Related papers: Factorization and subtraction
In the age of big data and interpretable machine learning, approaches need to work at scale and at the same time allow for a clear mathematical understanding of the method's inner workings. While there exist inherently interpretable…
We discuss modern ideas in Monte Carlo algorithms in the simplified setting of the one-dimensional anharmonic oscillator. After reviewing the connection between molecular dynamics and Monte Carlo, we introduce to the Metropolis and the…
Zero-bin subtractions are required to avoid double counting soft contributions in collinear loop integrals in Soft-Collinear Effective Theory (SCET). In traditional approaches to factorization, double counting is avoided by dividing jet…
The remarkable properties of the real scalar quartic quantum field theory on the Moyal plane in combination with its similarity to the Kontsevich model make the model's partition function an interesting object to study. However, direct…
We consider algorithms for the factorization of linear partial differential operators. We introduce several new theoretical notions in order to simplify such considerations. We define an obstacle and a ring of obstacles to factorizations.…
Factor Analysis is an effective way of dimensionality reduction achieved by revealing the low-rank plus sparse structure of the data covariance matrix. The corresponding model identification task is often formulated as an optimization…
The problem of decomposing a given covariance matrix as the sum of a positive semi-definite matrix of given rank and a positive semi-definite diagonal matrix, is considered. We present a projection-type algorithm to address this problem.…
The connection between Superstring theory and the low--energy world is analyzed. In particular, the soft Supersymmetry--breaking terms arising in Supergravity theories coming from Superstrings are computed. Several solutions proposed to…
This paper presents an adaptive randomized algorithm for computing the butterfly factorization of a $m\times n$ matrix with $m\approx n$ provided that both the matrix and its transpose can be rapidly applied to arbitrary vectors. The…
The model described in this paper belongs to the family of non-negative matrix factorization methods designed for data representation and dimension reduction. In addition to preserving the data positivity property, it aims also to preserve…
In this work, we analyze a sublinear-time algorithm for selecting a few rows and columns of a matrix for low-rank approximation purposes. The algorithm is based on an initial uniformly random selection of rows and columns, followed by a…
Matrix factorization is a popular approach for large-scale matrix completion. The optimization formulation based on matrix factorization can be solved very efficiently by standard algorithms in practice. However, due to the non-convexity…
Matrix factorization techniques have been widely used as a method for collaborative filtering for recommender systems. In recent times, different variants of deep learning algorithms have been explored in this setting to improve the task of…
In this proceeding we consider QCD radiative corrections to the production of colourless high-mass systems in hadron collisions. At small transverse momentum the logarithmically-enhanced contributions can be organized to all perturbative…
We investigate factorisation at small x using a variety of analytical and numerical techniques. Previous results on factorisation in collinear models are generalised to the case of the full BFKL equation, and illustrated in the example of a…
The factorisation of the hard amplitude for exclusive meson production in deep inelastic scattering is considered in the framework of a simple model. It is demonstrated explicitly how gauge invariance ensures the cancellation of…
Existing nonnegative matrix factorization methods focus on learning global structure of the data to construct basis and coefficient matrices, which ignores the local structure that commonly exists among data. In this paper, we propose a new…
We show that factorization holds for the deeply virtual Compton scattering amplitude in QCD, up to power suppressed terms, to all orders in perturbation theory. Furthermore, we show that the virtuality of the produced photon does not…
Non-negative matrix factorization (NMF) is one of the most popular decomposition techniques for multivariate data. NMF is a core method for many machine-learning related computational problems, such as data compression, feature extraction,…
We revisit the extrapolate dictionary for massless scattering in flat spacetime and identify a soft contribution that is typically dropped from the saddle point approximation. We show how to consistently regulate the extrapolation to…