In this paper, we study the multi-task learning problem with a new perspective of considering the structure of the residue error matrix and the low-rank approximation to the task covariance matrix simultaneously. In particular, we first introduce the Matrix Generalized Inverse Gaussian (MGIG) prior and define a Gaussian Matrix Generalized Inverse Gaussian (GMGIG) model for low-rank approximatio...

In this paper, estimation of the parameters of a certain family of two-parameter lifetime distributions based on progressively Type II right censored samples (including ordinary Type II right censoring) is studied. This family, of reverse hazard distributions, includes the Weibull, Gompertz and Lomax distributions. A new type of parameter estimation, named inverse estimation, is introduced for ...

In this paper, we present several probabilistic transforms related to classical urn models. These transforms render the dependent random variables describing the urn occupancies into independent random variables with appropriate distributions. This simplifies the analysis of a large number of problems for which a function under investigation depends on the urn occupancies. The approach used for...

We investigate intra-day foreign exchange (FX) time series using the inverse statistic analysis developed in [1,2]. Specifically, we study the time-averaged distributions of waiting times needed to obtain a certain increase (decrease) ρ in the price of an investment. The analysis is performed for the Deutsch mark (DM) against the $US for the full year of 1998, but similar results are obtained f...

This brief communication analyzes the statistics and methods Lotka used to derive his inverse square law of scientific productivity from the standpoint of modern theory. It finds that he violated the norms of this theory by extremely truncating his data on the right. It also proves that Lotka himself played an important role in establishing the commonly used method of identifying power-law beha...

Abstract. Researchers have studied the first passage time of financial time series and observed that the smallest time interval needed for a stock index to move a given distance is typically shorter for negative than for positive price movements. The same is not observed for the index constituents, the individual stocks. We use the discrete wavelet transform to illustrate that this is a long ra...

In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by noise. A proper data fidelity term (log-likelihood) is introduced to reflect the statistics of the noise (e.g. Gaussian, Poisson). On the other hand, as a prior, the images to restore are assumed to be positive and sparsely represented in a dictionary of waveforms. Piecing togethe...

We examine nonstationary inverse problems in which the time evolution of the unknown quantity is modelled by a stochastic partial differential equation. We consider the problem as a state estimation problem. The time discrete state evolution equation is exact since the solution is given by an analytic semigroup. For the practical reasons the space discretization of the time discrete state estim...

In order to research kinematic reliability of 3-UPS-PU parallel mechanism, the structure and kinematics analysis were performed. Inverse kinematics equation can be derived by homogeneous coordinate transformation formula. Position and orientation output error forward kinematics model was obtained by the differential transformation on the basis of inverse kinematic solution of the position. The ...

We consider three general classes of data-driven statistical tests. Neyman’s smooth tests, data-driven score tests and data-driven score tests for statistical inverse problems serve as important special examples for the classes of tests under consideration. Our tests are additionally incorporated with model selection rules. The rules are based on the penalization idea. Most of the optimal penal...