Related papers: Probabilistic Approach to Pattern Selection
A general principle is advanced allowing the classification of nonunique solutions to nonlinear evolution equations, corresponding to different spatio-temporal patterns. This is done by defining the probability distribution of patterns,…
In this paper we present a novel tool to evaluate problem solving systems. Instead of using a system to solve a problem, we suggest using the problem to evaluate the system. By finding a numerical representation of a problem's complexity,…
The phenomenon of turbulent photon filamentation occurs in lasers and other active optical media at high Fresnel numbers. A description of this phenomenon is suggested. The solutions to evolution equations are presented in the form of a…
Optical turbulence is the term that is used being based on the analogy between hydrodynamic and optical equations. The phenomenon of turbulent photon filamentation occurs in lasers and other active optical media at high Fresnel numbers. A…
The problem of describing optical turbulent structures, arising in resonant media with high Fresnel numbers, is reviewed. The consideration is based on the probabilistic approach to pattern selection, ascribing a probability distribution of…
Pattern forming systems allow for a wealth of states, where wavelengths and orientation of patterns varies and defects disrupt patches of monocrystalline regions. Growth of patterns has long been recognized as a strong selection mechanism.…
The task of learning to pick a single preferred example out a finite set of examples, an "optimal choice problem", is a supervised machine learning problem with complex, structured input. Problems of optimal choice emerge often in various…
We use a probabilistic method to produce some combinatorial inequalities by considering pattern containment in permutations and words.
In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is…
The last decade has seen a revolution in the theory and application of machine learning and pattern recognition. Through these advancements, variable ranking has emerged as an active and growing research area and it is now beginning to be…
A general Bayesian framework for model selection on random network models regarding their features is considered. The goal is to develop a principle Bayesian model selection approach to compare different fittable, not necessarily nested,…
Traditionally evolution is seen as a process where from a pool of possible variations of a population (e.g. biological species or industrial goods) a few variations get selected which survive and proliferate, whereas the others vanish.…
We address the problem of selecting $k$ representative nodes from a network, aiming to achieve two objectives: identifying the most influential nodes and ensuring the selection proportionally reflects the network's diversity. We propose two…
The linear ordering problem (LOP), which consists in ordering M objects from their pairwise comparisons, is commonly applied in many areas of research. While efforts have been made to devise efficient LOP algorithms, verification of whether…
Motivation: Gene selection has become a common task in most gene expression studies. The objective of such research is often to identify the smallest possible set of genes that can still achieve good predictive performance. The problem of…
A principled approach to understand network structures is to formulate generative models. Given a collection of models, however, an outstanding key task is to determine which one provides a more accurate description of the network at hand,…
We here introduce a novel classification approach adopted from the nonlinear model identification framework, which jointly addresses the feature selection and classifier design tasks. The classifier is constructed as a polynomial expansion…
In this article we consider the problem of choosing an optimal sampling scheme for the regression problem simultaneously with that of model selection. We consider a batch type approach and an on-line approach following algorithms recently…
A structure called a decision making problem is considered. The set of outcomes (consequences) is partially ordered according to the decision maker's preferences. The problem is how these preferences affect a decision maker to prefer one of…
The Algorithm Selection Problem is concerned with selecting the best algorithm to solve a given problem on a case-by-case basis. It has become especially relevant in the last decade, as researchers are increasingly investigating how to…