We present cutoff averaging", a technique for converting any conservative online learning algorithm into a batch learning algorithm. Most online-to-batch conversion techniques work well with certain types of online learning algorithms and not with others, whereas cutoff averaging explicitly tries to adapt to the characteristics of the online algorithm being converted. An attractive property of our technique is that it preserves the efficiency of the original online algorithm, making it approporiate for large-scale learning problems. We provide a statistical analysis of our technique and back our theoretical claims with experimental results."

While many advances have already been made in hierarchical classification learning, wetake a step back and examine how a hierarchical classification problem should be formally defined. We pay particular attention to the fact that many arbitrary decisionsgo into the design of the label taxonomy that is given with the training data. Moreover, many hand-designed taxonomies are unbalanced and misrepresent the class structure in the underlying data distribution. We attempt to correct these problems by using the data distribution itself to calibrate the hierarchical classificationloss function. This distribution-based correction must be done with care, to avoid introducing unmanageable statistical dependencies into the learning problem. This leads us off the beaten path of binomial-type estimation andinto the unfamiliar waters of geometric-type estimation. In this paper, we present a new calibrated definition of statistical risk for hierarchical classification, anunbiased estimator for this risk, and a new algorithmic reduction from hierarchical classification to cost-sensitive classification.

The standard Support Vector Machine formulation does not provide its user with the ability to explicitly control the number of support vectors used to define the generated classifier. We present a modified version of SVM that allows the user to set a budget parameter B and focuses on minimizing the loss attained by the B worst-classified examples while ignoring the remaining examples. This idea can be used to derive sparse versions of both L1-SVM and L2-SVM. Technically, we obtain these new SVM variants by replacing the 1-norm in the standard SVM formulation withvarious interpolation-norms. We also adapt the SMO optimization algorithm to our setting and report on some preliminary experimental results.

Online learning algorithms are typically fast, memory efficient, and simple to implement. However, many common learning problems fit more naturally in the batch learning setting. The power of online learning algorithms can be exploited in batch settings by using online-to-batch conversions techniques which build a new batch algorithm from an existing online algorithm. We first give a unified overview of three existing online-to-batch conversion techniques which do not use training data in the conversion process. We then build upon these data-independent conversions to derive and analyze data-driven conversions. Our conversions find hypotheses with a small risk by explicitly minimizing datadependent generalization bounds. We experimentally demonstrate the usefulness of our approach and in particular show that the data-driven conversions consistently outperform the data-independent conversions.

The Perceptron algorithm, despite its simplicity, often performs well on online classification tasks. The Perceptron becomes especially effective when it is used in conjunction with kernels. However, a common difficulty encounteredwhen implementing kernel-based online algorithms is the amount of memory required to store the online hypothesis, which may grow unboundedly. In this paper we present and analyze the Forgetron algorithmfor kernel-based online learning on a fixed memory budget. To our knowledge, this is the first online learning algorithm which, on one hand, maintains a strict limit on the number of examples it stores while, on the other hand, entertains a relative mistake bound. In addition to the formal results, we also present experiments with real datasets which underscore the merits of our approach.

Online learning algorithms are typically fast, memory efficient, and simple toimplement. However, many common learning problems fit more naturally in the batch learning setting. The power of online learning algorithms can be exploited in batch settings by using online-to-batch conversions techniques which build a new batch algorithm from an existing onlinealgorithm. We first give a unified overview of three existing online-to-batch conversion techniques which do not use training data in the conversion process. We then build upon these data-independent conversions to derive and analyze data-driven conversions.

Prediction suffix trees (PST) provide a popular and effective tool for tasks such as compression, classification, and language modeling.

Label ranking is the task of inferring a total order over a predefined set of labels for each given instance. We present a general framework for batch learning of label ranking functions from supervised data. We assume that each instance in the training data is associated with a list of preferences over the label-set, however we do not assume that this list is either complete or consistent. This enables us to accommodate a variety of ranking problems. In contrast to the general form of the supervision, our goal is to learn a ranking function that induces a total order over the entire set of labels. Special cases of our setting are multilabel categorization and hierarchical classification. We present a general boosting-based learning algorithm for the label ranking problem and prove a lower bound on the progress of each boosting iteration. The applicability of our approach is demonstrated with a set of experiments on a large-scale text corpus.

We present a unified view for online classification, regression, and uniclass problems. This view leads to a single algorithmic framework for the three problems. We prove worst case loss bounds for various algorithms for both the realizable case and the non-realizable case. A conversion of our main online algorithm to the setting of batch learning is also discussed. The end result is new algorithms and accompanying loss bounds for the hinge-loss.

Label ranking is the task of inferring a total order over a predefined set of labels for each given instance. We present a general framework for batch learning of label ranking functions from supervised data. We assume that each instance in the training data is associated with a list of preferences over the label-set, however we do not assume that this list is either complete orconsistent. This enables us to accommodate a variety of ranking problems. In contrast to the general form of the supervision, our goal is to learn a ranking function that induces a total order over the entire set of labels. Special cases of our setting are multilabel categorization and hierarchical classification. We present a general boosting-based learning algorithm for the label ranking problem and prove a lower bound on the progress of each boosting iteration. The applicability of our approach is demonstrated with a set of experiments on a large-scale text corpus.