Big 4 audit fee premiums for national and office-level industry leadership in the United Kingdom

The pricing of Big 4 industry leadership Is examined for a sample of U.K. publicly-listed companies, and adds to the evidence from the Australian and U.S. audit markets that city-specific industry leadership commands a fee premium. There is a significant fee premium for city-specific industry leaders relative to other Big 4 auditors, but no evidence that either the top-ranked or second-ranked firm nationally commands a fee premium relative to other Big 4 auditors, after controlling for city-level industry leadership. We also test for Big 4 fee premiums relative to non-Big 4 auditors and the U.K. data suggest a three-level hierarchy based on audit fee differentials: (1) Big 4 city-specific industry leaders have the largest fees; (2) other Big 4 auditors (noncity leaders) and second-tier national firms have comparable fees that are lower than Big 4 city leaders but larger than third-tier firms; and (3) third-tier accounting firms have the lowest fees.

Mixture density networks

Minimization of a sum-of-squares or cross-entropy error function leads to network outputs which approximate the conditional averages of the target data, conditioned on the input vector. For classifications problems, with a suitably chosen target coding scheme, these averages represent the posterior probabilities of class membership, and so can be regarded as optimal. For problems involving the prediction of continuous variables, however, the conditional averages provide only a very limited description of the properties of the target variables. This is particularly true for problems in which the mapping to be learned is multi-valued, as often arises in the solution of inverse problems, since the average of several correct target values is not necessarily itself a correct value. In order to obtain a complete description of the data, for the purposes of predicting the outputs corresponding to new input vectors, we must model the conditional probability distribution of the target data, again conditioned on the input vector. In this paper we introduce a new class of network models obtained by combining a conventional neural network with a mixture density model. The complete system is called a Mixture Density Network, and can in principle represent arbitrary conditional probability distributions in the same way that a conventional neural network can represent arbitrary functions. We demonstrate the effectiveness of Mixture Density Networks using both a toy problem and a problem involving robot inverse kinematics.

EM optimization of latent-variable density models

There is currently considerable interest in developing general non-linear density models based on latent, or hidden, variables. Such models have the ability to discover the presence of a relatively small number of underlying `causes' which, acting in combination, give rise to the apparent complexity of the observed data set. Unfortunately, to train such models generally requires large computational effort. In this paper we introduce a novel latent variable algorithm which retains the general non-linear capabilities of previous models but which uses a training procedure based on the EM algorithm. We demonstrate the performance of the model on a toy problem and on data from flow diagnostics for a multi-phase oil pipeline.

GTM: the generative topographic mapping

Latent variable models represent the probability density of data in a space of several dimensions in terms of a smaller number of latent, or hidden, variables. A familiar example is factor analysis which is based on a linear transformations between the latent space and the data space. In this paper we introduce a form of non-linear latent variable model called the Generative Topographic Mapping, for which the parameters of the model can be determined using the EM algorithm. GTM provides a principled alternative to the widely used Self-Organizing Map (SOM) of Kohonen (1982), and overcomes most of the significant limitations of the SOM. We demonstrate the performance of the GTM algorithm on a toy problem and on simulated data from flow diagnostics for a multi-phase oil pipeline.

A hierarchical latent variable model for data visualization

Visualization has proven to be a powerful and widely-applicable tool the analysis and interpretation of data. Most visualization algorithms aim to find a projection from the data space down to a two-dimensional visualization space. However, for complex data sets living in a high-dimensional space it is unlikely that a single two-dimensional projection can reveal all of the interesting structure. We therefore introduce a hierarchical visualization algorithm which allows the complete data set to be visualized at the top level, with clusters and sub-clusters of data points visualized at deeper levels. The algorithm is based on a hierarchical mixture of latent variable models, whose parameters are estimated using the expectation-maximization algorithm. We demonstrate the principle of the approach first on a toy data set, and then apply the algorithm to the visualization of a synthetic data set in 12 dimensions obtained from a simulation of multi-phase flows in oil pipelines and to data in 36 dimensions derived from satellite images.

GTM: the generative topographic mapping

Latent variable models represent the probability density of data in a space of several dimensions in terms of a smaller number of latent, or hidden, variables. A familiar example is factor analysis which is based on a linear transformations between the latent space and the data space. In this paper we introduce a form of non-linear latent variable model called the Generative Topographic Mapping, for which the parameters of the model can be determined using the EM algorithm. GTM provides a principled alternative to the widely used Self-Organizing Map (SOM) of Kohonen (1982), and overcomes most of the significant limitations of the SOM. We demonstrate the performance of the GTM algorithm on a toy problem and on simulated data from flow diagnostics for a multi-phase oil pipeline.

Magnification factors for the GTM algorithm

The Generative Topographic Mapping (GTM) algorithm of Bishop et al. (1997) has been introduced as a principled alternative to the Self-Organizing Map (SOM). As well as avoiding a number of deficiencies in the SOM, the GTM algorithm has the key property that the smoothness properties of the model are decoupled from the reference vectors, and are described by a continuous mapping from a lower-dimensional latent space into the data space. Magnification factors, which are approximated by the difference between code-book vectors in SOMs, can therefore be evaluated for the GTM model as continuous functions of the latent variables using the techniques of differential geometry. They play an important role in data visualization by highlighting the boundaries between data clusters, and are illustrated here for both a toy data set, and a problem involving the identification of crab species from morphological data.

Sparse representation for Gaussian process models

We develop an approach for a sparse representation for Gaussian Process (GP) models in order to overcome the limitations of GPs caused by large data sets. The method is based on a combination of a Bayesian online algorithm together with a sequential construction of a relevant subsample of the data which fully specifies the prediction of the model. Experimental results on toy examples and large real-world datasets indicate the efficiency of the approach.

Hierarchical GTM: Constructing localized non-linear projection manifolds in a principled way

It has been argued that a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex data sets, and therefore a hierarchical visualization system is desirable. In this paper we extend an existing locally linear hierarchical visualization system PhiVis ¸iteBishop98a in several directions: bf(1) We allow for em non-linear projection manifolds. The basic building block is the Generative Topographic Mapping. bf(2) We introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree. General training equations are derived, regardless of the position of the model in the tree. bf(3) Using tools from differential geometry we derive expressions for local directional curvatures of the projection manifold. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. It enables the user to interactively highlight those data in the parent visualization plot which are captured by a child model. We also incorporate into our system a hierarchical, locally selective representation of magnification factors and directional curvatures of the projection manifolds. Such information is important for further refinement of the hierarchical visualization plot, as well as for controlling the amount of regularization imposed on the local models. We demonstrate the principle of the approach on a toy data set and apply our system to two more complex 12- and 19-dimensional data sets.

GTM-based data visualisation with incomplete data

We analyse how the Generative Topographic Mapping (GTM) can be modified to cope with missing values in the training data. Our approach is based on an Expectation -Maximisation (EM) method which estimates the parameters of the mixture components and at the same time deals with the missing values. We incorporate this algorithm into a hierarchical GTM. We verify the method on a toy data set (using a single GTM) and a realistic data set (using a hierarchical GTM). The results show our algorithm can help to construct informative visualisation plots, even when some of the training points are corrupted with missing values.

Hierarchical GTM: constructing localized non-linear projection manifolds in a principled way

It has been argued that a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex data sets, and therefore a hierarchical visualization system is desirable. In this paper we extend an existing locally linear hierarchical visualization system PhiVis ¸iteBishop98a in several directions: bf(1) We allow for em non-linear projection manifolds. The basic building block is the Generative Topographic Mapping (GTM). bf(2) We introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree. General training equations are derived, regardless of the position of the model in the tree. bf(3) Using tools from differential geometry we derive expressions for local directional curvatures of the projection manifold. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. It enables the user to interactively highlight those data in the ancestor visualization plots which are captured by a child model. We also incorporate into our system a hierarchical, locally selective representation of magnification factors and directional curvatures of the projection manifolds. Such information is important for further refinement of the hierarchical visualization plot, as well as for controlling the amount of regularization imposed on the local models. We demonstrate the principle of the approach on a toy data set and apply our system to two more complex 12- and 18-dimensional data sets.

Semi-supervised learning of hierarchical latent trait models for data visualisation

An interactive hierarchical Generative Topographic Mapping (HGTM) ¸iteH_GTM has been developed to visualise complex data sets. In this paper, we build a more general visualisation system by extending the HGTM visualisation system in 3 directions: bf (1) We generalize HGTM to noise models from the exponential family of distributions. The basic building block is the Latent Trait Model (LTM) developed in ¸iteKaban_pami. bf (2) We give the user a choice of initializing the child plots of the current plot in either em interactive, or em automatic mode. In the interactive mode the user interactively selects ``regions of interest'' as in ¸iteH_GTM, whereas in the automatic mode an unsupervised minimum message length (MML)-driven construction of a mixture of LTMs is employed. bf (3) We derive general formulas for magnification factors in latent trait models. Magnification factors are a useful tool to improve our understanding of the visualisation plots, since they can highlight the boundaries between data clusters. The unsupervised construction is particularly useful when high-level plots are covered with dense clusters of highly overlapping data projections, making it difficult to use the interactive mode. Such a situation often arises when visualizing large data sets. We illustrate our approach on a toy example and apply our system to three more complex real data sets.

Dimensionality reduction in complex models

As a part of the Managing Uncertainty in Complex Models (MUCM) project, research at Aston University will develop methods for dimensionality reduction of the input and/or output spaces of models, as seen within the emulator framework. Towards this end this report describes a framework for generating toy datasets, whose underlying structure is understood, to facilitate early investigations of dimensionality reduction methods and to gain a deeper understanding of the algorithms employed, both in terms of how effective they are for given types of models / situations, and also their speed in applications and how this scales with various factors. The framework, which allows the evaluation of both screening and projection approaches to dimensionality reduction, is described. We also describe the screening and projection methods currently under consideration and present some preliminary results. The aim of this draft of the report is to solicit feedback from the project team on the dataset generation framework, the methods we propose to use, and suggestions for extensions that should be considered.

External audit in the National Health Service in England and Wales:a study of an oversight body's control of auditor remuneration

In the National Health Service (NHS) in England and Wales an oversight body, the Audit Commission (AC), defines the scope of the external auditors’ work, appoints the auditors and has oversight of their fees and audit quality. This heavily regulated audit regime mitigates some of the deficiencies observed in high profile corporate failures. Independence, it has been argued, is influenced by the total auditor remuneration paid by the client. In this study we examine total auditor remuneration in a regulated market which seeks to ensure audit independence and audit quality. In particular we undertake rigorous analysis of auditor remuneration by the type of auditor: We place emphasis on the differentiation between private sector firms and the AC’s in-house auditors (District Audit). Individual private audit firms charge premiums (up to 16%) for particular audit work in identified locations, but no premiums were found when we examined total auditor remuneration. The regime appears to permit efficient operation of the audit market while safeguarding both audit independence and standards.

Constructing localized non-linear projection manifolds in a principled way:hierarchical generative topographic mapping

It has been argued that a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex data sets, and therefore a hierarchical visualization system is desirable. In this paper we extend an existing locally linear hierarchical visualization system PhiVis (Bishop98a) in several directions: 1. We allow for em non-linear projection manifolds. The basic building block is the Generative Topographic Mapping. 2. We introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree. General training equations are derived, regardless of the position of the model in the tree. 3. Using tools from differential geometry we derive expressions for local directionalcurvatures of the projection manifold. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. It enables the user to interactively highlight those data in the parent visualization plot which are captured by a child model.We also incorporate into our system a hierarchical, locally selective representation of magnification factors and directional curvatures of the projection manifolds. Such information is important for further refinement of the hierarchical visualization plot, as well as for controlling the amount of regularization imposed on the local models. We demonstrate the principle of the approach on a toy data set andapply our system to two more complex 12- and 19-dimensional data sets.