Safe semi-supervised learning based on weighted likelihood.

We are interested in developing a safe semi-supervised learning that works in any situation. Semi-supervised learning postulates that n(') unlabeled data are available in addition to n labeled data. However, almost all of the previous semi-supervised methods require additional assumptions (not only unlabeled data) to make improvements on supervised learning. If such assumptions are not met, then the methods possibly perform worse than supervised learning. Sokolovska, Cappé, and Yvon (2008) proposed a semi-supervised method based on a weighted likelihood approach. They proved that this method asymptotically never performs worse than supervised learning (i.e., it is safe) without any assumption. Their method is attractive because it is easy to implement and is potentially general. Moreover, it is deeply related to a certain statistical paradox. However, the method of Sokolovska et al. (2008) assumes a very limited situation, i.e., classification, discrete covariates, n(')→∞ and a maximum likelihood estimator. In this paper, we extend their method by modifying the weight. We prove that our proposal is safe in a significantly wide range of situations as long as n≤n('). Further, we give a geometrical interpretation of the proof of safety through the relationship with the above-mentioned statistical paradox. Finally, we show that the above proposal is asymptotically safe even when n(')

A simple optimization can improve the performance of single feature polymorphism detection by Affymetrix expression arrays.

BACKGROUND: High-density oligonucleotide arrays are effective tools for genotyping numerous loci simultaneously. In small genome species (genome size: < approximately 300 Mb), whole-genome DNA hybridization to expression arrays has been used for various applications. In large genome species, transcript hybridization to expression arrays has been used for genotyping. Although rice is a fully sequenced model plant of medium genome size (approximately 400 Mb), there are a few examples of the use of rice oligonucleotide array as a genotyping tool. RESULTS: We compared the single feature polymorphism (SFP) detection performance of whole-genome and transcript hybridizations using the Affymetrix GeneChip Rice Genome Array, using the rice cultivars with full genome sequence, japonica cultivar Nipponbare and indica cultivar 93-11. Both genomes were surveyed for all probe target sequences. Only completely matched 25-mer single copy probes of the Nipponbare genome were extracted, and SFPs between them and 93-11 sequences were predicted. We investigated optimum conditions for SFP detection in both whole genome and transcript hybridization using differences between perfect match and mismatch probe intensities of non-polymorphic targets, assuming that these differences are representative of those between mismatch and perfect targets. Several statistical methods of SFP detection by whole-genome hybridization were compared under the optimized conditions. Causes of false positives and negatives in SFP detection in both types of hybridization were investigated. CONCLUSIONS: The optimizations allowed a more than 20% increase in true SFP detection in whole-genome hybridization and a large improvement of SFP detection performance in transcript hybridization. Significance analysis of the microarray for log-transformed raw intensities of PM probes gave the best performance in whole genome hybridization, and 22,936 true SFPs were detected with 23.58% false positives by whole genome hybridization. For transcript hybridization, stable SFP detection was achieved for highly expressed genes, and about 3,500 SFPs were detected at a high sensitivity (> 50%) in both shoot and young panicle transcripts. High SFP detection performances of both genome and transcript hybridizations indicated that microarrays of a complex genome (e.g., of Oryza sativa) can be effectively utilized for whole genome genotyping to conduct mutant mapping and analysis of quantitative traits such as gene expression levels.

Boosting method for local learning in statistical pattern recognition.

We propose a local boosting method in classification problems borrowing from an idea of the local likelihood method. Our proposal, local boosting, includes a simple device for localization for computational feasibility. We proved the Bayes risk consistency of the local boosting in the framework of Probably approximately correct learning. Inspection of the proof provides a useful viewpoint for comparing ordinary boosting and local boosting with respect to the estimation error and the approximation error. Both boosting methods have the Bayes risk consistency if their approximation errors decrease to zero. Compared to ordinary boosting, local boosting may perform better by controlling the trade-off between the estimation error and the approximation error. Ordinary boosting with complicated base classifiers or other strong classification methods, including kernel machines, may have classification performance comparable to local boosting with simple base classifiers, for example, decision stumps. Local boosting, however, has an advantage with respect to interpretability. Local boosting with simple base classifiers offers a simple way to specify which features are informative and how their values contribute to a classification rule even though locally. Several numerical studies on real data sets confirm these advantages of local boosting.

Common peak approach using mass spectrometry data sets for predicting the effects of anticancer drugs on breast cancer.

We propose a method for biomarker discovery from mass spectrometry data, improving the common peak approach developed by Fushiki et al. (BMC Bioinformatics, 7:358, 2006). The common peak method is a simple way to select the sensible peaks that are shared with many subjects among all detected peaks by combining a standard spectrum alignment and kernel density estimates. The key idea of our proposed method is to apply the common peak approach to each class label separately. Hence, the proposed method gains more informative peaks for predicting class labels, while minor peaks associated with specific subjects are deleted correctly. We used a SELDI-TOF MS data set from laser microdissected cancer tissues for predicting the treatment effects of neoadjuvant therapy using an anticancer drug on breast cancer patients. The AdaBoost algorithm is adopted for pattern recognition, based on the set of candidate peaks selected by the proposed method. The analysis gives good performance in the sense of test errors for classifying the class labels for a given feature vector of selected peak values.