Related papers: Completing correlation matrices
This contribution to the proceedings of the Cracow meeting on `Applications of Random Matrix Theory' summarizes a series of studies, some old and others more recent on financial applications of Random Matrix Theory (RMT). We first review…
Vertex clustering in a stochastic blockmodel graph has wide applicability and has been the subject of extensive research. In thispaper, we provide a short proof that the adjacency spectral embedding can be used to obtain perfect clustering…
We consider estimation of the covariance matrix of a multivariate random vector under the constraint that certain covariances are zero. We first present an algorithm, which we call Iterative Conditional Fitting, for computing the maximum…
In the paper we first construct a new cotorsion pair, in the category of chain complexes, from two given cotorsion pairs in the category of modules, and then we consider completeness of such pairs under certain conditions.
Correlation matrices are omnipresent in multivariate data analysis. When the number d of variables is large, the sample estimates of correlation matrices are typically noisy and conceal underlying dependence patterns. We consider the case…
Tensor completion is a problem of filling the missing or unobserved entries of partially observed tensors. Due to the multidimensional character of tensors in describing complex datasets, tensor completion algorithms and their applications…
We enumerate the connected graphs that contain a number of edges growing linearly with respect to the number of vertices. So far, only the first term of the asymptotics and a bound on the error were known. Using analytic combinatorics, ie…
The nature of monetary arrangements is often discussed without any reference to its detailed construction. We present a graph representation that allows for a clear understanding of modern monetary systems. First, we show that systems based…
Constraint Programming (CP) has proved an effective paradigm to model and solve difficult combinatorial satisfaction and optimisation problems from disparate domains. Many such problems arising from the commercial world are permeated by…
In this thesis, we analyze the stochastic completeness of a heat kernel on graphs which is a function of three variables: a pair of vertices and a continuous time, for infinite, locally finite, connected graphs. For general graphs, a…
A method of modeling data with gaps by a sequence of curves has been developed. The new method is a generalization of iterative construction of singular expansion of matrices with gaps. Under discussion are three versions of the method…
Detecting the components common or correlated across multiple data sets is challenging due to a large number of possible correlation structures among the components. Even more challenging is to determine the precise structure of these…
We discuss some methods to quantitatively investigate the properties of correlation matrices. Correlation matrices play an important role in portfolio optimization and in several other quantitative descriptions of asset price dynamics in…
Code completion is widely used by software developers to provide coding suggestions given a partially written code snippet. Apart from the traditional code completion methods, which only support single token completion at minimal positions,…
Given a bipartite graph that has a perfect matching, a prefect proportional allocation is an assignment of positive weights to the nodes of the right partition so that every left node is fractionally assigned to its neighbors in proportion…
Growth-optimal portfolios are guaranteed to accumulate higher wealth than any other investment strategy in the long run. However, they tend to be risky in the short term. For serially uncorrelated markets, similar portfolios with more…
We offer a method to estimate a covariance matrix in the special case that \textit{both} the covariance matrix and the precision matrix are sparse --- a constraint we call double sparsity. The estimation method is maximum likelihood,…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
This note proposes a new method to complete a triangulated category, which is based on the notion of a Cauchy sequence. We apply this to categories of perfect complexes. It is shown that the bounded derived category of finitely presented…
The present work builds on previous investigations of the authors (and their collaborators) regarding bridges, a certain type of morphisms between encryption schemes, making a step forward in developing a (category theory) language for…