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.
Improved variational approximation for deep Wishart process models.
A new method for deep Wishart processes improves kernel-based models.
Deep kernel processes unify various models using Gram matrices and kernel functions.
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…
New framework for calculating multivariate risk measures using Wishart process.
Study proposes a new model for joint survival annuity valuation.
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…
Paper explores Elliptical Wishart distributions in signal processing and machine learning.
Researchers develop a new SMC sampler for Wishart processes to improve dynamic covariance inference.
Bayesian inference for stochastic differential equations using Wishart diffusions.
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 …
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…
Develops a new MCMC-based Wishart prior for Gaussian Process covariance matrix.
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…
A new multivariate stochastic volatility estimation procedure for financial time series is proposed. A Wishart autoregressive process is considered for the volatility precision covariance matrix, for the estimation of which a two step procedure is adopted. The first step is the conditional inference on the autoregressi…
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…
New approach predicts generalization of deep neural networks in proportional-width regime.
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…
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…
We consider a short rate model, driven by a stochastic process on the cone of positive semidefinite matrices. We derive sufficient conditions ensuring that the model replicates normal, inverse or humped yield curves.
Bayesian framework for analyzing heterogeneous covariance data with a novel MoE-Wishart model.
New matrix ensembles better match deep neural network spectral densities.
We prove a large deviations principle for the class of multidimensional affine stochastic volatility models considered in (Gourieroux, C. and Sufana, R., J. Bus. Econ. Stat., 28(3), 2010), where the volatility matrix is modelled by a Wishart process. This class extends the very popular Heston model to the multivariate …
New method uses KL-divergence to create non-informative priors for multivariate Gaussian.
Study on eigenvalue distribution of correlated time series, showing deformation of Marchenko-Pastur distribution.
Bayesian deep neural networks converge to processes with α-stable marginals under infinite variance weights.
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 …
Paper interprets UMAP and t-SNE as probabilistic MAP inference.
A method for converting NIW parameters for better estimation.
New distribution simplifies covariance matrix inference.
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…
Matrix H-theory models stock market fluctuations using hierarchical multivariate distributions.
Develops methods for constructing parameter priors in DAG models.
We consider stochastic partial differential equations appearing as Markovian lifts of matrix valued (affine) Volterra type processes from the point of view of the generalized Feller property (see e.g., \cite{doetei:10}). We introduce in particular Volterra Wishart processes with fractional kernels and values in the con…
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…
Cone structures in quantum field theory linked to information geometry.
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,…
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…
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…
Iterative method 'Concent' corrects spectrum bias in covariance matrices.
Study on Gaussian ensemble of matrix products with mixed moments computed.
We introduce a mean-reverting SDE whose solution is naturally defined on the space of correlation matrices. This SDE can be seen as an extension of the well-known Wright-Fisher diffusion. We provide conditions that ensure weak and strong uniqueness of the SDE, and describe its ergodic limit. We also shed light on a use…
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…
Region-based classification of PolSAR data can be effectively performed by seeking for the assignment that minimizes a distance between prototypes and segments. Silva et al (2013) used stochastic distances between complex multivariate Wishart models which, differently from other measures, are computationally tractable.…
We provide a general and tractable framework under which all multiple yield curve modeling approaches based on affine processes, be it short rate, Libor market, or HJM modeling, can be consolidated. We model a numeraire process and multiplicative spreads between Libor rates and simply compounded OIS rates as functions …
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…
Unified treatment of eigenvalue processes using Riemannian geometry.
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…