Studies in Learning Automata and Pattern Recognition

我建议承担学习自动机(LA)、反贝叶斯模式识别(PR)和神经网络(NNS)等领域的各种项目。 LA已被用于对生物系统进行建模。由于它们能在随机环境中学习最优行为，因此引起了人们的极大兴趣。我们开创了在离散化概率空间中操作的LA的设计，并且可能是最快的LA的设计。我们还使用LA解决了许多现实生活中的困难问题，如最优Web轮询、MPLS流量的路由等。 反贝叶斯分类：在分类分类领域，虽然分类密度的矩已被用于分类，但分位数的性质一直未被使用。最近，我们提出了一种新的开创性范式CMQS，即按分位数统计量的矩进行分类，它具体地使用了这些方法。CMQS本质上是“反贝叶斯”的，因为它以一种反直觉的方式运作--它将测试样本与远离平均值的几个样本进行比较。我们已经提出了许多一维和多维分布的CMQS的基本理论。 提出的工作1.贝叶斯追踪算法。最快的LA家族，即追踪算法(PAS)，利用对奖励概率的估计。这些估计是最大可能性质的。我们建议调查涉及贝叶斯估计的PA家族。这里的工作将主要是分析性和基础性的。 拟议工作2.以“电梯”为基础的洛杉矶解决方案。LA的整个领域涉及的是要学习的动作是“无序的”的模型，即LA没有任何理由相信a1比a2更好，以此类推。然而，如果动作可以被排序，它们可以被认为是建筑物中的级别，因此学习问题是选择电梯自身必须停放的位置，以便将用户定义的标准降至最低。我们的研究将涉及到对学习范式的建模，以及分析广义的类似电梯的LA的未被探索的领域。 建议工作3.随机点定位(SPL)。早些时候，我们研究了LA在所谓的SPL问题中的应用，并提供了离散化、递归和分层的解决方案。我们建议设计新的递归d元搜索解，并将其用于随机优化。 拟议工作4.应用我们建议使用LA来解决古尔博弈，其中参与者也可以是叛徒，解决公共博弈，囚犯困境的推广，以及在认知无线电中。 建议的工作5.PR：我们建议为非参数应用、基于核的方案和无监督方案发展反贝叶斯PR理论。我们还将致力于混乱的公关。 建议的工作6.神经网络：我们提出开发神经网络来增强生长自组织映射(GSOM)，GSOM是一种基于Kohonen的自组织映射的神经网络聚类算法。

I propose to undertake various projects that concern the fields of Learning Automata (LA), Anti-Bayesian Pattern Recognition (PR) and Neural Networks (NNs). LA have been used to model biological systems. They have attracted considerable interest because they can learn the optimal action when operating in stochastic environments. We have pioneered the design of LA that operate in a discretized probability space, and the design of, probably, the fastest LA. We have also used LA to solve numerous real-life hard problems such as optimal web polling, routing for MPLS traffic etc. Anti-Bayesian PR: In the field of PR, although the moments of the densities of the classes have been used in classification, the properties of the Quantiles have been unused. Recently, we proposed a novel pioneering paradigm named CMQS, Classification by the Moments of Quantile Statistics, which specifically uses these. CMQS is essentially “anti-Bayesian” because it operates in a counter-intuitive manner – it compares the testing sample to a few samples distant from the mean. We have proposed the foundational theory of CMQS for many uni-dimensional and multi-dimensional distributions. Proposed Work 1. Bayesian Pursuit Algorithms. The fastest family of LA, the Pursuit Algorithms (PAs), utilize estimates of the reward probabilities. These estimates have been of the Maximum Likelihood nature. We propose to investigate families of PAs that involves Bayesian estimates. The work here will primarily be analytic and foundational. Proposed Work 2. “Elevator”-based LA Solutions. The entire field of LA deals with the model in which the actions that to be learnt are “unordered”, i.e., the LA does not have any reason to believe that a1 is better than a2, and so on. However, if the actions can be ordered, they can be considered to be as levels in a building, whereby the learning problem is one of choosing where an elevator must station itself so as to minimize a user-defined criterion. Our research will involve modeling the learning paradigm, and analyzing the unexplored field of generalized “Elevator”-like LA. Proposed Work 3. Stochastic Point Location (SPL). Earlier, we had studied the use of LA in the so-called SPL problem and provided discretized, recursive and hierarchical solutions. We propose to design new recursive d-ary search solutions, and to use them in stochastic optimization. Proposed Work 4. Applications. We propose to use LA to solve the Goore Game in which the players can also be traitors, to solve the COMMONS game, a generalization of the Prisoner’s Dilemma, and in cognitive radios. Proposed Work 5. PR: We propose to work to develop the theory of Anti-Bayesian PR for non-parametric applications, kernel-based, and unsupervised schemes. We also will work on Chaotic PR. Proposed Work 6. NN: We propose to develop NNs to enhance the Growing Self-Organizing Map (GSOM) which is a NN clustering algorithm based on Kohonen’s Self-Organizing Map.