Related papers: Conditionally Gaussian Random Sequences for an Int…
The main purpose of this paper is to study the problem of determining initial condition of nonlinear parabolic equation from noisy observations of the final condition. We introduce a regularized method to establish an approximate solution.…
The estimation of the covariance structure from a discretely observed multivariate Gaussian process under asynchronicity and noise is analysed under high-frequency asymptotics. Asymptotic lower and upper bounds are established for a general…
The analysis of the intraday dynamics of correlations among high-frequency returns is challenging due to the presence of asynchronous trading and market microstructure noise. Both effects may lead to significant data reduction and may…
This dissertation shows that careful injection of noise into sample data can substantially speed up Expectation-Maximization algorithms. Expectation-Maximization algorithms are a class of iterative algorithms for extracting maximum…
Gaussian Processes (GPs) are powerful kernelized methods for non-parameteric regression used in many applications. However, their use is limited to a few thousand of training samples due to their cubic time complexity. In order to scale GPs…
In independent component analysis it is assumed that the observed random variables are linear combinations of latent, mutually independent random variables called the independent components. Our model further assumes that only the…
In this work, we provide the first strong convergence result of numerical approximation of a general second order semilinear stochastic fractional order evolution equation involving a Caputo derivative in time of order $\alpha\in(\frac 34,…
Bayesian hierarchical models can provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models typically comprise a conditionally Gaussian prior model for the unknown which is augmented by a generalized…
In nonlinear latent variable models or dynamic models, if we consider the latent variables as confounders (common causes), the noise dependencies imply further relations between the observed variables. Such models are then closely related…
Gaussian processes are flexible probabilistic regression models which are widely used in statistics and machine learning. However, a drawback is their limited scalability to large data sets. To alleviate this, full-scale approximations…
Estimating covariances between financial assets plays an important role in risk management. In practice, when the sample size is small compared to the number of variables, the empirical estimate is known to be very unstable. Here, we…
The sum of Log-normal variates is encountered in many challenging applications such as in performance analysis of wireless communication systems and in financial engineering. Several approximation methods have been developed in the…
This paper proposes an event-triggered variational Bayesian filter for remote state estimation with unknown and time-varying noise covariances. After presetting multiple nominal process noise covariances and an initial measurement noise…
In inverse problems, it is widely recognized that the incorporation of a sparsity prior yields a regularization effect on the solution. This approach is grounded on the a priori assumption that the unknown can be appropriately represented…
We describe a procedure to perform approximate inference on the achieved signal-noise ratio of the Markowitz Portfolio under Gaussian i.i.d. returns. The procedure relies on a statistic similar to the Sharpe Ratio Information Criterion.…
Sparsity promoting norms are frequently used in high dimensional regression. A limitation of such Lasso-type estimators is that the optimal regularization parameter depends on the unknown noise level. Estimators such as the concomitant…
Second-order information -- such as curvature or data covariance -- is critical for optimisation, diagnostics, and robustness. However, in many modern settings, only the gradients are observable. We show that the gradients alone can reveal…
It is well-known that the posterior density of linear inverse problems with Gaussian prior and Gaussian likelihood is also Gaussian, hence completely described by its covariance and expectation. Sampling from a Gaussian posterior may be…
Sparse variational Gaussian process (GP) approximations based on inducing points have become the de facto standard for scaling GPs to large datasets, owing to their theoretical elegance, computational efficiency, and ease of implementation.…
Bayesian approach to inverse problems is studied in the case where the forward map is a linear hypoelliptic pseudodifferential operator and measurement error is additive white Gaussian noise. The measurement model for an unknown Gaussian…