Distribution matching for transduction

Many transductive inference algorithms assume that distributions over training and test estimates should be related, e.g. by providing a large margin of separation on both sets. We use this idea to design a transduction algorithm which can be used without modification for classification, regression, and structured estimation. At its heart we exploit the fact that for a good learner the distributions over the outputs on training and test sets should match. This is a classical two-sample problem which can be solved efficiently in its most general form by using distance measures in Hilbert Space. It turns out that a number of existing heuristics can be viewed as special cases of our approach.

The ABACOC Algorithm: a Novel Approach for Nonparametric Classification of Data Streams

Stream mining poses unique challenges to machine learning: predictive models are required to be scalable, incrementally trainable, must remain bounded in size (even when the data stream is arbitrarily long), and be nonparametric in order to achieve high accuracy even in complex and dynamic environments. Moreover, the learning system must be parameterless ---traditional tuning methods are problematic in streaming settings--- and avoid requiring prior knowledge of the number of distinct class labels occurring in the stream. In this paper, we introduce a new algorithmic approach for nonparametric learning in data streams. Our approach addresses all above mentioned challenges by learning a model that covers the input space using simple local classifiers. The distribution of these classifiers dynamically adapts to the local (unknown) complexity of the classification problem, thus achieving a good balance between model complexity and predictive accuracy. We design four variants of our approach of increasing adaptivity. By means of an extensive empirical evaluation against standard nonparametric baselines, we show state-of-the-art results in terms of accuracy versus model size. For the variant that imposes a strict bound on the model size, we show better performance against all other methods measured at the same model size value. Our empirical analysis is complemented by a theoretical performance guarantee which does not rely on any stochastic assumption on the source generating the stream

Generalized Boosting Algorithms for Convex Optimization

Boosting is a popular way to derive powerful learners from simpler hypothesis classes. Following previous work (Mason et al., 1999; Friedman, 2000) on general boosting frameworks, we analyze gradient-based descent algorithms for boosting with respect to any convex objective and introduce a new measure of weak learner performance into this setting which generalizes existing work. We present the weak to strong learning guarantees for the existing gradient boosting work for strongly-smooth, strongly-convex objectives under this new measure of performance, and also demonstrate that this work fails for non-smooth objectives. To address this issue, we present new algorithms which extend this boosting approach to arbitrary convex loss functions and give corresponding weak to strong convergence results. In addition, we demonstrate experimental results that support our analysis and demonstrate the need for the new algorithms we present.Comment: Extended version of paper presented at the International Conference on Machine Learning, 2011. 9 pages + appendix with proof

Convex Calibration Dimension for Multiclass Loss Matrices

We study consistency properties of surrogate loss functions for general multiclass learning problems, defined by a general multiclass loss matrix. We extend the notion of classification calibration, which has been studied for binary and multiclass 0-1 classification problems (and for certain other specific learning problems), to the general multiclass setting, and derive necessary and sufficient conditions for a surrogate loss to be calibrated with respect to a loss matrix in this setting. We then introduce the notion of convex calibration dimension of a multiclass loss matrix, which measures the smallest `size' of a prediction space in which it is possible to design a convex surrogate that is calibrated with respect to the loss matrix. We derive both upper and lower bounds on this quantity, and use these results to analyze various loss matrices. In particular, we apply our framework to study various subset ranking losses, and use the convex calibration dimension as a tool to show both the existence and non-existence of various types of convex calibrated surrogates for these losses. Our results strengthen recent results of Duchi et al. (2010) and Calauzenes et al. (2012) on the non-existence of certain types of convex calibrated surrogates in subset ranking. We anticipate the convex calibration dimension may prove to be a useful tool in the study and design of surrogate losses for general multiclass learning problems.Comment: Accepted to JMLR, pending editin

Interpretable multiclass classification by MDL-based rule lists

Interpretable classifiers have recently witnessed an increase in attention from the data mining community because they are inherently easier to understand and explain than their more complex counterparts. Examples of interpretable classification models include decision trees, rule sets, and rule lists. Learning such models often involves optimizing hyperparameters, which typically requires substantial amounts of data and may result in relatively large models. In this paper, we consider the problem of learning compact yet accurate probabilistic rule lists for multiclass classification. Specifically, we propose a novel formalization based on probabilistic rule lists and the minimum description length (MDL) principle. This results in virtually parameter-free model selection that naturally allows to trade-off model complexity with goodness of fit, by which overfitting and the need for hyperparameter tuning are effectively avoided. Finally, we introduce the Classy algorithm, which greedily finds rule lists according to the proposed criterion. We empirically demonstrate that Classy selects small probabilistic rule lists that outperform state-of-the-art classifiers when it comes to the combination of predictive performance and interpretability. We show that Classy is insensitive to its only parameter, i.e., the candidate set, and that compression on the training set correlates with classification performance, validating our MDL-based selection criterion

On the Generalization of the C-Bound to Structured Output Ensemble Methods

This paper generalizes an important result from the PAC-Bayesian literature for binary classification to the case of ensemble methods for structured outputs. We prove a generic version of the \Cbound, an upper bound over the risk of models expressed as a weighted majority vote that is based on the first and second statistical moments of the vote's margin. This bound may advantageously $(i)$ be applied on more complex outputs such as multiclass labels and multilabel, and $(ii)$ allow to consider margin relaxations. These results open the way to develop new ensemble methods for structured output prediction with PAC-Bayesian guarantees

iCaRL: Incremental Classifier and Representation Learning

A major open problem on the road to artificial intelligence is the development of incrementally learning systems that learn about more and more concepts over time from a stream of data. In this work, we introduce a new training strategy, iCaRL, that allows learning in such a class-incremental way: only the training data for a small number of classes has to be present at the same time and new classes can be added progressively. iCaRL learns strong classifiers and a data representation simultaneously. This distinguishes it from earlier works that were fundamentally limited to fixed data representations and therefore incompatible with deep learning architectures. We show by experiments on CIFAR-100 and ImageNet ILSVRC 2012 data that iCaRL can learn many classes incrementally over a long period of time where other strategies quickly fail.Comment: Accepted paper at CVPR 201