STARTS
Although researchers in clinical psychology routinely gather data in which many individuals respond at multiple times, there is not a standard way to analyze such data. A new approach for the analysis of such data is described. It is proposed that a person’s current standing on a variable is caused by 3 sources of variance: a term that does not change (trait), a term that changes (state), and a random term (error). It is shown how structural equation modeling can be used to estimate such a model. An extended example is presented in which the correlations between variables are quite different at the trait, state, and error levels. (PsycINFO Database Record (c) 2016 APA, all rights reserved) …

White Noise
In signal processing, white noise is a random signal with a constant power spectral density. The term is used, with this or similar meanings, in many scientific and technical disciplines, including physics, acoustic engineering, telecommunications, statistical forecasting, and many more. White noise refers to a statistical model for signals and signal sources, rather than to any specific signal. A ‘white noise’ image. In discrete time, white noise is a discrete signal whose samples are regarded as a sequence of serially uncorrelated random variables with zero mean and finite variance; a single realization of white noise is a random shock. Depending on the context, one may also require that the samples be independent and have the same probability distribution (in other words i.i.d is a simplest representative of the white noise). In particular, if each sample has a normal distribution with zero mean, the signal is said to be Gaussian white noise. The samples of a white noise signal may be sequential in time, or arranged along one or more spatial dimensions. In digital image processing, the pixels of a white noise image are typically arranged in a rectangular grid, and are assumed to be independent random variables with uniform probability distribution over some interval. The concept can be defined also for signals spread over more complicated domains, such as a sphere or a torus. Some ‘white noise’ sound. An infinite-bandwidth white noise signal is a purely theoretical construction. The bandwidth of white noise is limited in practice by the mechanism of noise generation, by the transmission medium and by finite observation capabilities. Thus, a random signal is considered ‘white noise’ if it is observed to have a flat spectrum over the range of frequencies that is relevant to the context. For an audio signal, for example, the relevant range is the band of audible sound frequencies, between 20 to 20,000 Hz. Such a signal is heard as a hissing sound, resembling the /sh/ sound in ‘ash’. In music and acoustics, the term ‘white noise’ may be used for any signal that has a similar hissing sound. White noise draws its name from white light, although light that appears white generally does not have a flat spectral power density over the visible band. The term white noise is sometimes used in the context of phylogenetically based statistical methods to refer to a lack of phylogenetic pattern in comparative data. It is sometimes used in non technical contexts, in the metaphoric sense of ‘random talk without meaningful contents’. …

Kernel Support Matrix Machine (KSMM)
Tensor is a natural and compact representation for real world data which are often multi-dimensional. Meanwhile, problems of supervised tensor learning (STL) are commonly encountered in applications. Most existing classifiers based on tensor representation, such as support tensor machine (STM) need to solve iteratively which occupy much time and may suffer from local minima. In this paper, we present a kernel support matrix machine (KSMM) connected with the matrix Hilbert space to perform supervised learning when data are represented as matrices. KSMM is a general framework for constructing matrix-based hyperplane to exploit information. We analyze a unifying optimization problem for which we propose an asymptotically convergent algorithm. The goal is to both determine the hyperplane as well as predict the unlabeled samples. Theoretical analysis for the generalization bounds is derived based on Rademacher complexity with respect to a probability distribution. We demonstrate the merits of the proposed method by exhaustive experiments on simulation study and a number of real-word datasets from a variety of application domains. …