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.

Distributed algorithms for global optimization on sparse networks of arbitrary bandwidths

The optimization of resource allocation in sparse networks with real variables is studied using methods of statistical physics. Efficient distributed algorithms are devised on the basis of insight gained from the analysis and are examined using numerical simulations, showing excellent performance and full agreement with the theoretical results.

The influence of memory in a threshold model for distributed task assignment

A nature inspired decentralised multi-agent algorithm is proposed to solve a problem of distributed task selection in which cities produce and store batches of different mail types. Agents must collect and process the mail batches, without a priori knowledge of the available mail at the cities or inter-agent communication. In order to process a different mail type than the previous one, agents must undergo a change-over during which it remains inactive. We propose a threshold based algorithm in order to maximise the overall efficiency (the average amount of mail collected). We show that memory, i.e. the possibility for agents to develop preferences for certain cities, not only leads to emergent cooperation between agents, but also to a significant increase in efficiency (above the theoretical upper limit for any memoryless algorithm), and we systematically investigate the influence of the various model parameters. Finally, we demonstrate the flexibility of the algorithm to changes in circumstances, and its excellent scalability.

Knowledge transfer in globally distributed teams:the role of transactive memory

This paper explores the role of transactive memory in enabling knowledge transfer between globally distributed teams. While the information systems literature has recently acknowledged the role transactive memory plays in improving knowledge processes and performance in colocated teams, little is known about its contribution to distributed teams. To contribute to filling this gap, knowledge-transfer challenges and processes between onsite and offshore teams were studied at TATA Consultancy Services. In particular, the paper describes the transfer of knowledge between onsite and offshore teams through encoding, storing and retrieving processes. An in-depth case study of globally distributed software development projects was carried out, and a qualitative, interpretive approach was adopted. The analysis of the case suggests that in order to overcome differences derived from the local contexts of the onsite and offshore teams (e.g. different work routines, methodologies and skills), some specific mechanisms supporting the development of codified and personalized ‘directories’ were introduced. These include the standardization of templates and methodologies across the remote sites as well as frequent teleconferencing sessions and occasional short visits. These mechanisms contributed to the development of the notion of ‘who knows what’ across onsite and offshore teams despite the challenges associated with globally distributed teams, and supported the transfer of knowledge between onsite and offshore teams. The paper concludes by offering theoretical and practical implications.

Resource allocation in sparse graphs

Resource allocation in sparsely connected networks, a representative problem of systems with real variables, is studied using the replica and Bethe approximation methods. An efficient distributed algorithm is devised on the basis of insights gained from the analysis and is examined using numerical simulations,showing excellent performance and full agreement with the theoretical results. The physical properties of the resource allocation model are discussed.

Message passing for task redistribution on sparse graphs

The problem of resource allocation in sparse graphs with real variables is studied using methods of statistical physics. An efficient distributed algorithm is devised on the basis of insight gained from the analysis and is examined using numerical simulations, showing excellent performance and full agreement with the theoretical results.

Parallel geostatistics for sparse and dense datasets

Very large spatially-referenced datasets, for example, those derived from satellite-based sensors which sample across the globe or large monitoring networks of individual sensors, are becoming increasingly common and more widely available for use in environmental decision making. In large or dense sensor networks, huge quantities of data can be collected over small time periods. In many applications the generation of maps, or predictions at specific locations, from the data in (near) real-time is crucial. Geostatistical operations such as interpolation are vital in this map-generation process and in emergency situations, the resulting predictions need to be available almost instantly, so that decision makers can make informed decisions and define risk and evacuation zones. It is also helpful when analysing data in less time critical applications, for example when interacting directly with the data for exploratory analysis, that the algorithms are responsive within a reasonable time frame. Performing geostatistical analysis on such large spatial datasets can present a number of problems, particularly in the case where maximum likelihood. Although the storage requirements only scale linearly with the number of observations in the dataset, the computational complexity in terms of memory and speed, scale quadratically and cubically respectively. Most modern commodity hardware has at least 2 processor cores if not more. Other mechanisms for allowing parallel computation such as Grid based systems are also becoming increasingly commonly available. However, currently there seems to be little interest in exploiting this extra processing power within the context of geostatistics. In this paper we review the existing parallel approaches for geostatistics. By recognising that diffeerent natural parallelisms exist and can be exploited depending on whether the dataset is sparsely or densely sampled with respect to the range of variation, we introduce two contrasting novel implementations of parallel algorithms based on approximating the data likelihood extending the methods of Vecchia [1988] and Tresp [2000]. Using parallel maximum likelihood variogram estimation and parallel prediction algorithms we show that computational time can be significantly reduced. We demonstrate this with both sparsely sampled data and densely sampled data on a variety of architectures ranging from the common dual core processor, found in many modern desktop computers, to large multi-node super computers. To highlight the strengths and weaknesses of the diffeerent methods we employ synthetic data sets and go on to show how the methods allow maximum likelihood based inference on the exhaustive Walker Lake data set.

Distributed routing algorithms for interconnected FDDI LANS

The Fibre Distributed Data Interface (FDDI) represents the new generation of local area networks (LANs). These high speed LANs are capable of supporting up to 500 users over a 100 km distance. User traffic is expected to be as diverse as file transfers, packet voice and video. As the proliferation of FDDI LANs continues, the need to interconnect these LANs arises. FDDI LAN interconnection can be achieved in a variety of different ways. Some of the most commonly used today are public data networks, dial up lines and private circuits. For applications that can potentially generate large quantities of traffic, such as an FDDI LAN, it is cost effective to use a private circuit leased from the public carrier. In order to send traffic from one LAN to another across the leased line, a routing algorithm is required. Much research has been done on the Bellman-Ford algorithm and many implementations of it exist in computer networks. However, due to its instability and problems with routing table loops it is an unsatisfactory algorithm for interconnected FDDI LANs. A new algorithm, termed ISIS which is being standardized by the ISO provides a far better solution. ISIS will be implemented in many manufacturers routing devices. In order to make the work as practical as possible, this algorithm will be used as the basis for all the new algorithms presented. The ISIS algorithm can be improved by exploiting information that is dropped by that algorithm during the calculation process. A new algorithm, called Down Stream Path Splits (DSPS), uses this information and requires only minor modification to some of the ISIS routing procedures. DSPS provides a higher network performance, with very little additional processing and storage requirements. A second algorithm, also based on the ISIS algorithm, generates a massive increase in network performance. This is achieved by selecting alternative paths through the network in times of heavy congestion. This algorithm may select the alternative path at either the originating node, or any node along the path. It requires more processing and memory storage than DSPS, but generates a higher network power. The final algorithm combines the DSPS algorithm with the alternative path algorithm. This is the most flexible and powerful of the algorithms developed. However, it is somewhat complex and requires a fairly large storage area at each node. The performance of the new routing algorithms is tested in a comprehensive model of interconnected LANs. This model incorporates the transport through physical layers and generates random topologies for routing algorithm performance comparisons. Using this model it is possible to determine which algorithm provides the best performance without introducing significant complexity and storage requirements.

Inference and optimization of real edges on sparse graphs:A statistical physics perspective

Inference and optimization of real-value edge variables in sparse graphs are studied using the Bethe approximation and replica method of statistical physics. Equilibrium states of general energy functions involving a large set of real edge variables that interact at the network nodes are obtained in various cases. When applied to the representative problem of network resource allocation, efficient distributed algorithms are also devised. Scaling properties with respect to the network connectivity and the resource availability are found, and links to probabilistic Bayesian approximation methods are established. Different cost measures are considered and algorithmic solutions in the various cases are devised and examined numerically. Simulation results are in full agreement with the theory. © 2007 The American Physical Society.

Competition for shortest paths on sparse graphs

Optimal paths connecting randomly selected network nodes and fixed routers are studied analytically in the presence of a nonlinear overlap cost that penalizes congestion. Routing becomes more difficult as the number of selected nodes increases and exhibits ergodicity breaking in the case of multiple routers. The ground state of such systems reveals nonmonotonic complex behaviors in average path length and algorithmic convergence, depending on the network topology, and densities of communicating nodes and routers. A distributed linearly scalable routing algorithm is also devised. © 2012 American Physical Society.

Dynamic causal modeling of load-dependent modulation of effective connectivity within the verbal working memory network

Neuroimaging studies have consistently shown that working memory (WM) tasks engage a distributed neural network that primarily includes the dorsolateral prefrontal cortex, the parietal cortex, and the anterior cingulate cortex. The current challenge is to provide a mechanistic account of the changes observed in regional activity. To achieve this, we characterized neuroplastic responses in effective connectivity between these regions at increasing WM loads using dynamic causal modeling of functional magnetic resonance imaging data obtained from healthy individuals during a verbal n-back task. Our data demonstrate that increasing memory load was associated with (a) right-hemisphere dominance, (b) increasing forward (i.e., posterior to anterior) effective connectivity within the WM network, and (c) reduction in individual variability in WM network architecture resulting in the right-hemisphere forward model reaching an exceedance probability of 99% in the most demanding condition. Our results provide direct empirical support that task difficulty, in our case WM load, is a significant moderator of short-term plasticity, complementing existing theories of task-related reduction in variability in neural networks. Hum Brain Mapp, 2013. © 2013 Wiley Periodicals, Inc.

Message-passing for inference and optimization of real variables on sparse graphs

The inference and optimization in sparse graphs with real variables is studied using methods of statistical mechanics. Efficient distributed algorithms for the resource allocation problem are devised. Numerical simulations show excellent performance and full agreement with the theoretical results. © Springer-Verlag Berlin Heidelberg 2006.

An improved memory management scheme for large scale graph computing engine GraphChi

GraphChi is the first reported disk-based graph engine that can handle billion-scale graphs on a single PC efficiently. GraphChi is able to execute several advanced data mining, graph mining and machine learning algorithms on very large graphs. With the novel technique of parallel sliding windows (PSW) to load subgraph from disk to memory for vertices and edges updating, it can achieve data processing performance close to and even better than those of mainstream distributed graph engines. GraphChi mentioned that its memory is not effectively utilized with large dataset, which leads to suboptimal computation performances. In this paper we are motivated by the concepts of 'pin ' from TurboGraph and 'ghost' from GraphLab to propose a new memory utilization mode for GraphChi, which is called Part-in-memory mode, to improve the GraphChi algorithm performance. The main idea is to pin a fixed part of data inside the memory during the whole computing process. Part-in-memory mode is successfully implemented with only about 40 additional lines of code to the original GraphChi engine. Extensive experiments are performed with large real datasets (including Twitter graph with 1.4 billion edges). The preliminary results show that Part-in-memory mode memory management approach effectively reduces the GraphChi running time by up to 60% in PageRank algorithm. Interestingly it is found that a larger portion of data pinned in memory does not always lead to better performance in the case that the whole dataset cannot be fitted in memory. There exists an optimal portion of data which should be kept in the memory to achieve the best computational performance.

Benchmarking of distributed computing engines spark and GraphLab for big data analytics

In this paper we evaluate and compare two representativeand popular distributed processing engines for large scalebig data analytics, Spark and graph based engine GraphLab. Wedesign a benchmark suite including representative algorithmsand datasets to compare the performances of the computingengines, from performance aspects of running time, memory andCPU usage, network and I/O overhead. The benchmark suite istested on both local computer cluster and virtual machines oncloud. By varying the number of computers and memory weexamine the scalability of the computing engines with increasingcomputing resources (such as CPU and memory). We also runcross-evaluation of generic and graph based analytic algorithmsover graph processing and generic platforms to identify thepotential performance degradation if only one processing engineis available. It is observed that both computing engines showgood scalability with increase of computing resources. WhileGraphLab largely outperforms Spark for graph algorithms, ithas close running time performance as Spark for non-graphalgorithms. Additionally the running time with Spark for graphalgorithms over cloud virtual machines is observed to increaseby almost 100% compared to over local computer clusters.