We review the literature on semi-supervised learning, which is an area in machine learning and more generally, artificial intelligence. There has been a whole spectrum of interesting ideas on how to learn from both labeled and unlabeled data, i.e. semi-supervised learning. This document is a chapter excerpt from the author’s doctoral thesis (Zhu, 2005). However the author plans to update the online version frequently to incorporate the latest development in the field. Please obtain the latest version at http://www.cs.wisc.edu/~jerryzhu/pub/ssl_survey.pdf

We propose a family of learning algorithms based on a new form of regularization that allows us to exploit the geometry of the marginal distribution. We focus on a semi-supervised framework that incorporates labeled and unlabeled data in a general-purpose learner. Some transductive graph learning algorithms and standard methods including Support Vector Machines and Regularized Least Squares can be obtained as special cases. We utilize properties of Reproducing Kernel Hilbert spaces to prove new Representer theorems that provide theoretical basis for the algorithms. As a result (in contrast to purely graph-based approaches) we obtain a natural out-of-sample extension to novel examples and so are able to handle both transductive and truly semi-supervised settings. We present experimental evidence suggesting that our semi-supervised algorithms are able to use unlabeled data effectively. Finally we have a brief discussion of unsupervised and fully supervised learning within our general framework. 1.

We consider the task of reinforcement learning with linear value function approximation. Temporal difference algorithms, and in particular the Least-Squares Temporal Difference (LSTD) algorithm, provide a method for learning the parameters of the value function, but when the number of features is large this algorithm can over-fit to the data and is computationally expensive. In this paper, we propose a regularization framework for the LSTD algorithm that overcomes these difficulties. In particular, we focus on the case of l1 regularization, which is robust to irrelevant features and also serves as a method for feature selection. Although the l1 regularized LSTD solution cannot be expressed as a convex optimization problem, we present an algorithm similar to the Least Angle Regression (LARS) algorithm that can efficiently compute the optimal solution. Finally, we demonstrate the performance of the algorithm experimentally. 1.

The construction of appearance-based object detection systems is time-consuming and difficult because a large number of training examples must be collected and manually labeled in order to capture variations in object appearance. Semi-supervised training is a means for reducing the effort needed to prepare the training set by training the model with a small number of fully labeled examples and an additional set of unlabeled or weakly labeled examples. In this work we present a semi-supervised approach to training object detection systems based on self-training. We implement our approach as a wrapper around the training process of an existing object detector and present empirical results. The key contributions of this empirical study is to demonstrate that a model trained in this manner can achieve results comparable to a model trained in the traditional manner using a much larger set of fully labeled data, and that a training data selection metric that is defined independently of the detector greatly outperforms a selection metric based on the detection confidence generated by the detector.

This paper presents multi-conditional learning (MCL), a training criterion based on a product of multiple conditional likelihoods. When combining the traditional conditional probability of “label given input ” with a generative probability of “input given label ” the later acts as a surprisingly effective regularizer. When applied to models with latent variables, MCL combines the structure-discovery capabilities of generative topic models, such as latent Dirichlet allocation and the exponential family harmonium, with the accuracy and robustness of discriminative classifiers, such as logistic regression and conditional random fields. We present results on several standard text data sets showing significant reductions in classification error due to MCL regularization, and substantial gains in precision and recall due to the latent structure discovered under MCL.

A graph-based prior is proposed for parametric semi-supervised classification. The prior utilizes both labelled and unlabelled data; it also integrates features from multiple views of a given sample (e.g., multiple sensors), thus implementing a Bayesian form of co-training. An EM algorithm for training the classifier automatically adjusts the tradeoff between the contributions of: (a) the labelled data; (b) the unlabelled data; and (c) the co-training information. Active label query selection is performed using a mutual information based criterion that explicitly uses the unlabelled data and the co-training information. Encouraging results are presented on public benchmarks and on measured data from single and multiple sensors. 1

In many modern large-scale learning applications, the amount of unlabeled data far exceeds that of labeled data. A common instance of this problem is the transductive setting where the unlabeled test points are known to the learning algorithm. This paper presents a study of regression problems in that setting. It presents explicit VC-dimension error bounds for transductive regression that hold for all bounded loss functions and coincide with the tight classification bounds of Vapnik when applied to classification. It also presents a new transductive regression algorithm inspired by our bound that admits a primal and kernelized closedform solution and deals efficiently with large amounts of unlabeled data. The algorithm exploits the position of unlabeled points to locally estimate their labels and then uses a global optimization to ensure robust predictions. Our study also includes the results of experiments with several publicly available regression data sets with up to 20,000 unlabeled examples. The comparison with other transductive regression algorithms shows that it performs well and that it can scale to large data sets. 1

We provide a principle for semi-supervised learning based on optimizing the rate of communicating labels for unlabeled points with side information.

Although semi-supervised learning has been an active area of research, its use in deployed applications is still relatively rare because the methods are often difficult to implement, fragile in tuning, or lacking in scalability. This paper presents expectation regularization, a semi-supervised learning method for exponential family parametric models that augments the traditional conditional label-likelihood objective function with an additional term that encourages model predictions on unlabeled data to match certain expectations—such as label priors. The method is extremely easy to implement, scales as well as logistic regression, and can handle non-independent features. We present experiments on five different data sets, showing accuracy improvements over other semi-supervised methods. 1.

We describe a new scalable algorithm for semi-supervised training of conditional random fields (CRF) and its application to partof-speech (POS) tagging. The algorithm uses a similarity graph to encourage similar n-grams to have similar POS tags. We demonstrate the efficacy of our approach on a domain adaptation task, where we assume that we have access to large amounts of unlabeled data from the target domain, but no additional labeled data. The similarity graph is used during training to smooth the state posteriors on the target domain. Standard inference can be used at test time. Our approach is able to scale to very large problems and yields significantly improved target domain accuracy. 1