Related papers: Relative Rank and Regularization
Low-rank approximation is a fundamental technique in modern data analysis, widely utilized across various fields such as signal processing, machine learning, and natural language processing. Despite its ubiquity, the mechanics of low-rank…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
We establish a result which states that regularizing an inverse problem with the gauge of a convex set $C$ yields solutions which are linear combinations of a few extreme points or elements of the extreme rays of $C$. These can be…
Iterative regularization is a classic idea in regularization theory, that has recently become popular in machine learning. On the one hand, it allows to design efficient algorithms controlling at the same time numerical and statistical…
Low-rank representation learning has emerged as a powerful tool for recovering missing values in power load data due to its ability to exploit the inherent low-dimensional structures of spatiotemporal measurements. Among various techniques,…
We consider the space of matrices, with given number of rows and of columns, equipped with the classic trace scalar product. With any matrix (source) norm, we associate a coupling, called Capra, between the space of matrices and itself.…
This paper presents an algorithm, Voted Kernel Regularization , that provides the flexibility of using potentially very complex kernel functions such as predictors based on much higher-degree polynomial kernels, while benefitting from…
We study a family of distance functions on rankings that allow for asymmetric treatments of alternatives and consider the distinct relevance of the top and bottom positions for ordered lists. We provide a full axiomatic characterization of…
Learning approaches have recently become very popular in the field of inverse problems. A large variety of methods has been established in recent years, ranging from bi-level learning to high-dimensional machine learning techniques. Most…
A ranking is an ordered sequence of items, in which an item with higher ranking score is more preferred than the items with lower ranking scores. In many information systems, rankings are widely used to represent the preferences over a set…
Place classification is a fundamental ability that a robot should possess to carry out effective human-robot interactions. It is a nontrivial classification problem which has attracted many research. In recent years, there is a high…
Simple method to improve traditional approaches to name taxa of higher ranks has been proposed. Instead of base name + postfixes (which vary between codes of nomenclature and sometimes not standardized at all), use numerical prefixes, where…
Low rank approximation is a commonly occurring problem in many computer vision and machine learning applications. There are two common ways of optimizing the resulting models. Either the set of matrices with a given rank can be explicitly…
Conditional on the extended Riemann hypothesis, we show that with high probability, the characteristic polynomial of a random symmetric $\{\pm 1\}$-matrix is irreducible. This addresses a question raised by Eberhard in recent work. The main…
Proportionality is an attractive fairness concept that has been applied to a range of problems including the facility location problem, a classic problem in social choice. In our work, we propose a concept called Strong Proportionality,…
We consider the problem of ranking a set of OT constraints in a manner consistent with data. We speed up Tesar and Smolensky's RCD algorithm to be linear on the number of constraints. This finds a ranking so each attested form x_i beats or…
We consider the problem of active coarse ranking, where the goal is to sort items according to their means into clusters of pre-specified sizes, by adaptively sampling from their reward distributions. This setting is useful in many social…
As an extension of the classical irreducibility result of Dumas, a factorization result for polynomials over any valued field with a Krull valuation of arbitrary rank is proved. Further, a lower degree factor bound on factors of a given…
We report an ongoing work on clustering algorithms for complex roots of a univariate polynomial $p$ of degree $d$ with real or complex coefficients. As in their previous best subdivision algorithms our root-finders are robust even for…
Low rank matrix factorization is a fundamental building block in machine learning, used for instance to summarize gene expression profile data or word-document counts. To be robust to outliers and differences in scale across features, a…