arXiv research

New approach predicts generalization of deep neural networks in proportional-width regime.

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…

Paper explores Elliptical Wishart distributions in signal processing and machine learning.

Bayesian framework for analyzing heterogeneous covariance data with a novel MoE-Wishart model.

Study proposes a new model for joint survival annuity valuation.

New framework for calculating multivariate risk measures using Wishart process.

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…

Improved variational approximation for deep Wishart process models.

WISDoM uses the Wishart distribution to analyze neurological data like EEG and brain connectivity.

New method uses KL-divergence to create non-informative priors for multivariate Gaussian.

Bayesian inference for stochastic differential equations using Wishart diffusions.

Researchers develop a new SMC sampler for Wishart processes to improve dynamic covariance inference.

New ansatz for generalized Kähler surfaces derived from hyperKähler ansatz.

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 …

A new method for deep Wishart processes improves kernel-based models.

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…

Expressive quantum circuits are harder to train due to flatter cost landscapes.

Develops methods for constructing parameter priors in DAG models.

Deep kernel processes unify various models using Gram matrices and kernel functions.

We describe a quaternionic-based Ansatz generalizing the Gibbons-Hawking Ansatz to a class of hyperkähler metrics with hidden symmetries. We then apply it to obtain explicit expressions for gravitational instanton metrics of type $D_k$.

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.

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.

A new approach to quantum machine learning circuits reduces training difficulties.

We propose a new input perturbation mechanism for publishing a covariance matrix to achieve $(ε,0)$-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 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 …

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.

Deep QMC ansatzes improve variational QMC accuracy.

It was observed by Tod and later by Dunajski and Tod that the Boyer-Finley (BF) and the dispersionless Kadomtsev-Petviashvili (dKP) equations possess solutions whose level surfaces are central quadrics in the space of independent variables (the so-called central quadric ansatz). It was demonstrated that generic solutio…

A homogeneous Gibbons-Hawking ansatz is described, leading to 4-dimensional hyperkahler metrics with homotheties. In combination with Blaschke products on the unit disc in the complex plane, this ansatz allows one to construct infinite-dimensional families of such hyperkahler metrics that are, in a suitable sense, comp…

MBQC linked to CQCA, yielding efficient Ansätze.

We show that a complete simply-connected hyperkaehler 4-manifold with an isometric triholomorphic circle action is obtained from the Gibbons-Hawking ansatz with some suitable harmonic function.

Study on Gaussian ensemble of matrix products with mixed moments computed.

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…

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, $Θ(d)$ calls to the oracle are nece…

Study Ricci flow on CP1-bundles over Kähler-Einstein manifolds.

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…

Barrier methods classify minimal submanifolds in hyperkaehler spaces.

The modified J-flow with Calabi ansatz shows convergence or blow-up behavior based on topological constants.

Develops methods to solve complex and real Hessian equations.

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…

Constructs scalar-flat Kähler metrics with varying conical singularities.

We discuss the Ricci-flat `model metrics' on $\mathbb{C}^2$ with cone singularities along the conic $\{zw=1\}$ constructed by Donaldson using the Gibbons-Hawking ansatz over wedges in $\mathbb{R}^3$. In particular we describe their asymptotic behavior at infinity and compute their energies.