Search results for "Probability vector"
showing 8 items of 8 documents
Channel selection in Cognitive Radio Networks: A Switchable Bayesian Learning Automata approach
2013
We consider the problem of a user operating within a Cognitive Radio Network (CRN) which involves N channels each associated with a Primary User (PU). The problem consists of allocating a channel which, at any given time instant is not being used by a PU, to a Secondary User (SU). Within our study, we assume that a SU is allowed to perform “channel switching”, i.e., to choose an alternate channel S times (where S +1 ≤ N) if the previous choice does not lead to a channel which is vacant. The paper first presents a formal probabilistic model for the problem itself, referred to as the Formal Secondary Channel Selection (FSCS) problem, and the characteristics of the FSCS are then analyzed. Ther…
Generalized Bayesian Pursuit: A Novel Scheme for Multi-Armed Bernoulli Bandit Problems
2011
In the last decades, a myriad of approaches to the multi-armed bandit problem have appeared in several different fields. The current top performing algorithms from the field of Learning Automata reside in the Pursuit family, while UCB-Tuned and the e-greedy class of algorithms can be seen as state-of-the-art regret minimizing algorithms. Recently, however, the Bayesian Learning Automaton (BLA) outperformed all of these, and other schemes, in a wide range of experiments. Although seemingly incompatible, in this paper we integrate the foundational learning principles motivating the design of the BLA, with the principles of the so-called Generalized Pursuit algorithm (GPST), leading to the Gen…
Statistical criteria for early-stopping of support vector machines
2007
This paper proposes the use of statistical criteria for early-stopping support vector machines, both for regression and classification problems. The method basically stops the minimization of the primal functional when moments of the error signal (up to fourth order) become stationary, rather than according to a tolerance threshold of primal convergence itself. This simple strategy induces lower computational efforts and no significant differences are observed in terms of performance and sparsity.
The Power of the “Pursuit” Learning Paradigm in the Partitioning of Data
2019
Traditional Learning Automata (LA) work with the understanding that the actions are chosen purely based on the “state” in which the machine is. This modus operandus completely ignores any estimation of the Random Environment’s (RE’s) (specified as \(\mathbb {E}\)) reward/penalty probabilities. To take these into consideration, Estimator/Pursuit LA utilize “cheap” estimates of the Environment’s reward probabilities to make them converge by an order of magnitude faster. This concept is quite simply the following: Inexpensive estimates of the reward probabilities can be used to rank the actions. Thereafter, when the action probability vector has to be updated, it is done not on the basis of th…
Cross-correlation and cross-power spectral density representation by complex spectral moments
2017
Abstract A new approach to provide a complete characterization of normal multivariate stochastic vector processes is presented in this paper. Such proposed method is based on the evaluation of the complex spectral moments of the processes. These quantities are strictly related to the Mellin transform and they are the generalization of the integer-order spectral moments introduced by Vanmarcke. The knowledge of the complex spectral moments permits to obtain the power spectral densities and their cross counterpart by a complex series expansions. Moreover, with just the aid of some mathematical properties the complex fractional moments permit to obtain also the correlation and cross-correlatio…
The Hierarchical Continuous Pursuit Learning Automation: A Novel Scheme for Environments With Large Numbers of Actions.
2019
Although the field of learning automata (LA) has made significant progress in the past four decades, the LA-based methods to tackle problems involving environments with a large number of actions is, in reality, relatively unresolved. The extension of the traditional LA to problems within this domain cannot be easily established when the number of actions is very large. This is because the dimensionality of the action probability vector is correspondingly large, and so, most components of the vector will soon have values that are smaller than the machine accuracy permits, implying that they will never be chosen . This paper presents a solution that extends the continuous pursuit paradigm to …
The Hierarchical Continuous Pursuit Learning Automation for Large Numbers of Actions
2018
Part 10: Learning - Intelligence; International audience; Although the field of Learning Automata (LA) has made significant progress in the last four decades, the LA-based methods to tackle problems involving environments with a large number of actions are, in reality, relatively unresolved. The extension of the traditional LA (fixed structure, variable structure, discretized, and pursuit) to problems within this domain cannot be easily established when the number of actions is very large. This is because the dimensionality of the action probability vector is correspondingly large, and consequently, most components of the vector will, after a relatively short time, have values that are smal…
Modal analysis for random response of MDOF systems
1990
The usefulness of the mode-superposition method of multidegrees of freedom systems excited by stochastic vector processes is here presented. The differential equations of moments of every order are written in compact form by means of the Kronecker algebra; then the method for integration of these equations is presented for both classically and non-classically damped systems, showing that the fundamental operator available for evaluating the response in the deterministic analysis is also useful for evaluating the response in the stochastic analysis.