Multi-output inference tasks, such as multi-label classification, have become increasingly important in recent years. A popular method for multi-label classification is classifier chains, in which the predictions of individual classifiers are cascaded along a chain, thus taking into account inter-label dependencies and improving the overall performance. Several varieties of classifier chain methods have been introduced, and many of them perform very competitively across a wide range of benchmark datasets. However, scalability limitations become apparent on larger datasets when modeling a fully-cascaded chain. In particular, the methods' strategies for discovering and modeling a good chain structure constitutes a mayor computational bottleneck. In this paper, we present the classifier trellis (CT) method for scalable multi-label classification. We compare CT with several recently proposed classifier chain methods to show that it occupies an important niche: it is highly competitive on standard multi-label problems, yet it can also scale up to thousands or even tens of thousands of labels.
The F-measure, which has originally been introduced in information retrieval, is nowadays routinely used as a performance metric for problems such as binary classification, multi-label classification, and structured output prediction. Optimizing this measure is a statistically and computationally challenging problem, since no closed-form solution exists. Adopting a decision-theoretic perspective, this article provides a formal and experimental analysis of different approaches for maximizing the F-measure. We start with a Bayes-risk analysis of related loss functions, such as Hamming loss and subset zero-one loss, showing that optimizing such losses as a surrogate of the F-measure leads to a high worst-case regret. Subsequently, we perform a similar type of analysis for F-measure maximizing algorithms, showing that such algorithms are approximate, while relying on additional assumptions regarding the statistical distribution of the binary response variables. Furthermore, we present a new algorithm which is not only computationally efficient but also Bayes-optimal, regardless of the underlying distribution. To this end, the algorithm requires only a quadratic (with respect to the number of binary responses) number of parameters of the joint distribution. We illustrate the practical performance of all analyzed methods by means of experiments with multi-label classification problems.
An important problem in multi-label classification is to capture label patterns or underlying structures that have an impact on such patterns. This paper addresses one such problem, namely how to exploit hierarchical structures over labels. We present a novel method to learn vector representations of a label space given a hierarchy of labels and label co-occurrence patterns. Our experimental results demonstrate qualitatively that the proposed method is able to learn regularities among labels by exploiting a label hierarchy as well as label co-occurrences. It highlights the importance of the hierarchical information in order to obtain regularities which facilitate analogical reasoning over a label space. We also experimentally illustrate the dependency of the learned representations on the label hierarchy.
We develop a learning principle and an efficient algorithm for batch learning from logged bandit feedback. This learning setting is ubiquitous in online systems (e.g., ad placement, web search, recommendation), where an algorithm makes a prediction (e.g., ad ranking) for a given input (e.g., query) and observes bandit feedback (e.g., user clicks on presented ads). We first address the counterfactual nature of the learning problem through propensity scoring. Next, we prove generalization error bounds that account for the variance of the propensity-weighted empirical risk estimator. These constructive bounds give rise to the Counterfactual Risk Minimization (CRM) principle. We show how CRM can be used to derive a new learning method -- called Policy Optimizer for Exponential Models (POEM) -- for learning stochastic linear rules for structured output prediction. We present a decomposition of the POEM objective that enables efficient stochastic gradient optimization. POEM is evaluated on several multi-label classification problems showing substantially improved robustness and generalization performance compared to the state-of-the-art.
The problem of maximizing precision at the top of a ranked list, often dubbed Precision@k (prec@k), finds relevance in myriad learning applications such as ranking, multi-label classification, and learning with severe label imbalance. However, despite its popularity, there exist significant gaps in our understanding of this problem and its associated performance measure. The most notable of these is the lack of a convex upper bounding surrogate for prec@k. We also lack scalable perceptron and stochastic gradient descent algorithms for optimizing this performance measure. In this paper we make key contributions in these directions. At the heart of our results is a family of truly upper bounding surrogates for prec@k. These surrogates are motivated in a principled manner and enjoy attractive properties such as consistency to prec@k under various natural margin/noise conditions. These surrogates are then used to design a class of novel perceptron algorithms for optimizing prec@k with provable mistake bounds. We also devise scalable stochastic gradient descent style methods for this problem with provable convergence bounds. Our proofs rely on novel uniform convergence bounds which require an in-depth analysis of the structural properties of prec@k and its surrogates. We conclude with experimental results comparing our algorithms with state-of-the-art cutting plane and stochastic gradient algorithms for maximizing prec@k.
We present a novel approach for automatic report generation from time-series data, in the context of student feedback generation. Our proposed methodology treats content selection as a multi-label classification (MLC) problem, which takes as input time-series data (students' learning data) and outputs a summary of these data (feedback). Unlike previous work, this method considers all data simultaneously using ensembles of classifiers, and therefore, it achieves higher accuracy and F- score compared to meaningful baselines.
In this paper, we address the problem of multi-label classification. We consider linear classifiers and propose to learn a prior over the space of labels to directly leverage the performance of such methods. This prior takes the form of a quadratic function of the labels and permits to encode both attractive and repulsive relations between labels. We cast this problem as a structured prediction one aiming at optimizing either the accuracies of the predictors or the F 1-score. This leads to an optimization problem closely related to the max-cut problem, which naturally leads to semidefinite and spectral relaxations. We show on standard datasets how such a general prior can improve the performances of multi-label techniques.
Auto-encoders are perhaps the best-known non-probabilistic methods for representation learning. They are conceptually simple and easy to train. Recent theoretical work has shed light on their ability to capture manifold structure, and drawn connections to density modelling. This has motivated researchers to seek ways of auto-encoder scoring, which has furthered their use in classification. Gated auto-encoders (GAEs) are an interesting and flexible extension of auto-encoders which can learn transformations among different images or pixel covariances within images. However, they have been much less studied, theoretically or empirically. In this work, we apply a dynamical systems view to GAEs, deriving a scoring function, and drawing connections to Restricted Boltzmann Machines. On a set of deep learning benchmarks, we also demonstrate their effectiveness for single and multi-label classification.
The objective in extreme multi-label learning is to train a classifier that can automatically tag a novel data point with the most relevant subset of labels from an extremely large label set. Embedding based approaches make training and prediction tractable by assuming that the training label matrix is low-rank and hence the effective number of labels can be reduced by projecting the high dimensional label vectors onto a low dimensional linear subspace. Still, leading embedding approaches have been unable to deliver high prediction accuracies or scale to large problems as the low rank assumption is violated in most real world applications. This paper develops the X-One classifier to address both limitations. The main technical contribution in X-One is a formulation for learning a small ensemble of local distance preserving embeddings which can accurately predict infrequently occurring (tail) labels. This allows X-One to break free of the traditional low-rank assumption and boost classification accuracy by learning embeddings which preserve pairwise distances between only the nearest label vectors. We conducted extensive experiments on several real-world as well as benchmark data sets and compared our method against state-of-the-art methods for extreme multi-label classification. Experiments reveal that X-One can make significantly more accurate predictions then the state-of-the-art methods including both embeddings (by as much as 35%) as well as trees (by as much as 6%). X-One can also scale efficiently to data sets with a million labels which are beyond the pale of leading embedding methods.
We analyze the RI-TIMEXes in temporally annotated corpora and propose two hypotheses regarding the normalization of RI-TIMEXes in the clinical narrative domain: the anchor point hypothesis and the anchor relation hypothesis. We annotate the RI-TIMEXes in three corpora to study the characteristics of RI-TMEXes in different domains. This informed the design of our RI-TIMEX normalization system for the clinical domain, which consists of an anchor point classifier, an anchor relation classifier and a rule-based RI-TIMEX text span parser. We experiment with different feature sets and perform error analysis for each system component. The annotation confirmed the hypotheses that we can simplify the RI-TIMEXes normalization task using two multi-label classifiers. Our system achieves anchor point classification, anchor relation classification and rule-based parsing accuracy of 74.68%, 87.71% and 57.2% (82.09% under relaxed matching criteria) respectively on the held-out test set of the 2012 i2b2 temporal relation challenge. Experiments with feature sets reveals some interesting findings such as the verbal tense feature does not inform the anchor relation classification in clinical narratives as much as the tokens near the RI-TIMEX. Error analysis shows that underrepresented anchor point and anchor relation classes are difficult to detect. We formulate the RI-TIMEX normalization problem as a pair of multi-label classification problems. Considering only the RI-TIMEX extraction and normalization, the system achieves statistically significant improvement over the RI-TIMEX results of the best systems in the 2012 i2b2 challenge.
This paper attempts multi-label classification by extending the idea of independent binary classification models for each output label, and exploring how the inherent correlation between output labels can be used to improve predictions. Logistic Regression, Naive Bayes, Random Forest, and SVM models were constructed, with SVM giving the best results: an improvement of 12.9\% over binary models was achieved for hold out cross validation by augmenting with pairwise correlation probabilities of the labels.
In recent years, multi-label classification has attracted a significant body of research, motivated by real-life applications, such as text classification and medical diagnoses. Although sparsely studied in this context, Learning Classifier Systems are naturally well-suited to multi-label classification problems, whose search space typically involves multiple highly specific niches. This is the motivation behind our current work that introduces a generalized multi-label rule format -- allowing for flexible label-dependency modeling, with no need for explicit knowledge of which correlations to search for -- and uses it as a guide for further adapting the general Michigan-style supervised Learning Classifier System framework. The integration of the aforementioned rule format and framework adaptations results in a novel algorithm for multi-label classification whose behavior is studied through a set of properly defined artificial problems. The proposed algorithm is also thoroughly evaluated on a set of multi-label datasets and found competitive to other state-of-the-art multi-label classification methods.
In many practical applications of supervised learning the task involves the prediction of multiple target variables from a common set of input variables. When the prediction targets are binary the task is called multi-label classification, while when the targets are continuous the task is called multi-target regression. In both tasks, target variables often exhibit statistical dependencies and exploiting them in order to improve predictive accuracy is a core challenge. A family of multi-label classification methods address this challenge by building a separate model for each target on an expanded input space where other targets are treated as additional input variables. Despite the success of these methods in the multi-label classification domain, their applicability and effectiveness in multi-target regression has not been studied until now. In this paper, we introduce two new methods for multi-target regression, called Stacked Single-Target and Ensemble of Regressor Chains, by adapting two popular multi-label classification methods of this family. Furthermore, we highlight an inherent problem of these methods - a discrepancy of the values of the additional input variables between training and prediction - and develop extensions that use out-of-sample estimates of the target variables during training in order to tackle this problem. The results of an extensive experimental evaluation carried out on a large and diverse collection of datasets show that, when the discrepancy is appropriately mitigated, the proposed methods attain consistent improvements over the independent regressions baseline. Moreover, two versions of Ensemble of Regression Chains perform significantly better than four state-of-the-art methods including regularization-based multi-task learning methods and a multi-objective random forest approach.
We propose sparsemax, a new activation function similar to the traditional softmax, but able to output sparse probabilities. After deriving its properties, we show how its Jacobian can be efficiently computed, enabling its use in a network trained with backpropagation. Then, we propose a new smooth and convex loss function which is the sparsemax analogue of the logistic loss. We reveal an unexpected connection between this new loss and the Huber classification loss. We obtain promising empirical results in multi-label classification problems and in attention-based neural networks for natural language inference. For the latter, we achieve a similar performance as the traditional softmax, but with a selective, more compact, attention focus.
Classifier chains are popular and effective method to tackle a multi-label classification problem. The aim of this paper is to study the asymptotic properties of the chain model in which the conditional probabilities are of the logistic form. In particular we find conditions on the number of labels and the distribution of feature vector under which the estimated mode of the joint distribution of labels converges to the true mode. Best of our knowledge, this important issue has not yet been studied in the context of multi-label learning. We also investigate how the order of model building in a chain influences the estimation of the joint distribution of labels. We establish the link between the problem of incorrect ordering in the chain and incorrect model specification. We propose a procedure of determining the optimal ordering of labels in the chain, which is based on using measures of correct specification and allows to find the ordering such that the consecutive logistic models are best possibly specified. The other important question raised in this paper is how accurately can we estimate the joint posterior probability when the ordering of labels is wrong or the logistic models in the chain are incorrectly specified. The numerical experiments illustrate the theoretical results.
We propose a simple and efficient method for ranking features in multi-label classification. The method produces a ranking of features showing their relevance in predicting labels, which in turn allows to choose a final subset of features. The procedure is based on Markov Networks and allows to model the dependencies between labels and features in a direct way. In the first step we build a simple network using only labels and then we test how much adding a single feature affects the initial network. More specifically, in the first step we use the Ising model whereas the second step is based on the score statistic, which allows to test a significance of added features very quickly. The proposed approach does not require transformation of label space, gives interpretable results and allows for attractive visualization of dependency structure. We give a theoretical justification of the procedure by discussing some theoretical properties of the Ising model and the score statistic. We also discuss feature ranking procedure based on fitting Ising model using $l_1$ regularized logistic regressions. Numerical experiments show that the proposed methods outperform the conventional approaches on the considered artificial and real datasets.
In this paper, we present a novel method to recognize the types of crowd movement from crowd trajectories using agent-based motion models (AMMs). Our idea is to apply a number of AMMs, referred to as exemplar-AMMs, to describe the crowd movement. Specifically, we propose an optimization framework that filters out the unknown noise in the crowd trajectories and measures their similarity to the exemplar-AMMs to produce a crowd motion feature. We then address our real-world crowd movement recognition problem as a multi-label classification problem. Our experiments show that the proposed feature outperforms the state-of-the-art methods in recognizing both simulated and real-world crowd movements from their trajectories. Finally, we have created a synthetic dataset, SynCrowd, which contains 2D crowd trajectories in various scenarios, generated by various crowd simulators. This dataset can serve as a training set or benchmark for crowd analysis work.
In multi-label classification, an instance may be associated with a set of labels simultaneously. Recently, the research on multi-label classification has largely shifted its focus to the other end of the spectrum where the number of labels is assumed to be extremely large. The existing works focus on how to design scalable algorithms that offer fast training procedures and have a small memory footprint. However they ignore and even compound another challenge - the label imbalance problem. To address this drawback, we propose a novel Representation-based Multi-label Learning with Sampling (RMLS) approach. To the best of our knowledge, we are the first to tackle the imbalance problem in multi-label classification with many labels. Our experimentations with real-world datasets demonstrate the effectiveness of the proposed approach.
Multi-label classification is a common supervised machine learning problem where each instance is associated with multiple classes. The key challenge in this problem is learning the correlations between the classes. An additional challenge arises when the labels of the training instances are provided by noisy, heterogeneous crowdworkers with unknown qualities. We first assume labels from a perfect source and propose a novel topic model where the present as well as the absent classes generate the latent topics and hence the words. We non-trivially extend our topic model to the scenario where the labels are provided by noisy crowdworkers. Extensive experimentation on real world datasets reveals the superior performance of the proposed model. The proposed model learns the qualities of the annotators as well, even with minimal training data.
Similarity metrics are a core component of many information retrieval and machine learning systems. In this work we propose a method capable of learning a similarity metric from data equipped with a binary relation. By considering only the similarity constraints, and initially ignoring the features, we are able to learn target vectors for each instance using one of several appropriately designed loss functions. A regression model can then be constructed that maps novel feature vectors to the same target vector space, resulting in a feature extractor that computes vectors for which a predefined metric is a meaningful measure of similarity. We present results on both multiclass and multi-label classification datasets that demonstrate considerably faster convergence, as well as higher accuracy on the majority of the intrinsic evaluation tasks and all extrinsic evaluation tasks.