Abstract We introduce the implicitly constrained least squares (ICLS) classifier, a novel semi-supervised version of the least squares classifier. This classifier minimizes the squared loss on the labeled data among the set of parameters implied by all possible labelings of the unlabeled data. Unlike other discriminative semi-supervised methods, this approach does not introduce explicit additional assumptions into the objective function, but leverages implicit assumptions already present in the choice of the supervised least squares classifier. This method can be formulated as a quadratic programming problem and its solution can be found using a simple gradient descent procedure. We prove that, in a limited 1-dimensional setting, this approach never leads to performance worse than the supervised classifier. Experimental results show that also in the general multidimensional case performance improvements can be expected, both in terms of the squared loss that is intrinsic to the classifier and in terms of the expected classification error.
Semi-supervised learning is a learning paradigm concerned with the study of how computers and natural systems such as humans learn in the presence of both labeled and unlabeled data. Traditionally, learning has been studied either in the unsupervised paradigm (e.g., clustering, outlier detection) where all the data is unlabeled, or in the supervised paradigm (e.g., classification, regression) where all the data is labeled.The goal of semi-supervised learning is to understand how combining labeled and unlabeled data may change the learning behavior, and design algorithms that take advantage of such a combination. Semi-supervised learning is of great interest in machine learning and data mining because it can use readily available unlabeled data to improve supervised learning tasks when the labeled data is scarce or expensive. Semi-supervised learning also shows potential as a quantitative tool to understand human category learning, where most of the input is self-evidently unlabeled. In this introductory book, we present some popular semi-supervised learning models, including self-training, mixture models, co-training and multiview learning, graph-based methods, and semi-supervised support vector machines. For each model, we discuss its basic mathematical formulation. The success of semi-supervised learning depends critically on some underlying assumptions. We emphasize the assumptions made by each model and give counterexamples when appropriate to demonstrate the limitations of the different models. In addition, we discuss semi-supervised learning for cognitive psychology. Finally, we give a computational learning theoretic perspective on semi-supervised learning, and we conclude the book with a brief discussion of open questions in the field. There is disclosed a liquid flow meter comprising a transparent glass tube upon which is positioned a pair of spaced photodetectors. The liquid to be measured is passed through the tube and through the detectors. A supply tank filled with gas at a suitable pressure is connected to a valve which, when actuated, injects into the liquid stream a bubble of predetermined size. Passage of the bubble through the two photodetectors actuates a timing circuit which displays the elapsed time, thereby giving an accurate measurement of flow rate. In part of speech tagging by Hidden Markov Model, a statistical model is used to assign grammatical categories to words in a text. Early work in the field relied on a corpus which had been tagged by a human annotator to train the model. More recently, (1992) suggest that training can be achieved with a minimal lexicon and a limited amount of a priori information about probabilities, by using an Baum-Welch re-estimation to automatically refine the model. In this paper, I report two experiments designed to determine how much manual training information is needed. The first experiment suggests that initial biasing of either lexical or transition probabilities is essential to achieve a good accuracy. The second experiment reveals that there are three distinct patterns of Baum-Welch reestimation. In two of the patterns, the re-estimation ultimately reduces the accuracy of the tagging rather than improving it. The pattern which is applicable can be predicted from the quality of the initial model and the similarity between the tagged training corpus (if any) and the corpus to be tagged. Heuristics for deciding how to use re-estimation in an effective manner are given. The conclusions are broadly in agreement with those of Merialdo (1994), but give greater detail about the contributions of different parts of the model. Motivation: Gene expression profiling has shown great potential in outcome prediction for different types of cancers. Nevertheless, small sample size remains a bottleneck in obtaining robust and accurate classifiers. Traditional supervised learning techniques can only work with labeled data. Consequently, a large number of microarray data that do not have sufficient follow-up information are disregarded. To fully leverage all of the precious data in public databases, we turned to a semi-supervised learning technique, low density separation (LDS). Results: Using a clinically important question of predicting recurrence risk in colorectal cancer patients, we demonstrated that (i) semi-supervised classification improved prediction accuracy as compared with the state of the art supervised method SVM, (ii) performance gain increased with the number of unlabeled samples, (iii) unlabeled data from different institutes could be employed after appropriate processing and (iv) the LDS method is robust with regard to the number of input features. To test the general applicability of this semi-supervised method, we further applied LDS on human breast cancer datasets and also observed superior performance. Our results demonstrated great potential of semi-supervised learning in gene expression-based outcome prediction for cancer patients. Contact: ude.tlibrednav@gnahz.gnib Supplementary Information: Supplementary data are available at Bioinformatics online. This paper analyzes the performance of semi-supervised learning of mixture models. We show that unlabeled data can lead to an increase in classification error even in situations where additional labeled data would decrease classification error. We present a mathematical analysis of this "degradation" phenomenon and show that it is due to the fact that bias may be adversely affected by unlabeled data. We discuss the impact of these theoretical results to practical situations.  Shotgun proteomics uses liquid chromatography-tandem mass spectrometry to identify proteins in complex biological samples. We describe an algorithm, called Percolator, for improving the rate of confident peptide identifications from a collection of tandem mass spectra. Percolator uses semi-supervised machine learning to discriminate between correct and decoy spectrum identifications, correctly assigning peptides to 17 more spectra from a tryptic Saccharomyces cerevisiae dataset, and up to 77 more spectra from non-tryptic digests, relative to a fully supervised approach. This paper shows that the accuracy of learned text classifiers can be improved by augmenting a small number of labeled training documents with a large pool of unlabeled documents. This is important because in many text classification problems obtaining training labels is expensive, while large quantities of unlabeled documents are readily available. We introduce an algorithm for learning from labeled and unlabeled documents based on the combination of Expectation-Maximization (EM) and a naive Bayes classifier. The algorithm first trains a classifier using the available labeled documents, and probabilistically labels the unlabeled documents. It then trains a new classifier using the labels for all the documents, and iterates to convergence. This basic EM procedure works well when the data conform to the generative assumptions of the model. However these assumptions are often violated in practice, and poor performance can result. We present two extensions to the algorithm that improve classification accuracy under these conditions: (1) a weighting factor to modulate the contribution of the unlabeled data, and (2) the use of multiple mixture components per class. Experimental results, obtained using text from three different real-world tasks, show that the use of unlabeled data reduces classification error by up to 30 .