A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Paper explores Elliptical Wishart distributions in signal processing and machine learning.
Improved variational approximation for deep Wishart process models.
Study proposes a new model for joint survival annuity valuation.
New method uses KL-divergence to create non-informative priors for multivariate Gaussian.
A method for converting NIW parameters for better estimation.
We show that the only parameter prior for complete Gaussian DAG models that satisfies global parameter independence, complete model equivalence, and some weak regularity assumptions, is the normal-Wishart distribution. Our analysis is based on the following new characterization of the Wishart distribution: let W be an …
New distribution simplifies covariance matrix inference.
A new method for deep Wishart processes improves kernel-based models.
Develops methods for constructing parameter priors in DAG models.
This work deals with the simulation of Wishart processes and affine diffusions on positive semidefinite matrices. To do so, we focus on the splitting of the infinitesimal generator, in order to use composition techniques as Ninomiya and Victoir or Alfonsi. Doing so, we have found a remarkable splitting for Wishart proc…
The scaled complex Wishart distribution is a widely used model for multilook full polarimetric SAR data whose adequacy has been attested in the literature. Classification, segmentation, and image analysis techniques which depend on this model have been devised, and many of them employ some type of dissimilarity measure…
WISDoM (Wishart Distributed Matrices) is a new framework for the quantification of deviation of symmetric positive-definite matrices associated to experimental samples, like covariance or correlation matrices, from expected ones governed by the Wishart distribution WISDoM can be applied to tasks of supervised learning,…
A Bayesian procedure is developed for multivariate stochastic volatility, using state space models. An autoregressive model for the log-returns is employed. We generalize the inverted Wishart distribution to allow for different correlation structure between the observation and state innovation vectors and we extend the…
Deep kernel processes unify various models using Gram matrices and kernel functions.
Researchers develop a new SMC sampler for Wishart processes to improve dynamic covariance inference.
Study on eigenvalue distribution of correlated time series, showing deformation of Marchenko-Pastur distribution.
We propose a new input perturbation mechanism for publishing a covariance matrix to achieve -differential privacy. Our mechanism uses a Wishart distribution to generate matrix noise. In particular, We apply this mechanism to principal component analysis. Our mechanism is able to keep the positive semi-definitene…
We implement gradient-based variational inference routines for Wishart and inverse Wishart processes, which we apply as Bayesian models for the dynamic, heteroskedastic covariance matrix of a multivariate time series. The Wishart and inverse Wishart processes are constructed from i.i.d. Gaussian processes, existing var…
This paper revisits the Bayesian CMA-ES and provides updates for normal Wishart. It emphasizes the difference between a normal and normal inverse Wishart prior. After some computation, we prove that the only difference relies surprisingly in the expected covariance. We prove that the expected covariance should be lower…
This paper introduces a novel theoretically sound approach for the celebrated CMA-ES algorithm. Assuming the parameters of the multi variate normal distribution for the minimum follow a conjugate prior distribution, we derive their optimal update at each iteration step. Not only provides this Bayesian framework a justi…
We investigate the computational complexity of several basic linear algebra primitives, including largest eigenvector computation and linear regression, in the computational model that allows access to the data via a matrix-vector product oracle. We show that for polynomial accuracy, calls to the oracle are nece…
Bayesian framework for analyzing heterogeneous covariance data with a novel MoE-Wishart model.
New framework for calculating multivariate risk measures using Wishart process.
Regression Prior Networks improve ensemble performance on regression tasks.
New method allows generating independent data matrices from summary statistics.
We establish an explicit expression for the conditional Laplace transform of the integrated Volterra Wishart process in terms of a certain resolvent of the covariance function. The core ingredient is the derivation of the conditional Laplace transform of general Gaussian processes in terms of Fredholm's determinant and…
Paper interprets UMAP and t-SNE as probabilistic MAP inference.
Matrix H-theory models stock market fluctuations using hierarchical multivariate distributions.
The paper studies the distribution of random degeneracy sets on complex manifolds.
Bayesian inference for stochastic differential equations using Wishart diffusions.
This thesis consists of two independent parts: random matrices, which form the first one-third of this thesis, and machine learning, which constitutes the remaining part. The main results of this thesis are as follows: a necessary and sufficient condition for the inverse moments of -Laguerre matrices and compo…
We put forward a complete theory on moment explosion for fairly general state-spaces. This includes a characterization of the validity of the affine transform formula in terms of minimal solutions of a system of generalized Riccati differential equations. Also, we characterize the class of positive semidefinite process…
A non-Hermitean extension of paradigmatic Wishart random matrices is introduced to set up a theoretical framework for statistical analysis of (real, complex and real quaternion) stochastic time series representing two "remote" complex systems. The first paper in a series provides a detailed spectral theory of non-Hermi…
New lower bounds for sampling from log-concave distributions in higher dimensions.
Cone structures in quantum field theory linked to information geometry.
We derive the explicit formula for the joint Laplace transform of the Wishart process and its time integral which extends the original approach of Bru. We compare our methodology with the alternative results given by the variation of constants method, the linearization of the Matrix Riccati ODE's and the Runge-Kutta al…
We investigate the Student-t process as an alternative to the Gaussian process as a nonparametric prior over functions. We derive closed form expressions for the marginal likelihood and predictive distribution of a Student-t process, by integrating away an inverse Wishart process prior over the covariance kernel of a G…
Develops a new MCMC-based Wishart prior for Gaussian Process covariance matrix.
We introduce a stochastic process with Wishart marginals: the generalised Wishart process (GWP). It is a collection of positive semi-definite random matrices indexed by any arbitrary dependent variable. We use it to model dynamic (e.g. time varying) covariance matrices. Unlike existing models, it can capture a diverse …
Optimal data splitting improves covariance matrix estimation in large datasets.
Attention learns PCA on Gaussian data, proving its connection to principal component analysis.
Researchers prove inner product recovery is impossible in latent space models.
Iterative method 'Concent' corrects spectrum bias in covariance matrices.
Paper extends Bayesian Cramér-Rao bound with geometric considerations.
Study on Gaussian ensemble of matrix products with mixed moments computed.
Random matrix theory is used to assess the significance of weak correlations and is well established for Gaussian statistics. However, many complex systems, with stock markets as a prominent example, exhibit statistics with power-law tails, that can be modelled with Levy stable distributions. We review comprehensively …
In this article, we propose an exact simulation method of the Wishart multidimensional stochastic volatility (WMSV) model, which was recently introduced by Da Fonseca et al. \cite{DGT08}. Our method is based onanalysis of the conditional characteristic function of the log-price given volatility level. In particular, we…
In the present work, eigenvalue distributions defined by a random rectangular matrix whose components are neither independently nor identically distributed are analyzed using replica analysis and belief propagation. In particular, we consider the case in which the components are independently but not identically distri…