we develop weighting strategies that enable short recursive…