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Online learning algorithms are fast, memory-efficient, easy to implement, and applicable to many prediction problems, including classification, regression, and ranking. Several online algorithms were proposed in the past few decades, some based on additive updates, like the Perceptron, and some on multiplicative updates, like Winnow. A unifying perspective on the design and the analysis of online algorithms is provided by online mirror descent, a general prediction strategy from which most first-order algorithms can be obtained as special cases. We generalize online mirror descent to time-varying regularizers with generic updates. Unlike standard mirror descent, our more general formulation also captures second order algorithms, algorithms for composite losses and algorithms for adaptive filtering. Moreover, we recover, and sometimes improve, known regret bounds as special cases of our analysis using specific regularizers. Finally, we show the power of our approach by deriving a new second order algorithm with a regret bound invariant with respect to arbitrary rescalings of individual features. [ABSTRACT FROM AUTHOR]

We investigate three variants of budgeted learning, a setting in which the learner is allowed to access a limited number of attributes from training or test examples. In the "local budget" setting, where a constraint is imposed on the number of available attributes per training example, we design and analyze an efficient algorithm for learning linear predictors that actively samples the attributes of each training instance. Our analysis bounds the number of additional examples sufficient to compensate for the lack of full information on the training set. This result is complemented by a general lower bound for the easier "global budget" setting, where it is only the overall number of accessible training attributes that is being constrained. In the third, "prediction on a budget" setting, when the constraint is on the number of available attributes per test example, we show that there are cases in which there exists a linear predictor with zero error but it is statistically impossible to achieve arbitrary accuracy without full information on test examples. Finally, we run simple experiments on a digit recognition problem that reveal that our algorithm has a good performance against both partial information and full information baselines. [ABSTRACT FROM AUTHOR]

We introduce efficient margin-based algorithms for selective sampling and filtering in binary classification tasks. Experiments on real-world textual data reveal that our algorithms perform significantly better than popular and similarly efficient competitors. Using the so-called Mammen-Tsybakov low noise condition to parametrize the instance distribution, and assuming linear label noise, we show bounds on the convergence rate to the Bayes risk of a weaker adaptive variant of our selective sampler. Our analysis reveals that, excluding logarithmic factors, the average risk of this adaptive sampler converges to the Bayes risk at rate N where N denotes the number of queried labels, and α>0 is the exponent in the low noise condition. For all $\alpha>\sqrt{3}-1\approx0.73$ this convergence rate is asymptotically faster than the rate N achieved by the fully supervised version of the base selective sampler, which queries all labels. Moreover, for α→∞ (hard margin condition) the gap between the semi- and fully-supervised rates becomes exponential. [ABSTRACT FROM AUTHOR]

We survey a number of recent results concerning the behaviour of algorithms for learning classifiers based on the solution of a regularized least-squares problem. [Copyright &y& Elsevier]

A selective sampling algorithm is a learning algorithm for classification that, based on the past observed data, decides whether to ask the label of each new instance to be classified. In this paper, we introduce a general technique for turning linear-threshold classification algorithms from the general additive family into randomized selective sampling algorithms. For the most popular algorithms in this family we derive mistake bounds that hold for individual sequences of examples. These bounds show that our semi-supervised algorithms can achieve, on average, the same accuracy as that of their fully supervised counterparts, but using fewer labels. Our theoretical results are corroborated by a number of experiments on real-world textual data. The outcome of these experiments is essentially predicted by our theoretical results: Our selective sampling algorithms tend to perform as well as the algorithms receiving the true label after each classification, while observing in practice substantially fewer labels. [ABSTRACT FROM AUTHOR]

We study the problem of classifying data in a given taxonomy when classifications associated with multiple and/or partial paths are allowed. We introduce a new algorithm that incrementally learns a linear-threshold classifier for each node of the taxonomy. A hierarchical classification is obtained by evaluating the trained node classifiers in a top-down fashion. To evaluate classifiers in our multipath framework, we define a new hierarchical loss function, the H-loss, capturing the intuition that whenever a classification mistake is made on a node of the taxonomy, then no loss should be charged for any additional mistake occurring in the subtree of that node. Making no assumptions on the mechanism generating the data instances, and assuming a linear noise model for the labels, we bound the H-loss of our on-line algorithm in terms of the H-loss of a reference classifier knowing the true parameters of the label-generating process. We show that, in expectation, the excess cumulative H-loss grows at most logarithmically in the length of the data sequence. Furthermore, our analysis reveals the precise dependence of the rate of convergence on the eigenstructure of the data each node observes. Our theoretical results are complemented by a number of experiments on texual corpora. In these experiments we show that, after only one epoch of training, our algorithm performs much better than Perceptron-based hierarchical classifiers, and reasonably close to a hierarchical support vector machine. [ABSTRACT FROM AUTHOR]

Kernel-based linear-threshold algorithms, such as support vector machines and Perceptron-like algorithms, are among the best available techniques for solving pattern classification problems. In this paper, we describe an extension of the classical Perceptron algorithm, called second-order Perceptron, and analyze its performance within the mistake bound model of on-line learning. The bound achieved by our algorithm depends on the sensitivity to second-order data information and is the best known mistake bound for (efficient) kernel-based linear-threshold classifiers to date. This mistake bound, which strictly generalizes the well-known Perceptron bound, is expressed in terms of the eigenvalues of the empirical data correlation matrix and depends on a parameter controlling the sensitivity of the algorithm to the distribution of these eigenvalues. Since the optimal setting of this parameter is not known a priori, we also analyze two variants of the second-order Perceptron algorithm: one that adaptively sets the value of the parameter in terms of the number of mistakes made so far, and one that is parameterless, based on pseudoinverses. [ABSTRACT FROM AUTHOR]

In this paper, it is shown how to extract a hypothesis with small risk from the ensemble of hypotheses generated by an arbitrary on-line learning algorithm run on an independent and identically distributed (i.i.d.) sample of data. Using a simple large deviation argument, we prove fight data-dependent bounds for the risk of this hypothesis in terms of an easily computable statistic Mn associated with the on-line performance of the ensemble. Via sharp pointwise bounds on Mn, we then obtain risk tail bounds for kernel Perceptron algorithms in terms of the spectrum of the empirical kernel matrix. These bounds reveal that the linear hypotheses found via our approach achieve optimal tradeoffs between hinge loss and margin size over the class of all linear functions, an issue that was left open by previous results. A distinctive feature of our approach is that the key tools for our analysis come from the model of prediction of individual sequences; i.e., a model making no probabilistic assumptions on the source generating the data. In fact, these tools turn out to be so powerful that we only need very elementary statistical facts to obtain our final risk bounds. [ABSTRACT FROM AUTHOR]

We study on-line learning in the linear regression framework. Most of the performance bounds for on-line algorithms in this framework assume a constant learning rate. To achieve these bounds the learning rate must be optimized based on a posteriori information. This information depends on the whole sequence of examples and thus it is not available to any strictly on-line algorithm. We introduce new techniques for adaptively tuning the learning rate as the data sequence is progressively revealed. Our techniques allow us to prove essentially the same bounds as if we knew the optimal learning rate in advance. Moreover, such techniques apply to a wide class of on-line algorithms, including p-norm algorithms for generalized linear regression and Weighted Majority for linear regression with absolute loss. Our adaptive tunings are radically different from previous techniques, such as the so-called doubling trick. Whereas the doubling trick restarts the on-line algorithm several times using a constant learning rate for each run, our methods save information by changing the value of the learning rate very smoothly. In fact, for Weighted Majority over a finite set of experts our analysis provides a better leading constant than the doubling trick. [Copyright &y& Elsevier]

Recognising human activities from streaming sources poses unique challenges to learning algorithms. Predictive models need to be scalable, incrementally trainable, and must remain bounded in size even when the data stream is arbitrarily long. In order to achieve high accuracy even in complex and dynamic environments methods should be also nonparametric, i.e., their structure should adapt in response to the incoming data. Furthermore, as tuning is problematic in a streaming setting, suitable approaches should be parameterless (as initially tuned parameter values may not prove optimal for future streams). Here, we present an approach to the recognition of human actions from streaming data which meets all these requirements by: (1) incrementally learning a model which adaptively covers the feature space with simple and local classifiers; (2) employing an active learning strategy to reduce annotation requests; (3) achieving good accuracy within a fixed model size. Although in this work we focus on human activity recognition, our approach is completely independent from the feature extraction and can deal with any supervised matrix (set of feature vectors). Hence, it can be adapted to a wide range of applications (e.g., speech recognition, image classification, object recognition, pose recognition, and image matching). Extensive experiments on standard benchmarks show that our approach is competitive with state-of-the-art non-incremental methods, while outperforming the existing active incremental baselines. [ABSTRACT FROM AUTHOR]

We describe new loss functions for regression problems along with an accompanying algorithmic framework which utilizes these functions. These loss functions are derived by symmetrization of margin-based losses commonly used in boosting algorithms, namely, the logistic loss and the exponential loss. The resulting symmetric logistic loss can be viewed as a smooth approximation to the ε-insensitive hinge loss used in support vector regression. We describe and analyze two parametric families of batch learning algorithms for minimizing these symmetric losses. The first family employs an iterative log-additive update which can be viewed as a regression counterpart to recent boosting algorithms. The second family utilizes an iterative additive update step. We also describe and analyze online gradient descent (GD) and exponentiated gradient (EG) algorithms for the symmetric logistic loss. A byproduct of our work is a new simple form of regularization for boosting-based classification and regression algorithms. Our regression framework also has implications on classification algorithms, namely, a new additive update boosting algorithm for classification. We demonstrate the merits of our algorithms in a series of experiments. [ABSTRACT FROM AUTHOR]