The exact sample complexity of PAC-learning problems with unit VC dimension

The Vapnik-Chervonenkis (VC) dimension is a combinatorial measure of a certain class of machine learning problems, which may be used to obtain upper and lower bounds on the number of training examples needed to learn to prescribed levels of accuracy. Most of the known bounds apply to the Probably Approximately Correct (PAC) framework, which is the framework within which we work in this paper. For a learning problem with some known VC dimension, much is known about the order of growth of the sample-size requirement of the problem, as a function of the PAC parameters. The exact value of sample-size requirement is however less well-known, and depends heavily on the particular learning algorithm being used. This is a major obstacle to the practical application of the VC dimension. Hence it is important to know exactly how the sample-size requirement depends on VC dimension, and with that in mind, we describe a general algorithm for learning problems having VC dimension 1. Its sample-size requirement is minimal (as a function of the PAC parameters), and turns out to be the same for all non-trivial learning problems having VC dimension 1. While the method used cannot be naively generalised to higher VC dimension, it suggests that optimal algorithm-dependent bounds may improve substantially on current upper bounds.

On the annealed VC entropy for margin classifiers: A statistical mechanics study

Using techniques from Statistical Physics, the annealed VC entropy for hyperplanes in high dimensional spaces is calculated as a function of the margin for a spherical Gaussian distribution of inputs.

Modelling data and voice traffic over IP networks using continuous-time Markov models

Common approaches to IP-traffic modelling have featured the use of stochastic models, based on the Markov property, which can be classified into black box and white box models based on the approach used for modelling traffic. White box models, are simple to understand, transparent and have a physical meaning attributed to each of the associated parameters. To exploit this key advantage, this thesis explores the use of simple classic continuous-time Markov models based on a white box approach, to model, not only the network traffic statistics but also the source behaviour with respect to the network and application. The thesis is divided into two parts: The first part focuses on the use of simple Markov and Semi-Markov traffic models, starting from the simplest two-state model moving upwards to n-state models with Poisson and non-Poisson statistics. The thesis then introduces the convenient to use, mathematically derived, Gaussian Markov models which are used to model the measured network IP traffic statistics. As one of the most significant contributions, the thesis establishes the significance of the second-order density statistics as it reveals that, in contrast to first-order density, they carry much more unique information on traffic sources and behaviour. The thesis then exploits the use of Gaussian Markov models to model these unique features and finally shows how the use of simple classic Markov models coupled with use of second-order density statistics provides an excellent tool for capturing maximum traffic detail, which in itself is the essence of good traffic modelling. The second part of the thesis, studies the ON-OFF characteristics of VoIP traffic with reference to accurate measurements of the ON and OFF periods, made from a large multi-lingual database of over 100 hours worth of VoIP call recordings. The impact of the language, prosodic structure and speech rate of the speaker on the statistics of the ON-OFF periods is analysed and relevant conclusions are presented. Finally, an ON-OFF VoIP source model with log-normal transitions is contributed as an ideal candidate to model VoIP traffic and the results of this model are compared with those of previously published work.

Language independent on-off voice over IP source model with lognormal transitions

The recent explosive growth of voice over IP (VoIP) solutions calls for accurate modelling of VoIP traffic. This study presents measurements of ON and OFF periods of VoIP activity from a significantly large database of VoIP call recordings consisting of native speakers speaking in some of the world's most widely spoken languages. The impact of the languages and the varying dynamics of caller interaction on the ON and OFF period statistics are assessed. It is observed that speaker interactions dominate over language dependence which makes monologue-based data unreliable for traffic modelling. The authors derive a semi-Markov model which accurately reproduces the statistics of composite dialogue measurements. © The Institution of Engineering and Technology 2013.

The value of innovation:the interaction of competition, R&D and IP

This paper analyses market valuations of UK companies using a new data set of their R&D and IP activities (1989–2002). In contrast to previous studies, the analysis is conducted at the sectoral-level, where the sectors are based on the technological classification originating from Pavitt [Pavitt, K., 1984. Sectoral patterns of technical change. Research Policy 13, 343–373]. The first main result is that the valuation of R&D varies substantially across these sectors. Another important result is that, on average, firms that receive only UK patents tend to have no significant market premium. In direct contrast, patenting through the European Patent Office does raise market value, as does the registration of trade marks in the UK for most sectors. To explore these variations the paper links competitive conditions with the market valuation of innovation. Using profit persistence as a measure of competitive pressure, we find that the sectors that are the most competitive have the lowest market valuation of R&D. Furthermore, within the most competitive sector (‘science based’ manufacturing), firms with larger market shares (an inverse indicator of competitive pressure) also have higher R&D valuations, as well as some positive return to UK patents. We conclude that this evidence supports Schumpeter by finding higher returns to innovation in less than fully competitive markets and contradicts Arrow [Arrow, K., 1962. Economic welfare and the allocation of resources for invention. In: Nelson, R. (Ed.), The Rate and Direction of Inventive Activity. Princeton University Press, Princeton], who argued that, with the existence of IP rights, competitive market structure provides higher incentives to innovate.

The association between the use of IP by UK SMEs in 2001 and subsequent performance in 2002 to 2004

This report analyses the 2001 cohort of UK SMEs. The specific focus is on the link between IP activity in 2001 and subsequent performance (to 2004). The 2001 cohort contains 130,082 SMEs of which 3,123 were IP active (2.4%). Specifically, 1,872 SMEs had at least one UK trade mark publication; 697 had one or more Community trade mark registrations; 646 SMEs had one or more UK patents; and 443 had one or more EPO patent publications. The outcome and financial performance of the SMEs is analysed in various ways. Initially, we look at the determinants of survival to 2004. We then look at growth of assets and turnover for the period 2001 to 2004.