Related papers: On optimal wavelet bases for the realization of mi…
Two-phase designs involve measuring extra variables on a subset of the cohort where some variables are already measured. The goal of two-phase designs is to choose a subsample of individuals from the cohort and analyse that subsample…
The notion of wavelets is defined. It is briefly described {\it what} are wavelets, {\it how} to use them, {\it when} we do need them, {\it why} they are preferred and {\it where} they have been applied. Then one proceeds to the…
Structured prediction tasks pose a fundamental trade-off between the need for model complexity to increase predictive power and the limited computational resources for inference in the exponentially-sized output spaces such models require.…
The orthonormal basis generated by a wavelet of $L^2(\mathbb R)$ has poor frequency localization. To overcome this disadvantage Coifman, Meyer, and Wickerhauser constructed wavelet packets. We extend this concept to the higher dimensions…
We use hyperbolic wavelet regression for the fast reconstruction of high-dimensional functions having only low dimensional variable interactions. Compactly supported periodic Chui-Wang wavelets are used for the tensorized hyperbolic wavelet…
Finding a succinct representation to describe the ground state of a disordered interacting system could be very helpful in understanding the interplay between the interactions that is manifested in a quantum phase transition. In this work…
This paper shows how the variational Bayes method provides a computational efficient technique in the context of hierarchical modelling using Dirichlet process priors, in particular without requiring conjugate prior assumption. It shows,…
We consider an approach to the analysis of nonstationary processes based on the application of wavelet basis sets constructed using segments of the analyzed time series. The proposed method is applied to the analysis of time series…
The paper is devoted to deriving necessary optimality conditions in a general optimal control problem for dynamical systems governed by controlled sweeping processes with hard-constrained control actions entering both polyhedral moving sets…
When the complete understanding of a complex system is not available, as, e.g., for systems considered in the real-world, we need a top-down approach to complexity. In this approach one may start with the desire to understand general…
In this paper we consider the wavelet synopsis construction problem without the restriction that we only choose a subset of coefficients of the original data. We provide the first near optimal algorithm. We arrive at the above algorithm by…
In a previous paper it was shown that a machine learning regression problem can be solved within the framework of random function theory, with the optimal kernel analytically derived from symmetry and indifference principles and coinciding…
A method for the design of Fast Haar wavelet for signal processing and image processing has been proposed. In the proposed work, the analysis bank and synthesis bank of Haar wavelet is modified by using polyphase structure. Finally, the…
This paper presents a new family of localized orthonormal bases - sinlets - which are well suited for both signal and image processing and analysis. One-dimensional sinlets are related to specific solutions of the time-dependent harmonic…
Cascade processes are responsible for many important phenomena in natural and social sciences. Simple models of irreversible dynamics on graphs, in which nodes activate depending on the state of their neighbors, have been successfully…
Across scientific domains, a fundamental challenge is to characterize and compute the mappings from underlying physical processes to observed signals and measurements. While nonlinear neural networks have achieved considerable success, they…
Cellular signaling networks have evolved to cope with intrinsic fluctuations, coming from the small numbers of constituents, and the environmental noise. Stochastic chemical kinetics equations govern the way biochemical networks process…
The multiscale dynamics of glow discharge plasma is analysed through wavelet transform, whose scale dependent variable window size aptly captures both transients and non-stationary periodic behavior. The optimal time-frequency localization…
Causal discovery from observational data is an important tool in many branches of science. Under certain assumptions it allows scientists to explain phenomena, predict, and make decisions. In the large sample limit, sound and complete…
It is of interest to study a wavelet system with a minimum number of generators. It has been showed by X. Dai, D. R. Larson, and D. M. Speegle in [11] that for any $d\times d$ real-valued expansive matrix M, a homogeneous orthonormal…