Good-turing estimation for the frequentist n-tuple classifier

We present results concerning the application of the Good-Turing (GT) estimation method to the frequentist n-tuple system. We show that the Good-Turing method can, to a certain extent rectify the Zero Frequency Problem by providing, within a formal framework, improved estimates of small tallies. We also show that it leads to better tuple system performance than Maximum Likelihood estimation (MLE). However, preliminary experimental results suggest that replacing zero tallies with an arbitrary constant close to zero before MLE yields better performance than that of GT system.

The n-tuple network: coping with sub-optimality

The subject of this thesis is the n-tuple net.work (RAMnet). The major advantage of RAMnets is their speed and the simplicity with which they can be implemented in parallel hardware. On the other hand, this method is not a universal approximator and the training procedure does not involve the minimisation of a cost function. Hence RAMnets are potentially sub-optimal. It is important to understand the source of this sub-optimality and to develop the analytical tools that allow us to quantify the generalisation cost of using this model for any given data. We view RAMnets as classifiers and function approximators and try to determine how critical their lack of' universality and optimality is. In order to understand better the inherent. restrictions of the model, we review RAMnets showing their relationship to a number of well established general models such as: Associative Memories, Kamerva's Sparse Distributed Memory, Radial Basis Functions, General Regression Networks and Bayesian Classifiers. We then benchmark binary RAMnet. model against 23 other algorithms using real-world data from the StatLog Project. This large scale experimental study indicates that RAMnets are often capable of delivering results which are competitive with those obtained by more sophisticated, computationally expensive rnodels. The Frequency Weighted version is also benchmarked and shown to perform worse than the binary RAMnet for large values of the tuple size n. We demonstrate that the main issues in the Frequency Weighted RAMnets is adequate probability estimation and propose Good-Turing estimates in place of the more commonly used :Maximum Likelihood estimates. Having established the viability of the method numerically, we focus on providillg an analytical framework that allows us to quantify the generalisation cost of RAMnets for a given datasetL. For the classification network we provide a semi-quantitative argument which is based on the notion of Tuple distance. It gives a good indication of whether the network will fail for the given data. A rigorous Bayesian framework with Gaussian process prior assumptions is given for the regression n-tuple net. We show how to calculate the generalisation cost of this net and verify the results numerically for one dimensional noisy interpolation problems. We conclude that the n-tuple method of classification based on memorisation of random features can be a powerful alternative to slower cost driven models. The speed of the method is at the expense of its optimality. RAMnets will fail for certain datasets but the cases when they do so are relatively easy to determine with the analytical tools we provide.

Interactive semantics

Much research pursues machine intelligence through better representation of semantics. What is semantics? People in different areas view semantics from different facets although it accompanies interaction through civilization. Some researchers believe that humans have some innate structure in mind for processing semantics. Then, what the structure is like? Some argue that humans evolve a structure for processing semantics through constant learning. Then, how the process is like? Humans have invented various symbol systems to represent semantics. Can semantics be accurately represented? Turing machines are good at processing symbols according to algorithms designed by humans, but they are limited in ability to process semantics and to do active interaction. Super computers and high-speed networks do not help solve this issue as they do not have any semantic worldview and cannot reflect themselves. Can future cyber-society have some semantic images that enable machines and individuals (humans and agents) to reflect themselves and interact with each other with knowing social situation through time? This paper concerns these issues in the context of studying an interactive semantics for the future cyber-society. It firstly distinguishes social semantics from natural semantics, and then explores the interactive semantics in the category of social semantics. Interactive semantics consists of an interactive system and its semantic image, which co-evolve and influence each other. The semantic worldview and interactive semantic base are proposed as the semantic basis of interaction. The process of building and explaining semantic image can be based on an evolving structure incorporating adaptive multi-dimensional classification space and self-organized semantic link network. A semantic lens is proposed to enhance the potential of the structure and help individuals build and retrieve semantic images from different facets, abstraction levels and scales through time.

Parametric pattern selection in a reaction-diffusion model

We compare spot patterns generated by Turing mechanisms with those generated by replication cascades, in a model one-dimensional reaction-diffusion system. We determine the stability region of spot solutions in parameter space as a function of a natural control parameter (feed-rate) where degenerate patterns with different numbers of spots coexist for a fixed feed-rate. While it is possible to generate identical patterns via both mechanisms, we show that replication cascades lead to a wider choice of pattern profiles that can be selected through a tuning of the feed-rate, exploiting hysteresis and directionality effects of the different pattern pathways.

Mode-locking via dissipative Faraday instability

Emergence of coherent structures and patterns at the nonlinear stage of modulation instability of a uniform state is an inherent feature of many biological, physical and engineering systems. There are several well-studied classical modulation instabilities, such as Benjamin-Feir, Turing and Faraday instability, which play a critical role in the self-organization of energy and matter in non-equilibrium physical, chemical and biological systems. Here we experimentally demonstrate the dissipative Faraday instability induced by spatially periodic zig-zag modulation of a dissipative parameter of the system - spectrally dependent losses - achieving generation of temporal patterns and high-harmonic mode-locking in a fibre laser. We demonstrate features of this instability that distinguish it from both the Benjamin-Feir and the purely dispersive Faraday instability. Our results open the possibilities for new designs of mode-locked lasers and can be extended to other fields of physics and engineering.