On the Relationship Between Generalization Error, Hypothesis Complexity, and Sample Complexity for Radial Basis Functions

In this paper, we bound the generalization error of a class of Radial Basis Function networks, for certain well defined function learning tasks, in terms of the number of parameters and number of examples. We show that the total generalization error is partly due to the insufficient representational capacity of the network (because of its finite size) and partly due to insufficient information about the target function (because of finite number of samples). We make several observations about generalization error which are valid irrespective of the approximation scheme. Our result also sheds light on ways to choose an appropriate network architecture for a particular problem.

Multiple Resolution Image Classification

Binary image classifiction is a problem that has received much attention in recent years. In this paper we evaluate a selection of popular techniques in an effort to find a feature set/ classifier combination which generalizes well to full resolution image data. We then apply that system to images at one-half through one-sixteenth resolution, and consider the corresponding error rates. In addition, we further observe generalization performance as it depends on the number of training images, and lastly, compare the system's best error rates to that of a human performing an identical classification task given teh same set of test images.

Justified Generalization: Acquiring Procedures from Examples

This thesis describes an implemented system called NODDY for acquiring procedures from examples presented by a teacher. Acquiring procedures form examples involves several different generalization tasks. Generalization is an underconstrained task, and the main issue of machine learning is how to deal with this underconstraint. The thesis presents two principles for constraining generalization on which NODDY is based. The first principle is to exploit domain based constraints. NODDY demonstrated how such constraints can be used both to reduce the space of possible generalizations to manageable size, and how to generate negative examples out of positive examples to further constrain the generalization. The second principle is to avoid spurious generalizations by requiring justification before adopting a generalization. NODDY demonstrates several different ways of justifying a generalization and proposes a way of ordering and searching a space of candidate generalizations based on how much evidence would be required to justify each generalization. Acquiring procedures also involves three types of constructive generalizations: inferring loops (a kind of group), inferring complex relations and state variables, and inferring predicates. NODDY demonstrates three constructive generalization methods for these kinds of generalization.

Developing the ability for making evaluative judgements.

It is suggested that a more specific emphasis should be placed in undergraduate education on the explicit development of the ability to make evaluative judgements. This higher level cognitive ability is highlighted as the foundation for much sound and successful personal and professional development throughout education, and in lifelong development. Yet it seldom seems to receive the explicit attention which is given in curricula in higher education to analysis and creativity. The paper includes several examples of activities which have been used and judged effective in developing the ability to make evaluative judgements, often at an early stage in undergraduate courses. Keywords: evaluative judgement; personal development; self-assessment; peerassessment; lifelong learning Outline

An assessment of the ability of the stay-green phenotype in Lolium species to provide an improved protein supply for ruminants

Kingston-Smith, A. H., Bollard, A. L., Humphreys, M. O,, Theodorou, M. K. (2002). An assessment of the ability of the stay-green phenotype in Lolium species to provide an improved protein supply for ruminants. Annals of Botany, 89(6), 731-740. Sponsorship: BBSRC/MAFF/Milk Development Council/Meat and Livestock Commission/Industry. RAE2008

Non-anonymous ballot aggregation: an axiomatic generalization of Approval Voting

We study axiomatically situations in which the society agrees to treat voters with different characteristics distinctly. In this setting, we propose a set of intuitive axioms and show that they jointly characterize a new class of voting procedures, called Type-weighted Approval Voting. According to this family, each voter has a strictly positive and finite weight (the weight is necessarily the same for all voters with the same characteristics) and the alternative with the highest number of weighted votes is elected. The implemented voting procedure reduces to Approval Voting in case all voters are identical or the procedure assigns the same weight to all types. Using this idea, we also obtain a new characterization of Approval Voting.

On the Relationship Between the Generalized Equality Classifier and ART 2 Neural Networks

In this paper, we introduce the Generalized Equality Classifier (GEC) for use as an unsupervised clustering algorithm in categorizing analog data. GEC is based on a formal definition of inexact equality originally developed for voting in fault tolerant software applications. GEC is defined using a metric space framework. The only parameter in GEC is a scalar threshold which defines the approximate equality of two patterns. Here, we compare the characteristics of GEC to the ART2-A algorithm (Carpenter, Grossberg, and Rosen, 1991). In particular, we show that GEC with the Hamming distance performs the same optimization as ART2. Moreover, GEC has lower computational requirements than AR12 on serial machines.

Fast Learning VIEWNET Architectures for Recognizing 3-D Objects from Multiple 2-D Views

The recognition of 3-D objects from sequences of their 2-D views is modeled by a family of self-organizing neural architectures, called VIEWNET, that use View Information Encoded With NETworks. VIEWNET incorporates a preprocessor that generates a compressed but 2-D invariant representation of an image, a supervised incremental learning system that classifies the preprocessed representations into 2-D view categories whose outputs arc combined into 3-D invariant object categories, and a working memory that makes a 3-D object prediction by accumulating evidence from 3-D object category nodes as multiple 2-D views are experienced. The simplest VIEWNET achieves high recognition scores without the need to explicitly code the temporal order of 2-D views in working memory. Working memories are also discussed that save memory resources by implicitly coding temporal order in terms of the relative activity of 2-D view category nodes, rather than as explicit 2-D view transitions. Variants of the VIEWNET architecture may also be used for scene understanding by using a preprocessor and classifier that can determine both What objects are in a scene and Where they are located. The present VIEWNET preprocessor includes the CORT-X 2 filter, which discounts the illuminant, regularizes and completes figural boundaries, and suppresses image noise. This boundary segmentation is rendered invariant under 2-D translation, rotation, and dilation by use of a log-polar transform. The invariant spectra undergo Gaussian coarse coding to further reduce noise and 3-D foreshortening effects, and to increase generalization. These compressed codes are input into the classifier, a supervised learning system based on the fuzzy ARTMAP algorithm. Fuzzy ARTMAP learns 2-D view categories that are invariant under 2-D image translation, rotation, and dilation as well as 3-D image transformations that do not cause a predictive error. Evidence from sequence of 2-D view categories converges at 3-D object nodes that generate a response invariant under changes of 2-D view. These 3-D object nodes input to a working memory that accumulates evidence over time to improve object recognition. ln the simplest working memory, each occurrence (nonoccurrence) of a 2-D view category increases (decreases) the corresponding node's activity in working memory. The maximally active node is used to predict the 3-D object. Recognition is studied with noisy and clean image using slow and fast learning. Slow learning at the fuzzy ARTMAP map field is adapted to learn the conditional probability of the 3-D object given the selected 2-D view category. VIEWNET is demonstrated on an MIT Lincoln Laboratory database of l28x128 2-D views of aircraft with and without additive noise. A recognition rate of up to 90% is achieved with one 2-D view and of up to 98.5% correct with three 2-D views. The properties of 2-D view and 3-D object category nodes are compared with those of cells in monkey inferotemporal cortex.

Evaluation of rhizobacterial colonisation and the ability to induce Globodera pallida hatch

Three bacterial isolates, SB13 (Acinetobacter sp.), SB14 (Arthrobacter sp.) and SB15 (Bacillus sp.), were previously isolated from the rhizosphere of sugar beet (Beta vulgaris ssp. vulgaris) plants and shown to increase hatch of potato cyst nematodes in vitro. In this study, the three isolates were assayed for rhizosphere competence. Each isolate was applied to seeds at each of four concentrations (105-108 CFU ml−1) and the inoculated seeds were planted in plastic microcosms containing coarse sand. All three isolates were shown to colonise the rhizosphere, although to differing degrees, with the higher inoculation densities providing significantly better colonisation. The isolates increased sugar beet root and shoot dry weight. Isolates SB14 and SB15 were analysed for their ability to induce in vivo hatch of Globodera pallida in non-sterile soil planted with sugar beet. After 4 and 6 weeks, both isolates had induced significantly greater percentage hatch compared to controls.

Optimal assessment of the ability of children with recurrent respiratory tract infections to produce anti-polysaccharide antibodies.

Specific anti-polysaccharide antibody deficiency (SPAD) is an immune disorder. Diagnostic criteria have not yet been defined clearly. One hundred and seventy-six children evaluated for recurrent respiratory tract infections were analysed retrospectively. For each subject, specific anti-pneumococcal antibodies had been measured with two enzyme-linked immunosorbent assays (ELISAs), one overall assay (OA) using the 23-valent pneumococcal polysaccharide vaccine (23-PPSV) as detecting antigen and the other purified pneumococcal polysaccharide serotypes (serotype-specific assay, SSA) (serotypes 14, 19F and 23F). Antibody levels were measured before (n = 176) and after (n = 93) immunization with the 23-PPSV. Before immunization, low titres were found for 138 of 176 patients (78%) with OA, compared to 20 of 176 patients (11%) with the SSA. We found a significant correlation between OA and SSA results. After immunization, 88% (71 of 81) of the patients considered as responders in the OA test were also responders in the SSA; 93% (71 of 76) of the patients classified as responders according to the SSA were also responders in the OA. SPAD was diagnosed in 8% (seven of 93) of patients on the basis of the absence of response in both tests. Thus, we propose to use OA as a screening test for SPAD before 23-PPSV immunization. After immunization, SSA should be used only in case of a low response in OA. Only the absence of or a very low antibody response detected by both tests should be used as a diagnostic criterion for SPAD.

Beyond signaling and human capital: Education and the revelation of ability

We provide evidence that college graduation plays a direct role in revealing ability to the labor market. Using the NLSY79, our results suggest that ability is observed nearly perfectly for college graduates, but is revealed to the labor market more gradually for high school graduates. Consequently, from the beginning of their careers, college graduates are paid in accordance with their own ability, while the wages of high school graduates are initially unrelated to their own ability. This view of ability revelation in the labor market has considerable power in explaining racial differences in wages, education, and returns to ability.

An active learning approach for rapid characterization of endothelial cells in human tumors.

Currently, no available pathological or molecular measures of tumor angiogenesis predict response to antiangiogenic therapies used in clinical practice. Recognizing that tumor endothelial cells (EC) and EC activation and survival signaling are the direct targets of these therapies, we sought to develop an automated platform for quantifying activity of critical signaling pathways and other biological events in EC of patient tumors by histopathology. Computer image analysis of EC in highly heterogeneous human tumors by a statistical classifier trained using examples selected by human experts performed poorly due to subjectivity and selection bias. We hypothesized that the analysis can be optimized by a more active process to aid experts in identifying informative training examples. To test this hypothesis, we incorporated a novel active learning (AL) algorithm into FARSIGHT image analysis software that aids the expert by seeking out informative examples for the operator to label. The resulting FARSIGHT-AL system identified EC with specificity and sensitivity consistently greater than 0.9 and outperformed traditional supervised classification algorithms. The system modeled individual operator preferences and generated reproducible results. Using the results of EC classification, we also quantified proliferation (Ki67) and activity in important signal transduction pathways (MAP kinase, STAT3) in immunostained human clear cell renal cell carcinoma and other tumors. FARSIGHT-AL enables characterization of EC in conventionally preserved human tumors in a more automated process suitable for testing and validating in clinical trials. The results of our study support a unique opportunity for quantifying angiogenesis in a manner that can now be tested for its ability to identify novel predictive and response biomarkers.

Fear learning circuitry is biased toward generalization of fear associations in posttraumatic stress disorder.

Fear conditioning is an established model for investigating posttraumatic stress disorder (PTSD). However, symptom triggers may vaguely resemble the initial traumatic event, differing on a variety of sensory and affective dimensions. We extended the fear-conditioning model to assess generalization of conditioned fear on fear processing neurocircuitry in PTSD. Military veterans (n=67) consisting of PTSD (n=32) and trauma-exposed comparison (n=35) groups underwent functional magnetic resonance imaging during fear conditioning to a low fear-expressing face while a neutral face was explicitly unreinforced. Stimuli that varied along a neutral-to-fearful continuum were presented before conditioning to assess baseline responses, and after conditioning to assess experience-dependent changes in neural activity. Compared with trauma-exposed controls, PTSD patients exhibited greater post-study memory distortion of the fear-conditioned stimulus toward the stimulus expressing the highest fear intensity. PTSD patients exhibited biased neural activation toward high-intensity stimuli in fusiform gyrus (P<0.02), insula (P<0.001), primary visual cortex (P<0.05), locus coeruleus (P<0.04), thalamus (P<0.01), and at the trend level in inferior frontal gyrus (P=0.07). All regions except fusiform were moderated by childhood trauma. Amygdala-calcarine (P=0.01) and amygdala-thalamus (P=0.06) functional connectivity selectively increased in PTSD patients for high-intensity stimuli after conditioning. In contrast, amygdala-ventromedial prefrontal cortex (P=0.04) connectivity selectively increased in trauma-exposed controls compared with PTSD patients for low-intensity stimuli after conditioning, representing safety learning. In summary, fear generalization in PTSD is biased toward stimuli with higher emotional intensity than the original conditioned-fear stimulus. Functional brain differences provide a putative neurobiological model for fear generalization whereby PTSD symptoms are triggered by threat cues that merely resemble the index trauma.

Layers of generality and types of generalization in pattern activities

Pattern generalization is considered one of the prominent routes for in-troducing students to algebra. However, not all generalizations are al-gebraic. In the use of pattern generalization as a route to algebra, we —teachers and educators— thus have to remain vigilant in order not to confound algebraic generalizations with other forms of dealing with the general. But how to distinguish between algebraic and non-algebraic generalizations? On epistemological and semiotic grounds, in this arti-cle I suggest a characterization of algebraic generalizations. This char-acterization helps to bring about a typology of algebraic and arithmetic generalizations. The typology is illustrated with classroom examples.

Graphical representation and generalization in sequences problems

In this paper we present different ways used by Secondary students to generalize when they try to solve problems involving sequences. 359 Spanish students solved generalization problems in a written test. These problems were posed through particular terms expressed in different representations. We present examples that illustrate different ways of achieving various types of generalization and how students express generalization. We identify graphical representation of generalization as a useful tool of getting other ways of expressing generalization, and we analyze its connection with other ways of expressing it.