The sample complexity of pattern classification with neural networks: the size of the weights is more important than the size of the network

Sample complexity results from computational learning theory, when applied to neural network learning for pattern classification problems, suggest that for good generalization performance the number of training examples should grow at least linearly with the number of adjustable parameters in the network. Results in this paper show that if a large neural network is used for a pattern classification problem and the learning algorithm finds a network with small weights that has small squared error on the training patterns, then the generalization performance depends on the size of the weights rather than the number of weights. For example, consider a two-layer feedforward network of sigmoid units, in which the sum of the magnitudes of the weights associated with each unit is bounded by A and the input dimension is n. We show that the misclassification probability is no more than a certain error estimate (that is related to squared error on the training set) plus A3 √((log n)/m) (ignoring log A and log m factors), where m is the number of training patterns. This may explain the generalization performance of neural networks, particularly when the number of training examples is considerably smaller than the number of weights. It also supports heuristics (such as weight decay and early stopping) that attempt to keep the weights small during training. The proof techniques appear to be useful for the analysis of other pattern classifiers: when the input domain is a totally bounded metric space, we use the same approach to give upper bounds on misclassification probability for classifiers with decision boundaries that are far from the training examples.

A learning-based approach to reactive security

Despite the conventional wisdom that proactive security is superior to reactive security, we show that reactive security can be competitive with proactive security as long as the reactive defender learns from past attacks instead of myopically overreacting to the last attack. Our game-theoretic model follows common practice in the security literature by making worst-case assumptions about the attacker: we grant the attacker complete knowledge of the defender’s strategy and do not require the attacker to act rationally. In this model, we bound the competitive ratio between a reactive defense algorithm (which is inspired by online learning theory) and the best fixed proactive defense. Additionally, we show that, unlike proactive defenses, this reactive strategy is robust to a lack of information about the attacker’s incentives and knowledge.

Common variation in the fibroblast growth factor receptor 2 gene is not associated with endometriosis risk

BACKGROUND Endometriosis is a polygenic disease with a complex and multifactorial aetiology that affects 8-10% of women of reproductive age. Epidemiological data support a link between endometriosis and cancers of the reproductive tract. Fibroblast growth factor receptor 2 (FGFR2) has recently been implicated in both endometrial and breast cancer. Our previous studies on endometriosis identified significant linkage to a novel susceptibility locus on chromosome 10q26 and the FGFR2 gene maps within this linkage region. We therefore hypothesized that variation in FGFR2 may contribute to the risk of endometriosis. METHODS We genotyped 13 single nucleotide polymorphisms (SNPs) densely covering a 27 kb region within intron 2 of FGFR2 including two SNPs (rs2981582 and rs1219648) significantly associated with breast cancer and a total 40 tagSNPs across 150 kb of the FGFR2 gene. SNPs were genotyped in 958 endometriosis cases and 959 unrelated controls. RESULTS We found no evidence for association between endometriosis and FGFR2 intron 2 SNPs or SNP haplotypes and no evidence for association between endometriosis and variation across the FGFR2 gene. CONCLUSIONS Common variation in the breast-cancer implicated intron 2 and other highly plausible causative candidate regions of FGFR2 do not appear to be a major contributor to endometriosis susceptibility in our large Australian sample.

Generalized binomial Tau-leap method for biochemical kinetics incorporating both delay and intrinsic noise

The delay stochastic simulation algorithm (DSSA) by Barrio et al. [Plos Comput. Biol.2, 117–E (2006)] was developed to simulate delayed processes in cell biology in the presence of intrinsic noise, that is, when there are small-to-moderate numbers of certain key molecules present in a chemical reaction system. These delayed processes can faithfully represent complex interactions and mechanisms that imply a number of spatiotemporal processes often not explicitly modeled such as transcription and translation, basic in the modeling of cell signaling pathways. However, for systems with widely varying reaction rate constants or large numbers of molecules, the simulation time steps of both the stochastic simulation algorithm (SSA) and the DSSA can become very small causing considerable computational overheads. In order to overcome the limit of small step sizes, various τ-leap strategies have been suggested for improving computational performance of the SSA. In this paper, we present a binomial τ- DSSA method that extends the τ-leap idea to the delay setting and avoids drawing insufficient numbers of reactions, a common shortcoming of existing binomial τ-leap methods that becomes evident when dealing with complex chemical interactions. The resulting inaccuracies are most evident in the delayed case, even when considering reaction products as potential reactants within the same time step in which they are produced. Moreover, we extend the framework to account for multicellular systems with different degrees of intercellular communication. We apply these ideas to two important genetic regulatory models, namely, the hes1 gene, implicated as a molecular clock, and a Her1/Her 7 model for coupled oscillating cells.

Manufacturing practices and performances: A Malaysian study

The purpose of this study is to identify the most common manufacturing practices adopted by the Malaysian manufacturers, company performance factors and relationship between practices and performances. To fulfil the study objectives, 400 manufacturers were surveyed by a standard 400 questionnaire. Three research methodologies such as descriptive analysis, ANOVA and regression analysis have been employed in this study. The analysis revealed that Malaysian manufacturers focus on optimizing three critical performance factors: product development, less customer return rate and on time delivery (OTD). The most important competitive factor was found to be company reputation and design and manufacturing capacity is the least important factor. The findings also proved that manufacturing practices significantly influence company performances