Performance analysis of l0 norm constrained Recursive least Squares (RLS) algorithm is attempted in this paper. Though the performance pretty attractive compared to its various alternatives, no thorough study of theoretical analysis has been performed. Like the popular l0 Least Mean Squares (LMS) algorithm, in l0 RLS, a l0 norm penalty is added to provide zero tap attractions on the instantaneo...

The large deviations principle for Gaussian measures in Banach space is given by the generalized Schilder's theorem. After assigning a norm ||f|| to paths f in the reproducing kernel Hilbert space of the underlying Gaussian process, the probability of an event A can be studied by minimizing the norm over all paths in A. The minimizing path f*, if it exists, is called the most probable path and ...

In this paper, we present a unified analysis of matrix completion under general low-dimensional structural constraints induced by any norm regularization. We consider two estimators for the general problem of structured matrix completion, and provide unified upper bounds on the sample complexity and the estimation error. Our analysis relies on results from generic chaining, and we establish two...

The antisymmetrization of the composite particles in cluster model calculations manifests itself in Pauli forbidden states (ghost states), if one restricts oneself on undeformed cluster in the low energy region. The resonating group method and the generating coordinate method rely on a property of the norm kernel, which introduces some of the ghost states. The norm kernel has been usually calcu...

Bayesian analyses of spatial data often use a conditionally autoregressive (CAR) prior, which can be written as the kernel of an improper density that depends on a precision parameter tau that is typically unknown. To include tau in the Bayesian analysis, the kernel must be multiplied by tau(k) for some k. This article rigorously derives k = (n - I)/2 for the L2 norm CAR prior (also called a Ga...

In [1], with the evidence framework, the almost inversely linear dependency between the optimal parameter r in norm-r support vector regression machine r-SVR and the Gaussian input noise is theoretically derived. When r takes a non-integer value, r-SVR cannot be easily realized using the classical QP optimization method. This correspondence attempts to achieve two goals: (1) The Newton-decent-m...

Differential privacy is a framework for privately releasing summaries of a database. Previous work has focused mainly on methods for which the output is a finite dimensional vector, or an element of some discrete set. We develop methods for releasing functions while preserving differential privacy. Specifically, we show that adding an appropriate Gaussian process to the function of interest yie...

This paper considers regularizing a covariance matrix of p variables estimated from n observations, by hard thresholding. We show that the thresholded estimate is consistent in the operator norm as long as the true covariance matrix is sparse in a suitable sense, the variables are Gaussian or sub-Gaussian, and (log p)/n→ 0, and obtain explicit rates. The results are uniform over families of cov...

Let G be a compact connected Lie group with trivial center. Using the action of G on its Lie algebra, we define an operator norm | |G which induces a bi-invariant metric dG(x, y) = |Ad(yx−1)|G on G. We prove the existence of a constant β ≈ .23 (independent of G) such that for any closed subgroup H ( G, the diameter of the quotient G/H (in the induced metric) is ≥ β.

This study aimed to determine the factors associated with exercise behavior based on the theory of planned behavior (TPB) among the sarcopenic elderly people in Cheras, Kuala Lumpur. A total of 65 subjects with mean ages of 67.5±5.2 (men) and 66.1±5.1 (women) years participated in this study. Subjects were divided into two groups: 1) exercise group (n=34; 25 men, nine women); and 2) the control...