arXiv research

Novel risk matrix for optimal portfolio choice with tail risk considerations.

We study the convergence of a variant of distributed gradient descent (DGD) on a distributed low-rank matrix approximation problem wherein some optimization variables are used for consensus (as in classical DGD) and some optimization variables appear only locally at a single node in the network. We term the resulting a…

The paper studies transformations of Frobenius manifolds and their properties.

Many modern datasets can be represented as graphs and hence spectral decompositions such as graph principal component analysis (PCA) can be useful. Distinct from previous graph decomposition approaches based on subspace projection of a single topological feature, e.g., the Fiedler vector of centered graph adjacency mat…

Many pattern recognition methods rely on statistical information from centered data, with the eigenanalysis of an empirical central moment, such as the covariance matrix in principal component analysis (PCA), as well as partial least squares regression, canonical-correlation analysis and Fisher discriminant analysis. R…

We consider the effects of the 2008 global financial crisis on the global stock market before, during, and after the crisis. We generate complex networks from a cross-correlation matrix such as the threshold network (TN) and the minimal spanning tree (MST). In the threshold network, we assign a threshold value by using…

New framework values football players based on in-game interactions.

Federated multi-view matrix factorization learns from multiple data sources without centralizing user data.

We prove a central limit theorem for the components of the largest eigenvectors of the adjacency matrix of a finite-dimensional random dot product graph whose true latent positions are unknown. In particular, we follow the methodology outlined in \citet{sussman2012universally} to construct consistent estimates for the …

Solved a specific case of Salter's question on Burau representation.

The paper uses RMT to analyze global banking network changes since 2000.

New centrality-based graph shift operators improve graph neural networks.

New model improves DNA methylation data analysis.

Given a central extension of Lie groups, we study the classification problem of lifting the structure group together with a given connection. For reductive structure groups we introduce a new connective structure on the lifting gerbe associated to this problem. Our main result classifies all connections on the central …

Study characterizes training and test risks for MAP regression with Gaussian priors.

Community detection has been one of the central problems in network studies and directed network is particularly challenging due to asymmetry among its links. In this paper, we found that incorporating the direction of links reveals new perspectives on communities regarding to two different roles, source and terminal, …

The paper connects disentanglement to manifold charts and commutativity.

New arithmetic phenomenon 'murmurations' detected using AI.

Counterexamples show Salter's question on Burau image is negative for n=4.

The paper develops statistical inference for gradient flows in optimization.

A hypersurface $M$ in $\mathbb{R}^n$, $n \geq 4$, has central ovaloid property if $M$ intersects some hyperplane transversally along an ovaloid and every such ovaloid on $M$ has central symmetry. We show that a complete, connected, smooth hypersurface with central ovaloid property must either be a cylinder over a centr…

Improves detection of low-rank signals from noisy data matrices.

We analyze the influence and interactions of 60 largest world banks for 195 world countries using the reduced Google matrix algorithm for the English Wikipedia network with 5 416 537 articles. While the top asset rank positions are taken by the banks of China, with China Industrial and Commercial Bank of China at the f…

In many signal processing and machine learning applications, datasets containing private information are held at different locations, requiring the development of distributed privacy-preserving algorithms. Tensor and matrix factorizations are key components of many processing pipelines. In the distributed setting, diff…

Given a limited number of entries from the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, recovery of the low-rank and sparse components is a fundamental task subsuming compressed sensing, matrix completion, and principal components pursuit. This paper devel…

In "The Yang-Mills equations over Riemann surfaces", Atiyah and Bott studied Yang-Mills functional over a Riemann surface from the point of view of Morse theory. We generalize their study to all closed, compact, connected, possibly nonorientable surfaces. We introduce the notion of "super central extension" of the fund…

In this paper we study the tensor powers of the standard representation of the quantum super-algebra $U_q(sl(2|1)$, focusing on the rings of its algebra endomorphisms, called centraliser algebras and denoted by $LG_n$. Their dimensions were conjectured by I. Marin and E. Wagner \cite{MW}. We prove this conjecture, desc…

Study finds central points of double heptagon surface are not connection points.

The paper introduces fixed-point centralities for networks and graphons.

DMF improves POI recommendation privacy and efficiency.

Paper relaxes factor analysis for noisy data, improving robustness.

The paper encloses computation of simple centralizer of simple braids and their connection with Fibonacci numbers. Planarity of some commuting graphs is also discussed in the last section.

Abstract: Connections between Lie algebras and symplectic nilmanifolds explored.

Study on connection points on double regular polygons, providing coordinates and proving non-connection points.

Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size. This paper presents two parallel GP regression methods that exploit low-rank co…

Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size. This paper presents two parallel GP regression methods that exploit low-rank co…

Complex network analysis reveals dominant stocks in financial stock returns correlations.

Matrix Factorization (MF) on large scale matrices is computationally as well as memory intensive task. Alternative convergence techniques are needed when the size of the input matrix is higher than the available memory on a Central Processing Unit (CPU) and Graphical Processing Unit (GPU). While alternating least squar…

A new hybrid Newton algorithm improves convergence in logistic regression.

We prove: If a complete connected smooth surface M in euclidean 3-space has general position, intersects some plane along a clean figure-8 (a loop with total curvature zero) and all compact intersections with planes have central symmetry, then M is a (geometric) cylinder over some central figure-8. On the way, we estab…

The knockoff filter introduced by Barber and Candès 2016 is an elegant framework for controlling the false discovery rate in variable selection. While empirical results indicate that this methodology is not too conservative, there is no conclusive theoretical result on its power. When the predictors are i.i.d. Gaussian…

We study non-abelian differentiable gerbes over stacks using the theory of Lie groupoids. More precisely, we develop the theory of connections on Lie groupoid $G$-extensions, which we call "connections on gerbes", and study the induced connections on various associated bundles. We also prove analogues of the Bianchi id…

Tensor networks improve unsupervised learning performance.

In this paper, we consider the concept of connection cochain of central extensions introduced by Moriyoshi and apply it to the abelian case. We will show the relationship between connection cochain and connection $1$-form of a principal bundle whose structure group is abelian.

Analyzes Berry phases and connection matrices on Siegel-Jacobi spaces.

Let $Σ$ be a closed surface, $G$ a compact Lie group, not necessarily connected, with Lie algebra $g$, endowed with an adjoint action invariant scalar product, let $ξ\colon P \to Σ$ be a principal $G$-bundle, and pick a Riemannian metric and orientation on $Σ$, so that the corresponding Yang-Mills equations $$d_A*K_A =…

We simplify word embeddings by removing sigmoid in SGNS, revealing connections to hyperbolic spaces.

This study analyzes how cryptocurrency networks adapt to financial disruptions.