Learning curves for Gaussian processes models: fluctuations and universality

Based on a statistical mechanics approach, we develop a method for approximately computing average case learning curves and their sample fluctuations for Gaussian process regression models. We give examples for the Wiener process and show that universal relations (that are independent of the input distribution) between error measures can be derived.

A variational approach to learning curves

We combine the replica approach from statistical physics with a variational approach to analyze learning curves analytically. We apply the method to Gaussian process regression. As a main result we derive approximative relations between empirical error measures, the generalization error and the posterior variance.

An illustration of variable precision rough sets model:an analysis of the findings of the UK Monopolies and Mergers Commission

This paper introduces a new technique in the investigation of limited-dependent variable models. This paper illustrates that variable precision rough set theory (VPRS), allied with the use of a modern method of classification, or discretisation of data, can out-perform the more standard approaches that are employed in economics, such as a probit model. These approaches and certain inductive decision tree methods are compared (through a Monte Carlo simulation approach) in the analysis of the decisions reached by the UK Monopolies and Mergers Committee. We show that, particularly in small samples, the VPRS model can improve on more traditional models, both in-sample, and particularly in out-of-sample prediction. A similar improvement in out-of-sample prediction over the decision tree methods is also shown.

Growth curves of four crustose lichens

The growth curves of four common species of crustose lichens, viz., Buellia aethalea (Ach.) Th. Fr., Lecidea tumida Massai., Rhizocarpon geographicum (L.) DC., and Rhizocarpon reductum Th. Fr. were studied at a site in south Gwynedd, north Wales, UK. Radial growth rates (RGR, mm 1.5 yr-1) were greatest in thalli of R. reductum and least in R. geographicum. Variation in RGR between thalli was greater in B. aethalea and L. tumida than in the species of Rhizocarpon. The relationship between growth rate and thallus diameter was not asymptotic; RGR increasing in smaller thalli to a maximum and then declining in larger diameter thalli. A polynomial curve was fitted to the data; the growth curves being fitted best by a second-order (quadratic) curve, the best fit to this model being shown by B. aethalea. A significant linear regression with a negative slope was also fitted to the growth of the larger thalli of each species. The data suggest that the growth curves of the four crustose lichens differ significantly from the asymptotic curves of foliose lichen species. A phase of declining RGR in larger thalli appears to be characteristic of crustose lichens and is consistent with data from lichenometric studies.

Lexical database enrichment through semi-automated morphological analysis

Derivational morphology proposes meaningful connections between words and is largely unrepresented in lexical databases. This thesis presents a project to enrich a lexical database with morphological links and to evaluate their contribution to disambiguation. A lexical database with sense distinctions was required. WordNet was chosen because of its free availability and widespread use. Its suitability was assessed through critical evaluation with respect to specifications and criticisms, using a transparent, extensible model. The identification of serious shortcomings suggested a portable enrichment methodology, applicable to alternative resources. Although 40% of the most frequent words are prepositions, they have been largely ignored by computational linguists, so addition of prepositions was also required. The preferred approach to morphological enrichment was to infer relations from phenomena discovered algorithmically. Both existing databases and existing algorithms can capture regular morphological relations, but cannot capture exceptions correctly; neither of them provide any semantic information. Some morphological analysis algorithms are subject to the fallacy that morphological analysis can be performed simply by segmentation. Morphological rules, grounded in observation and etymology, govern associations between and attachment of suffixes and contribute to defining the meaning of morphological relationships. Specifying character substitutions circumvents the segmentation fallacy. Morphological rules are prone to undergeneration, minimised through a variable lexical validity requirement, and overgeneration, minimised by rule reformulation and restricting monosyllabic output. Rules take into account the morphology of ancestor languages through co-occurrences of morphological patterns. Multiple rules applicable to an input suffix need their precedence established. The resistance of prefixations to segmentation has been addressed by identifying linking vowel exceptions and irregular prefixes. The automatic affix discovery algorithm applies heuristics to identify meaningful affixes and is combined with morphological rules into a hybrid model, fed only with empirical data, collected without supervision. Further algorithms apply the rules optimally to automatically pre-identified suffixes and break words into their component morphemes. To handle exceptions, stoplists were created in response to initial errors and fed back into the model through iterative development, leading to 100% precision, contestable only on lexicographic criteria. Stoplist length is minimised by special treatment of monosyllables and reformulation of rules. 96% of words and phrases are analysed. 218,802 directed derivational links have been encoded in the lexicon rather than the wordnet component of the model because the lexicon provides the optimal clustering of word senses. Both links and analyser are portable to an alternative lexicon. The evaluation uses the extended gloss overlaps disambiguation algorithm. The enriched model outperformed WordNet in terms of recall without loss of precision. Failure of all experiments to outperform disambiguation by frequency reflects on WordNet sense distinctions.

Length, lexicality, and articulatory suppression in immediate recall:evidence against the articulatory loop

Influential models of short-term memory have attributed the fact that short words are recalled better than longer words in serial recall (the length effect) to articulatory rehearsal. Crucial for this link is the finding that the length effect disappears under articulatory suppression. We show, instead, that, under suppression, the length effect is abolished or reversed for real words but remains robust for nonwords. The latter finding is demonstrated in a variety of conditions: with lists of three and four nonwords, with nonwords drawn from closed and open sets, with spoken and written presentation, and with written and spoken output. Our interpretation is that the standard length effect derives from the number of phonological units to be retained. The length effect is abolished or reversed under suppression because this condition encourages reliance on lexical-semantic representations. Using these representations, longer words can more easily be reconstructed from degraded phonology than shorter words. © 2005 Elsevier Inc. All rights reserved.

Optimizing measurement of subjective amplitude of accommodation with defocus curves

PURPOSE: To determine whether letter sequences and/or lens-presentation order should be randomized when measuring defocus curves and to assess the most appropriate criterion for calculating the subjective amplitude of accommodation (AoA) from defocus curves. SETTING: Eye Clinic, School of Life & Health Sciences, Aston University, Birmingham, United Kingdom. METHODS: Defocus curves (from +3.00 diopters [D] to -3.00 D in 0.50 D steps) for 6 possible combinations of randomized or nonrandomized letter sequences and/or lens-presentation order were measured in a random order in 20 presbyopic subjects. Subjective AoA was calculated from the defocus curves by curve fitting using various published criteria, and each was correlated to subjective push-up AoA. Objective AoA was measured for comparison of blur tolerance and pupil size. RESULTS: Randomization of lens-presentation order and/or letter sequences, or lack of, did not affect the measured defocus curves (P>.05, analysis of variance). The range of defocus that maintains highest achievable visual acuity (allowing for variability of repeated measurement) was better correlated to (r = 0.84) and agreed best with ( 0.50 D) subjective push-up AoA than any other relative or absolute acuity criterion used in previous studies. CONCLUSIONS: Nonrandomized letters and lens presentation on their own did not affect subjective AoA measured by defocus curves, although their combination should be avoided. Quantification of subjective AoA from defocus curves should be standardized to the range of defocus that maintains the best achievable visual acuity.

Multifocal intraocular lens differentiation using defocus curves

Purpose: To determine the most appropriate analysis technique for the differentiation of multifocal intraocular lens (MIOL) designs using defocus curve assessment of visual capability.Methods:Four groups of fifteen subjects were implanted bilaterally with either monofocal intraocular lenses, refractive MIOLs, diffractive MIOLs, or a combination of refractive and diffractive MIOLs. Defocus curves between -5.0D and +1.5D were evaluated using an absolute and relative depth-of-focus method, the direct comparison method and a new 'Area-of-focus' metric. The results were correlated with a subjective perception of near and intermediate vision. Results:Neither depth-of-focus method of analysis were sensitive enough to differentiate between MIOL groups (p>0.05). The direct comparison method indicated that the refractive MIOL group performed better at +1.00, -1.00 and -1.50 D and worse at -3.00, -3.50, -4.00 and -5.00D compared to the diffractive MIOL group (p

High stability interleaved fibre Michelson interferometer for on-line precision displacement measurements

A self-reference fiber Michelson interferometer measurement system, which employs fiber Bragg gratings (FBGs) as in-fiber reflective mirrors and interleaves together two fiber Michelson interferometers that share the common-interferometric-optical path, is presented. One of the fiber interferometers is used to stabilise the system by the use of an electronic feedback loop to compensate the influences resulting from the environmental disturbances, while the other one is used to perform the measurement task. The influences resulting from the environmental disturbances have been eliminated by the compensating action of the electronic feedback loop, this makes the system suitable for on-line precision measurement. By means of the homodyne phase-tracking technique, the linearity of the measurement results of displacement measurements has been very high.

Size distribution curves of senile plaques in patients with Alzheimer’s disease: do plaques grow according to the log-normal model?

The size frequency distributions of diffuse, primitive and cored senile plaques (SP) were studied in single sections of the temporal lobe from 10 patients with Alzheimer’s disease (AD). The size distribution curves were unimodal and positively skewed. The size distribution curve of the diffuse plaques was shifted towards larger plaques while those of the neuritic and cored plaques were shifted towards smaller plaques. The neuritic/diffuse plaque ratio was maximal in the 11 – 30 micron size class and the cored/ diffuse plaque ratio in the 21 – 30 micron size class. The size distribution curves of the three types of plaque deviated significantly from a log-normal distribution. Distributions expressed on a logarithmic scale were ‘leptokurtic’, i.e. with excess of observations near the mean. These results suggest that SP in AD grow to within a more restricted size range than predicted from a log-normal model. In addition, there appear to be differences in the patterns of growth of diffuse, primitive and cored plaques. If neuritic and cored plaques develop from earlier diffuse plaques, then smaller diffuse plaques are more likely to be converted to mature plaques.

A comparison of the growth curves of the foliose lichen Parmelia conspersa determined by a cross-sectional study and by direct measurement

Changes in the radial growth rate (RGR mm/yr) through life were studied in thalli of the foliose lichen Parmelia conspersa by two methods: (1) a cross-sectional study (Study A) in which the RGR was measured in 60 thalli from 0.2 to 13 cm in diameter, and (2) by radial growth measurements over 4.5 years of fragments, consisting of a single major lobe, which were removed from large thalli and glued to pieces of slate (Study B). Both studies suggested there was a phase of increasing RGR in small thalli followed by a more constant phase, the latter beginning at approximately a thallus radius of 6-8 mm. However, in Study B significantly increased RGR was observed during the second 6-month growth period. This phase of growth was more likely to be due to an increase in lobe width than to an effect of climate. In addition, a lobe in a large thallus with both adjacent lobes removed significantly increased in width over 1 year compared with control lobes. These results suggest that (1) mean lobe width in a thallus may be determined by the intensity of marginal competition between adjacent lobes, and (2) changes in lobe width during the life of a lichen thallus may be a factor determining the establishment of the linear phase of growth in foliose lichens. © 1992.

Neural population coding is optimized by discrete tuning curves

The sigmoidal tuning curve that maximizes the mutual information for a Poisson neuron, or population of Poisson neurons, is obtained. The optimal tuning curve is found to have a discrete structure that results in a quantization of the input signal. The number of quantization levels undergoes a hierarchy of phase transitions as the length of the coding window is varied. We postulate, using the mammalian auditory system as an example, that the presence of a subpopulation structure within a neural population is consistent with an optimal neural code.

In search of a theory of list memory: an inquiry into the efects of long-term information on short-term recall

Over recent years, evidence has been accumulating in favour of the importance of long-term information as a variable which can affect the success of short-term recall. Lexicality, word frequency, imagery and meaning have all been shown to augment short term recall performance. Two competing theories as to the causes of this long-term memory influence are outlined and tested in this thesis. The first approach is the order-encoding account, which ascribes the effect to the usage of resources at encoding, hypothesising that word lists which require less effort to process will benefit from increased levels of order encoding, in turn enhancing recall success. The alternative view, trace redintegration theory, suggests that order is automatically encoded phonologically, and that long-term information can only influence the interpretation of the resultant memory trace. The free recall experiments reported here attempted to determine the importance of order encoding as a facilitatory framework and to determine the locus of the effects of long-term information in free recall. Experiments 1 and 2 examined the effects of word frequency and semantic categorisation over a filled delay, and experiments 3 and 4 did the same for immediate recall. Free recall was improved by both long-term factors tested. Order information was not used over a short filled delay, but was evident in immediate recall. Furthermore, it was found that both long-term factors increased the amount of order information retained. Experiment 5 induced an order encoding effect over a filled delay, leaving a picture of short-term processes which are closely associated with long-term processes, and which fit conceptions of short-term memory being part of language processes rather better than either the encoding or the retrieval-based models. Experiments 6 and 7 aimed to determine to what extent phonological processes were responsible for the pattern of results observed. Articulatory suppression affected the encoding of order information where speech rate had no direct influence, suggesting that it is ease of lexical access which is the most important factor in the influence of long-term memory on immediate recall tasks. The evidence presented in this thesis does not offer complete support for either the retrieval-based account or the order encoding account of long-term influence. Instead, the evidence sits best with models that are based upon language-processing. The path urged for future research is to find ways in which this diffuse model can be better specified, and which can take account of the versatility of the human brain.

Automatic indexing and retrieval of encounter-specific evidence for point-of-care support

Evidence-based medicine relies on repositories of empirical research evidence that can be used to support clinical decision making for improved patient care. However, retrieving evidence from such repositories at local sites presents many challenges. This paper describes a methodological framework for automatically indexing and retrieving empirical research evidence in the form of the systematic reviews and associated studies from The Cochrane Library, where retrieved documents are specific to a patient-physician encounter and thus can be used to support evidence-based decision making at the point of care. Such an encounter is defined by three pertinent groups of concepts - diagnosis, treatment, and patient, and the framework relies on these three groups to steer indexing and retrieval of reviews and associated studies. An evaluation of the indexing and retrieval components of the proposed framework was performed using documents relevant for the pediatric asthma domain. Precision and recall values for automatic indexing of systematic reviews and associated studies were 0.93 and 0.87, and 0.81 and 0.56, respectively. Moreover, precision and recall for the retrieval of relevant systematic reviews and associated studies were 0.89 and 0.81, and 0.92 and 0.89, respectively. With minor modifications, the proposed methodological framework can be customized for other evidence repositories. © 2010 Elsevier Inc.