Study forecasts volatility and risk in electricity markets using matrix-HAR models.
problem Forecasting volatility and risk in electricity markets.
method Constructed a parsimonious matrix-HAR type model to estimate realized covariation and risk premia in electricity markets.
result Inclusion of longer time horizons and renewable generation information improves forecasts.
Paper proposes a deep learning method for better covariance matrix forecasting.
problem Suboptimal predictive performance in traditional matrix volatility forecasting.
method Riemannian-geometry-aware deep learning framework for symmetric positive definite matrices.
result Our method outperforms traditional approaches in predictive accuracy.
This paper develops copula-based models for forecasting multivariate realized volatility.
problem Forecasting multivariate realized volatility matrices with hidden dependence structure.
method Copula-based time series models to capture hidden dependence structure and ensure positive definiteness.
result Copula-based models achieve significant performance in volatility matrix forecasting.
Improved covariance matrix forecasting for S&P 500 using factor models and shrinkage.
problem Forecasting large covariance matrices of returns in finance.
method Decompose covariance matrix into firm-level factors and sectoral restrictions. Estimate using VHAR models with LASSO.
result Significantly improved forecasting precision compared to benchmarks.
Paper shows how a Lie superalgebra can be realized using matrices.
problem Realizing the Lie superalgebra of contact projective vector fields.
method Using embedding techniques from projectively equivariant quantizations, the paper constructs a matrix realization.
result The Lie superalgebra spo(2l+2∣n) is realized as the intersection of pgl(2l+2∣n) and K(2l+1∣n). Study improves Hayashi-Yoshida estimator for high-dimensional stock covolatility.
problem Inconsistent performance of Hayashi-Yoshida estimator in high dimensions.
method Analyzed the limiting spectral distribution of the Hayashi-Yoshida estimator.
result Established the connection between the estimator's spectrum and the true covariance matrix in high dimensions.
The affine Grassmannian is realized as a matrix manifold for optimization.
problem Optimization on noncompact manifolds like the affine Grassmannian.
method Riemannian optimization algorithms extended to the affine Grassmannian.
result Standard numerical linear algebra suffices for optimization on the affine Grassmannian.
Recently Kearton showed that any Seifert matrix of a knot is S--equivalent to the Seifert matrix of a prime knot. We show in this note that such a matrix is in fact S--equivalent to the Seifert matrix of a hyperbolic knot. This result follows from reinterpreting this problem in terms of Blanchfield pairings and by appl…
The paper introduces a dynamic MVP model using high-frequency financial data.
problem Capturing the dynamics of minimum variance portfolio weights in financial markets.
method Imposes autoregressive structure on MVP processes and uses CLIME and LASSO for estimation.
result Proposes DR-MVP model with established asymptotic properties.
Paper solves the realizability of Gauss diagrams and constructs meanders.
problem Realizing Gauss diagrams as plane curves.
method Direct approach using conditions based on exits, entrances, and Jordan curve theorem.
result Conditions for realizability of Gauss diagrams and an algorithm to construct meanders.
Proposes a Structural Matrix Autoregressive model for joint analysis of asset returns, realized volatility, and trading volume.
problem Joint analysis of asset returns, realized volatility, and trading volume
method Structural Matrix Autoregressive model
result Volatility is primary driver of trading activity, with informational shocks incorporated through price variability.
Reformulates RBF networks for graph-based data.
problem Applying RBF networks to graph data.
method Reformulate RBF networks for adjacency matrices, derive gradient updates.
result Guaranteed same responses as vector-based RBF networks.
The paper establishes a minimal state-space realization for VAR models using Kalman's theorem.
problem Finding a minimal state-space realization for Vector Autoregressive Models (VARX).
method Introducing AR-state-space realization and applying Kalman's theorem to VAR models.
result Each VARX model has a minimal AR-state-space realization with specific matrix properties.
A parameterization that is a modified version of a previous work is proposed for the returns and correlation matrix of financial time series and its properties are studied. This parameterization allows easy introduction of non-stationarity and it shows several of the characteristics of the true, observed realizations, …
The study explores how Matrix Product States can represent boolean and continuous functions.
problem Representing arbitrary boolean and continuous functions using Matrix Product States.
method Developed a construction method for MPS to represent boolean gates and proved density in continuous function space.
result MPS can accurately represent arbitrary boolean functions and continuous functions densely.
The use of improved covariance matrix estimators as an alternative to the sample estimator is considered an important approach for enhancing portfolio optimization. Here we empirically compare the performance of 9 improved covariance estimation procedures by using daily returns of 90 highly capitalized US stocks for th…
Innovates rotation index for matrix pairs, solving group action problems.
problem Solving group actions problems, especially Nielsen realization and higher-rank Anosov actions.
method Rotation index and Milnor--Munkres--Novikov pairing applied to Z2 group actions. result Solved specific group action problems using new matrix pair invariant.
Paper speeds up GP inference by reducing precision matrix computation.
problem High computational complexity in computing kernel precision matrices.
method Splitting precision matrix into Hankel-Toeplitz matrices and computing only unique entries.
result Precision matrix computation reduced from O(NM2) to O(NM). Starting from the free field realization of Kac-Moody Lie algebra, we define a generalized Yang-Yang function. Then for the Lie algebra of type An, we derive braiding and fusion matrix by braiding the thimble from the generalized Yang-Yang function. One can construct a knots invariant H(K) from the braiding and …
Faster matrix completion through randomized SVD algorithms.
problem Efficiently completing large sparse matrices for applications like image inpainting and recommender systems.
method Proposed two fast randomized algorithms (rSVD-PI and rSVD-BKI) and a new subspace recycling technique to accelerate singular value thresholding (SVT) method.
result The proposed algorithms achieve up to 15X faster computation time for image inpainting and movie rating estimation problems.
We consider the problem of the statistical uncertainty of the correlation matrix in the optimization of a financial portfolio. We show that the use of clustering algorithms can improve the reliability of the portfolio in terms of the ratio between predicted and realized risk. Bootstrap analysis indicates that this impr…
Method cleans covariance matrices for better statistical inference.
problem Reducing estimation noise in covariance matrices for better statistical inference.
method Robust yet flexible hierarchical ansatz with bootstrap procedure.
result Lower realized risk in global minimum variance portfolios.
Predict missing movie ratings or graph embeddings with low rank matrices.
problem Predicting missing entries in a ratings matrix or graph embeddings with known linear relations.
method Low rank matrix completion approach applied to graph embeddings.
result Effective methods for predicting missing entries in matrices and graph embeddings.
SDP approach recovers communities in multilayer hypergraphs from aggregated similarity matrices.
problem Community recovery in multilayer hypergraphs using aggregated similarity matrices.
method Semidefinite programming (SDP) approach.
result Information-theoretic conditions for exact recovery in both assortative and disassortative cases.
Study Brownian motion on Grassmann manifold using matrix stochastic calculus.
problem Understanding Brownian motion on non-compact Grassmann manifold.
method Realize Brownian motion as matrix diffusion process, use matrix stochastic calculus, and hyperbolic Stiefel fibration.
result Connection to generalized Maass Laplacian of complex hyperbolic space.
The truncated singular value decomposition (SVD) of the measurement matrix is the optimal solution to the_representation_ problem of how to best approximate a noisy measurement matrix using a low-rank matrix. Here, we consider the (unobservable)_denoising_ problem of how to best approximate a low-rank signal matrix bur…
Basket links are shown to be isotopic to T(2,n+1).
problem Understanding isotopy of basket links to torus links.
method Using symmetrized Seifert form congruence to An matrix. result Basket links are isotopic to T(2,n+1). Researchers use statistical methods to infer transmission matrices in complex media.
problem Comprehending and exploiting photon scattering through disordered media.
method Pseudolikelihood decimation to learn the coupling matrix via random sampling.
result Transmission matrices can be inferred and used like normal optical elements.
Exploring how noise and curvature affect optimization and generalization.
problem The interaction between noise and curvature in optimization and generalization.
method Analyzing the speed of minimizing expected loss with stochastic methods, distinguishing between Fisher, Hessian, and gradient covariance matrices.
result Clarifying the role of curvature and noise in estimating the generalization gap.
Calculates Gordian distances using algebraic methods.
problem Determining when Alexander polynomials can't be realized by matrices with Gordian distance one.
method Using Blanchfield pairings and quadratic equations with integer solutions.
result Shows that certain Alexander polynomials cannot be realized by matrices with Gordian distance one.
Compressed sensing (CS) shows that a signal having a sparse or compressible representation can be recovered from a small set of linear measurements. In classical CS theory, the sampling matrix and representation matrix are assumed to be known exactly in advance. However, uncertainties exist due to sampling distortion, …
Large deviations for fat tailed distributions, i.e. those that decay slower than exponential, are not only relatively likely, but they also occur in a rather peculiar way where a finite fraction of the whole sample deviation is concentrated on a single variable. The regime of large deviations is separated from the regi…
Curious structure of special orthogonal, unitary, and symplectic groups as products of Grassmannians discovered.
problem Understanding the structure of special orthogonal, unitary, and symplectic groups.
method Expressing these groups as products of Grassmannians realized as involution matrices.
result Special orthogonal, special unitary, and symplectic groups can be expressed as products of their corresponding Grassmannians.
We study the design of portfolios under a minimum risk criterion. The performance of the optimized portfolio relies on the accuracy of the estimated covariance matrix of the portfolio asset returns. For large portfolios, the number of available market returns is often of similar order to the number of assets, so that t…
We consider the estimation of integrated covariance (ICV) matrices of high dimensional diffusion processes based on high frequency observations. We start by studying the most commonly used estimator, the realized covariance (RCV) matrix. We show that in the high dimensional case when the dimension p and the observati…
Infinitesimal holomorphic realizations for the Schrödinger-Weil representation and the discrete series representations of the Jacobi group are constructed. Explicit expressions of the basic differential operators are obtained. The squeezed states for the unitary irreducible representation of the Jacobi group are introd…
New model reduces matrix factorization bias, yielding truly low-rank solutions.
problem Gradient descent's implicit bias in matrix factorization.
method Introducing a new factorization model with constrained factors and diagonal components.
result The new model consistently exhibits a strong implicit bias, yielding truly low-rank solutions.
This paper improves sample efficiency in noisy inductive matrix completion with side-information.
problem Improving sample efficiency in noisy inductive matrix completion with side-information.
method Nonconvex projected gradient descent algorithm with spectral initialization.
result Achieves linear convergence and stable recovery at a sample complexity governed by the effective side-information dimension.
PL-NMF improves parallel NMF by optimizing data locality.
problem Data movement costs dominate in parallel NMF applications.
method Developed a parallel NMF algorithm based on HALS with data locality optimizations.
result Significant performance improvement over existing parallel NMF algorithms.
Study connects curvature to graph theory and reveals differences.
problem Exploring differences between Quadratic Orthogonal Bisectional Curvature and Real Bisectional Curvature.
method Real (1,1)--forms and Weitzenböck curvature operator used to represent graph Dirichlet energy.
result Curvature differences illuminated between Quadratic Orthogonal Bisectional Curvature and Real Bisectional Curvature.
In the first quarter of 2006 Chicago Board Options Exchange (CBOE) introduced, as one of the listed products, options on its implied volatility index (VIX). This created the challenge of developing a pricing framework that can simultaneously handle European options, forward-starts, options on the realized variance and …
Paper uses Random Matrix Theory for optimal training-testing data split.
problem Finding ideal training-testing data split for linear regression.
method Random Matrix Theory applied to Gaussian multivariate data.
result Ideal training and test sizes derived for any model.
Quantum-inspired model generates samples from data efficiently.
problem Unsupervised generative modeling from data.
method Matrix product states for efficient learning and direct sampling.
result Efficient direct sampling approach for generative tasks.
An algorithm finds a compact Hankel submatrix for spectral learning.
problem Efficiently computing SVD for large Hankel matrices in spectral learning.
method Maximal bipartite matching algorithm to select rows and columns of Hankel matrix.
result Compact Hankel submatrix with full structural rank.
Explicit matrix presentations of Blanchfield pairings and twisted pairings for torus knots.
problem Computing explicit matrix presentations of Blanchfield and twisted Blanchfield pairings for torus knots.
method Using a taut identity to construct a chain complex with few generators, and describing the twisted Alexander module.
result Explicit matrix presentations of the Blanchfield pairing and twisted pairings for (m,n)-torus knots. Study confirms sparse coding in whole brain using MRI data.
problem Sparse coding in the whole brain's neural activities.
method Applied various matrix factorization methods to fMRI data.
result Sparse coding hypothesis in information representation in the whole human brain is confirmed.
We analyze a class of estimators based on convex relaxation for solving high-dimensional matrix decomposition problems. The observations are noisy realizations of a linear transformation X of the sum of an approximately) low rank matrix Θ⋆ with a second matrix Γ⋆ endowed with a complementary …
Study active learning for multi-level user preferences in recommendation systems.
problem Efficiently learning user preferences through active querying in recommendation systems.
method Proposes a theoretically optimal active learning strategy based on Fisher information matrix for collective matrix factorization.
result Demonstrates strong improvements over active learning methods in personalized, cold-start, and noisy data settings.