A Manifestly Gauge-Invariant Approach to Quantum Theories of Gauge Fields

In gauge theories, physical histories are represented by space-time connections modulo gauge transformations. The space of histories is thus intrinsically non-linear. The standard framework of constructive quantum field theory has to be extended to face these {\it kinematical} non-linearities squarely. We first present a pedagogical account of this problem and then suggest an avenue for its resolution.Comment: 27 pages, CGPG-94/8-2, latex, contribution to the Cambridge meeting proceeding

Prediction of Clinical Scores from Neuroimaging Data with Censored Likelihood Gaussian Processes

In this paper, we explore the use of Censored Likelihoods in Gaussian Process Regression when predicting bounded clinical scores from neuroimaging data. The standard approach, which uses a Gaussian Likelihood, does not respect the fact that the clinical scores are bounded, and so may produce suboptimal models. Conversely, Censored Likelihoods explicitly model the restricted range of such clinical scores and carry this property through inference. We apply both the standard approach and the Censored Likelihood approach to the prediction of the MMSE score from structural MRI. Overall, we find small improvements in mean squared error when using the Censored Likelihood and in addition, the censored models are more favoured from a Bayesian perspective. We also discuss the qualitative nature of the predictions of the two approaches

Stability-based multivariate mapping using SCoRS

Recently we proposed a feature selection method based on stability theory (SCoRS - Survival Count on Random Subspaces) and showed that the proposed approach was able to improve classification accuracy using different datasets. In the present work we propose: (i) an extension of SCoRS using reproducibility instead of model accuracy as the parameter optimization criterion and (ii) a procedure to estimate the rate of false positive selection associated with the set of features obtained. Our results using the proposed framework showed that, as expected, the optimal parameter was more stable across the cross-validation folds, the spatial map displaying the features selected was less noisy and there was no decrease in classification accuracy. In addition, our results suggest that the estimated false positive rate for the features selected by SCoRS is under 0.05 for both optimization approaches, nevertheless lower when optimizing reproducibility in comparison with the standard optimization approach

Coherent state transforms for spaces of connections

The Segal-Bargmann transform plays an important role in quantum theories of linear fields. Recently, Hall obtained a non-linear analog of this transform for quantum mechanics on Lie groups. Given a compact, connected Lie group G with its normalized Haar measure mu(H), the Hall transform is an isometric isomorphism hem L(2)(G, mu(H)) to H(G(C)) boolean AND L(2)(G(C), v), where G(C) the complexification of G, H(G(C)) the space of holomorphic functions on G(C), and v an appropriate heat-kernel measure on G(C). We extend the Hall transform to the infinite dimensional context of non-Abelian gauge theories by replacing the Lie group G by (a certain extension of) the space A/g of connections module gauge transformations. The resulting ''coherent state transform'' provides a holomorphic representation of the holonomy C* algebra of real gauge fields. This representation is expected to play a key role in a non-perturbative, canonical approach to quantum gravity in 4 dimensions. (C) 1996 Academic Press, Inc.info:eu-repo/semantics/publishedVersio

Predictive Modelling using Neuroimaging Data in the Presence of Confounds

When training predictive models from neuroimaging data, we typically have available non-imaging variables such as age and gender that affect the imaging data but which we may be uninterested in from a clinical perspective. Such variables are commonly referred to as 'confounds'. In this work, we firstly give a working definition for confound in the context of training predictive models from samples of neuroimaging data. We define a confound as a variable which affects the imaging data and has an association with the target variable in the sample that differs from that in the population-of-interest, i.e., the population over which we intend to apply the estimated predictive model. The focus of this paper is the scenario in which the confound and target variable are independent in the population-of-interest, but the training sample is biased due to a sample association between the target and confound. We then discuss standard approaches for dealing with confounds in predictive modelling such as image adjustment and including the confound as a predictor, before deriving and motivating an Instance Weighting scheme that attempts to account for confounds by focusing model training so that it is optimal for the population-of-interest. We evaluate the standard approaches and Instance Weighting in two regression problems with neuroimaging data in which we train models in the presence of confounding, and predict samples that are representative of the population-of-interest. For comparison, these models are also evaluated when there is no confounding present. In the first experiment we predict the MMSE score using structural MRI from the ADNI database with gender as the confound, while in the second we predict age using structural MRI from the IXI database with acquisition site as the confound. Considered over both datasets we find that none of the methods for dealing with confounding gives more accurate predictions than a baseline model which ignores confounding, although including the confound as a predictor gives models that are less accurate than the baseline model. We do find, however, that different methods appear to focus their predictions on specific subsets of the population-of-interest, and that predictive accuracy is greater when there is no confounding present. We conclude with a discussion comparing the advantages and disadvantages of each approach, and the implications of our evaluation for building predictive models that can be used in clinical practice