We address the problem of learning a symmetric positive definite matrix. The central issue is to design parameter updates that preserve positive definiteness. Our updates are motivated with the von Neumann divergence. Rather than treating the most general case, we focus on two key applications that exemplify our methods: On-line learning with a simple square loss and finding a symmetric positiv...

Updating a system modeled as a real symmetric quadratic eigenvalue problem to match observed spectral information has been an important task for practitioners in different disciplines. It is often desirable in the process to match only the newly measured data without tampering with the other unmeasured and often unknown eigenstructure inherent in the original model. Such an updating, known as n...

Missing data in longitudinal studies can create enormous challenges in data analysis when coupled with the positive-definiteness constraint on a covariance matrix. For complete balanced data, the Cholesky decomposition of a covariance matrix makes it possible to remove the positive-definiteness constraint and use a generalized linear model setup to jointly model the mean and covariance using co...

Design-relevant information is sometimes vague or linguistic (technically speaking, f-granular) (e.g., design a slim shaft with light weight where dimensions are critical than weight). This puts obstacle in practicing the information axiom (minimize the information content of the design) of axiomatic design theory, a theory that establishes a science base for design. In such a situation, how on...

Many parameters and positive-definiteness are two major obstacles in estimating and modelling a correlation matrix for longitudinal data. In addition, when longitudinal data is incomplete, incorrectly modelling the correlation matrix often results in bias in estimating mean regression parameters. In this paper, we introduce a flexible and parsimonious class of regression models for a covariance...

versus concrete processing modes, and ask people to predict the consequences of positive and negative events. Such a study could also include measures of emotional impact in order to directly test whether shifts in construal level yield opposite effects on evaluations of consequences versus affective reactions (Terum & Svartdal, submitted). Final Remarks By the advent of CLT, scholars gained a ...

An improved algorithm, together with its implementation, is presented for the automatic computation of the complete root classification of a real parametric polynomial. The algorithm offers improved efficiency and a new test for non-realizable conditions. The improvement lies in the direct use of ‘sign lists’, obtained from the discriminant sequence, rather than ‘revised sign lists’. It is show...

Newton-type methods and quasi-Newton methods have proven to be very successful in solving dense unconstrained optimization problems. Recently there has been considerable interest in extending these methods to solving large problems when the Hessian matrix has a known a priori sparsity pattern, This paper treats sparse quasi-Newton methods in a uniform fashion and shows the effect of loss of pos...

This paper presents a new relaxed stability condition for Takagi-Sugeno (T-S) fuzzy control systems. Using quadratic fuzzy Lyapunov functions (QFLFs), the stability of closed-loop control system is guaranteed by the negative definiteness of several fuzzy summations. However, since the membership functions are continuous, the negative definiteness of these fuzzy summations implies an infinite nu...

In 4 experiments, we used self-paced reading and eye tracking to demonstrate that readers are, under some conditions, sensitive to the presuppositions of definite versus indefinite determiner phrases (DPs). Reading was faster when the context stereotypically provided a single possible referent for a definite DP or multiple possible referents for an indefinite DP than when context and DP definit...