A flexible cost function model with risk

In examining bank cost efficiency in banking inclusion of risk-taking of banks is very important. In this paper we depart from the standard modeling approach and view risk intimately related to the technology. Thus, instead of controlling for risk by viewing them as covariates in the standard cost function we argue that the technology differs with risk, thereby meaning that the parameters of the parametric cost function changes with risk in a fully flexible manner. This is accomplished by viewing the parameters of the cost function as nonparametric functions of risk. We also control for country-specific effects in a fully flexible manner by using them as arguments of the nonparametric functions along with the risk variable. The resulting cost function then becomes semiparametric. The standard parametric model becomes a special case of our semiparametric model. We use the above modeling approach for banks in the EU countries. Actually, European financial integration is seen as a stepping stone for the development of a competitive single EU market that promotes efficiency and increases consumer welfare, changing the risk profile of the European banks. Particularly, financial integration allows more risk diversification and permits banks to use more advanced risk management instruments and systems, however it has at the same time increased the probability of systematic risks. Financial integration has increased the risk of contagion and changed its nature and scope. Consequently the bank’s risk seems to be an important issue to be investigated.

The impact of privatisation and regulation on the water and sewerage industry in England and Wales:a translog cost function approach

After the ten Regional Water Authorities (RWAs) of England and Wales were privatized in November 1989, the successor Water and Sewerage Companies (WASCs) faced a new regulatory regime that was designed to promote economic efficiency while simultaneously improving drinking water and environmental quality. As legally mandated quality improvements necessitated a costly capital investment programme, the industry's economic regulator, the Office of Water Services (Ofwat), implemented a retail price index (RPI)+K pricing system, which was designed to compensate the WASCs for their capital investment programme while also encouraging gains in economic efficiency. In order to analyse jointly the impact of privatization, as well as the impact of increasingly stringent economic and environmental regulation on the WASCs' economic performance, this paper estimates a translog multiple output cost function model for the period 1985–1999. Given the significant costs associated with water quality improvements, the model is augmented to include the impact of drinking water quality and environmental quality on total costs. The model is then employed to determine the extent of scale and scope economies in the water and sewerage industry, as well as the impact of privatization and economic regulation on economic efficiency.

Minimum description length, regularisation and multi-modal data

Relationships between clustering, description length, and regularisation are pointed out, motivating the introduction of a cost function with a description length interpretation and the unusual and useful property of having its minimum approximated by the densest mode of a distribution. A simple inverse kinematics example is used to demonstrate that this property can be used to select and learn one branch of a multi-valued mapping. This property is also used to develop a method for setting regularisation parameters according to the scale on which structure is exhibited in the training data. The regularisation technique is demonstrated on two real data sets, a classification problem and a regression problem.

First year qualifying report: neural networks for extracting wind vectors from satellite scatterometer data

The ERS-1 Satellite was launched in July 1991 by the European Space Agency into a polar orbit at about km800, carrying a C-band scatterometer. A scatterometer measures the amount of radar back scatter generated by small ripples on the ocean surface induced by instantaneous local winds. Operational methods that extract wind vectors from satellite scatterometer data are based on the local inversion of a forward model, mapping scatterometer observations to wind vectors, by the minimisation of a cost function in the scatterometer measurement space.par This report uses mixture density networks, a principled method for modelling conditional probability density functions, to model the joint probability distribution of the wind vectors given the satellite scatterometer measurements in a single cell (the `inverse' problem). The complexity of the mapping and the structure of the conditional probability density function are investigated by varying the number of units in the hidden layer of the multi-layer perceptron and the number of kernels in the Gaussian mixture model of the mixture density network respectively. The optimal model for networks trained per trace has twenty hidden units and four kernels. Further investigation shows that models trained with incidence angle as an input have results comparable to those models trained by trace. A hybrid mixture density network that incorporates geophysical knowledge of the problem confirms other results that the conditional probability distribution is dominantly bimodal.par The wind retrieval results improve on previous work at Aston, but do not match other neural network techniques that use spatial information in the inputs, which is to be expected given the ambiguity of the inverse problem. Current work uses the local inverse model for autonomous ambiguity removal in a principled Bayesian framework. Future directions in which these models may be improved are given.

Minimum description length, regularisation and multi-modal data

Conventional feed forward Neural Networks have used the sum-of-squares cost function for training. A new cost function is presented here with a description length interpretation based on Rissanen's Minimum Description Length principle. It is a heuristic that has a rough interpretation as the number of data points fit by the model. Not concerned with finding optimal descriptions, the cost function prefers to form minimum descriptions in a naive way for computational convenience. The cost function is called the Naive Description Length cost function. Finding minimum description models will be shown to be closely related to the identification of clusters in the data. As a consequence the minimum of this cost function approximates the most probable mode of the data rather than the sum-of-squares cost function that approximates the mean. The new cost function is shown to provide information about the structure of the data. This is done by inspecting the dependence of the error to the amount of regularisation. This structure provides a method of selecting regularisation parameters as an alternative or supplement to Bayesian methods. The new cost function is tested on a number of multi-valued problems such as a simple inverse kinematics problem. It is also tested on a number of classification and regression problems. The mode-seeking property of this cost function is shown to improve prediction in time series problems. Description length principles are used in a similar fashion to derive a regulariser to control network complexity.

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.

A pragmatic Bayesian approach to wind field retrieval

The ERS-1 Satellite was launched in July 1991 by the European Space Agency into a polar orbit at about 800 km, carrying a C-band scatterometer. A scatterometer measures the amount of backscatter microwave radiation reflected by small ripples on the ocean surface induced by sea-surface winds, and so provides instantaneous snap-shots of wind flow over large areas of the ocean surface, known as wind fields. Inherent in the physics of the observation process is an ambiguity in wind direction; the scatterometer cannot distinguish if the wind is blowing toward or away from the sensor device. This ambiguity implies that there is a one-to-many mapping between scatterometer data and wind direction. Current operational methods for wind field retrieval are based on the retrieval of wind vectors from satellite scatterometer data, followed by a disambiguation and filtering process that is reliant on numerical weather prediction models. The wind vectors are retrieved by the local inversion of a forward model, mapping scatterometer observations to wind vectors, and minimising a cost function in scatterometer measurement space. This thesis applies a pragmatic Bayesian solution to the problem. The likelihood is a combination of conditional probability distributions for the local wind vectors given the scatterometer data. The prior distribution is a vector Gaussian process that provides the geophysical consistency for the wind field. The wind vectors are retrieved directly from the scatterometer data by using mixture density networks, a principled method to model multi-modal conditional probability density functions. The complexity of the mapping and the structure of the conditional probability density function are investigated. A hybrid mixture density network, that incorporates the knowledge that the conditional probability distribution of the observation process is predominantly bi-modal, is developed. The optimal model, which generalises across a swathe of scatterometer readings, is better on key performance measures than the current operational model. Wind field retrieval is approached from three perspectives. The first is a non-autonomous method that confirms the validity of the model by retrieving the correct wind field 99% of the time from a test set of 575 wind fields. The second technique takes the maximum a posteriori probability wind field retrieved from the posterior distribution as the prediction. For the third technique, Markov Chain Monte Carlo (MCMC) techniques were employed to estimate the mass associated with significant modes of the posterior distribution, and make predictions based on the mode with the greatest mass associated with it. General methods for sampling from multi-modal distributions were benchmarked against a specific MCMC transition kernel designed for this problem. It was shown that the general methods were unsuitable for this application due to computational expense. On a test set of 100 wind fields the MAP estimate correctly retrieved 72 wind fields, whilst the sampling method correctly retrieved 73 wind fields.

Hand somatosensory subcortical and cortical sources assessed by functional source separation:an EEG study

We propose a novel electroencephalographic application of a recently developed cerebral source extraction method (Functional Source Separation, FSS), which starts from extracranial signals and adds a functional constraint to the cost function of a basic independent component analysis model without requiring solutions to be independent. Five ad-hoc functional constraints were used to extract the activity reflecting the temporal sequence of sensory information processing along the somatosensory pathway in response to the separate left and right median nerve galvanic stimulation. Constraints required only the maximization of the responsiveness at specific latencies following sensory stimulation, without taking into account that any frequency or spatial information. After source extraction, the reliability of identified FS was assessed based on the position of single dipoles fitted on its retroprojected signals and on a discrepancy measure. The FS positions were consistent with previously reported data (two early subcortical sources localized in the brain stem and thalamus, the three later sources in cortical areas), leaving negligible residual activity at the corresponding latencies. The high-frequency component of the oscillatory activity (HFO) of the extracted component was analyzed. The integrity of the low amplitude HFOs was preserved for each FS. On the basis of our data, we suggest that FSS can be an effective tool to investigate the HFO behavior of the different neuronal pools, recruited at successive times after median nerve galvanic stimulation. As FSs are reconstructed along the entire experimental session, directional and dynamic HFO synchronization phenomena can be studied.

Decentralised supply chain formation:a belief propagation-based approach

Decentralised supply chain formation involves determining the set of producers within a network able to supply goods to one or more consumers at the lowest cost. This problem is frequently tackled using auctions and negotiations. In this paper we show how it can be cast as an optimisation of a pairwise cost function. Optimising this class of functions is NP-hard but good approximations to the global minimum can be obtained using Loopy Belief Propagation (LBP). Here we detail a LBP-based approach to the supply chain formation problem, involving decentralised message-passing between potential participants. Our approach is evaluated against a well-known double-auction method and an optimal centralised technique, showing several improvements: it obtains better solutions for most networks that admit a competitive equilibrium Competitive equilibrium as defined in [3] is used as a means of classifying results on certain networks to allow for minor inefficiencies in their auction protocol and agent bidding strategies. while also solving problems where no competitive equilibrium exists, for which the double-auction method frequently produces inefficient solutions.

Vertical and horizontal scope economies in the regulated US electricity power industry

This paper investigates vertical economies between generation and distribution of electric power, and horizontal economies between different types of power generation in the U.S. electric utility industry. Our quadratic cost function model includes three generation output measures (hydro, nuclear and fossil fuels), which allows us to analyze the effect that generation mix has on vertical economies. Our results provide (sample mean) estimates of vertical economies of 8.1% and horizontal economies of 5.4%. An extensive sensitivity analysis is used to show how the scope measures vary across alternative model specifications and firm types. © 2012 Blackwell Publishing Ltd and the Editorial Board of The Journal of Industrial Economics.

Automatic object segmentation from calibrated images

This paper addresses the problem of automatically obtaining the object/background segmentation of a rigid 3D object observed in a set of images that have been calibrated for camera pose and intrinsics. Such segmentations can be used to obtain a shape representation of a potentially texture-less object by computing a visual hull. We propose an automatic approach where the object to be segmented is identified by the pose of the cameras instead of user input such as 2D bounding rectangles or brush-strokes. The key behind our method is a pairwise MRF framework that combines (a) foreground/background appearance models, (b) epipolar constraints and (c) weak stereo correspondence into a single segmentation cost function that can be efficiently solved by Graph-cuts. The segmentation thus obtained is further improved using silhouette coherency and then used to update the foreground/background appearance models which are fed into the next Graph-cut computation. These two steps are iterated until segmentation convergences. Our method can automatically provide a 3D surface representation even in texture-less scenes where MVS methods might fail. Furthermore, it confers improved performance in images where the object is not readily separable from the background in colour space, an area that previous segmentation approaches have found challenging. © 2011 IEEE.

Decentralized supply chain formation using max-sum loopy belief propagation

Supply chain formation is the process by which a set of producers within a network determine the subset of these producers able to form a chain to supply goods to one or more consumers at the lowest cost. This problem has been tackled in a number of ways, including auctions, negotiations, and argumentation-based approaches. In this paper we show how this problem can be cast as an optimization of a pairwise cost function. Optimizing this class of energy functions is NP-hard but efficient approximations to the global minimum can be obtained using loopy belief propagation (LBP). Here we detail a max-sum LBP-based approach to the supply chain formation problem, involving decentralized message-passing between supply chain participants. Our approach is evaluated against a well-known decentralized double-auction method and an optimal centralized technique, showing several improvements on the auction method: it obtains better solutions for most network instances which allow for competitive equilibrium (Competitive equilibrium in Walsh and Wellman is a set of producer costs which permits a Pareto optimal state in which agents in the allocation receive non-negative surplus and agents not in the allocation would acquire non-positive surplus by participating in the supply chain) while also optimally solving problems where no competitive equilibrium exists, for which the double-auction method frequently produces inefficient solutions. © 2012 Wiley Periodicals, Inc.

Stochastic control strategies and adaptive critic methods

Adaptive critic methods have common roots as generalizations of dynamic programming for neural reinforcement learning approaches. Since they approximate the dynamic programming solutions, they are potentially suitable for learning in noisy, nonlinear and nonstationary environments. In this study, a novel probabilistic dual heuristic programming (DHP) based adaptive critic controller is proposed. Distinct to current approaches, the proposed probabilistic (DHP) adaptive critic method takes uncertainties of forward model and inverse controller into consideration. Therefore, it is suitable for deterministic and stochastic control problems characterized by functional uncertainty. Theoretical development of the proposed method is validated by analytically evaluating the correct value of the cost function which satisfies the Bellman equation in a linear quadratic control problem. The target value of the critic network is then calculated and shown to be equal to the analytically derived correct value.