Extreme multilabel classification (XMLC) problems occur in settings such as related product recommendation, large-scale document tagging, or ad prediction, and are characterized by a label space that can span millions of possible labels. There are two implicit tasks that the classifier performs: Evaluating each potential label for its expected worth, and then selecting the best candidates. For the latter task, only the relative order of scores matters, and this is what is captured by the standard evaluation procedure in the XMLC literature. However, in many practical applications, it is important to have a good estimate of the actual probability of a label being relevant, e.g., to decide whether to pay the fee to be allowed to display the corresponding ad. To judge whether an extreme classifier is indeed suited to this task, one can look, for example, to whether it returns calibrated probabilities, which has hitherto not been done in this field. Therefore, this paper aims to establish the current status quo of calibration in XMLC by providing a systematic evaluation, comprising nine models from four different model families across seven benchmark datasets. As naive application of Expected Calibration Error (ECE) leads to meaningless results in long-tailed XMC datasets, we instead introduce the notion of calibration@k (e.g., ECE@k), which focusses on the top-k probability mass, offering a more appropriate measure for evaluating probability calibration in XMLC scenarios. While we find that different models can exhibit widely varying reliability plots, we also show that post-training calibration via a computationally efficient isotonic regression method enhances model calibration without sacrificing prediction accuracy. Thus, the practitioner can choose the model family based on accuracy considerations, and leave calibration to isotonic regression.

Extreme Multi-label Classification (XMC) involves predicting a subset of relevant labels from an extremely large label space, given an input query and labels with textual features.Models developed for this problem have conventionally made use of dual encoder (DE) to embed the queries and label texts and one-vs-all (OvA) classifiers to rerank the shortlisted labels by the DE.While such methods have shown empirical success, a major drawback is their computational cost, often requiring upto 16 GPUs to train on the largest public dataset.Such a high cost is a consequence of calculating the loss over the entire label space.While shortlisting strategies have been proposed for classifiers, we aim to study such methods for the DE framework.In this work, we develop UniDEC, a loss-independent, end-to-end trainable framework which trains the DE and classifier together in a unified manner with a multi-class loss, while reducing the computational cost by 4 -16×.This is done via the proposed pick-some-label (PSL) reduction, which aims to compute the loss on only a subset of positive and negative labels.These labels are carefully chosen in-batch so as to maximise their supervisory signals.Not only does the proposed framework achieve state-of-the-art results on datasets with labels in the order of millions, it is also computationally and resource efficient in achieving this performance on a single GPU.Code is made available at https://github.com/the-catalyst/UniDEC.

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Automatic annotation of short-text data to a large number of target labels, referred to as Short Text Extreme Classification, has found numerous applications including prediction of related searches and product recommendation. In this paper, we propose a convolutional architecture InceptionXML which is light-weight, yet powerful, and robust to the inherent lack of word-order in short-text queries encountered in search and recommendation. We demonstrate the efficacy of applying convolutions by recasting the operation along the embedding dimension instead of the word dimension as applied in conventional CNNs for text classification. Towards scaling our model to datasets with millions of labels, we also propose SyncXML pipeline which improves upon the shortcomings of the recently proposed dynamic hard-negative mining technique for label shortlisting by synchronizing the label-shortlister and extreme classifier. SyncXML not only reduces the inference time to half but is also an order of magnitude smaller than state-of-the-art Astec in terms of model size. Through a comprehensive empirical comparison, we show that not only can InceptionXML outperform existing approaches on benchmark datasets but also the transformer baselines requiring only 2% FLOPs. The code for InceptionXML is available at https://github.com/xmc-aalto.

The propensity model introduced by Jain et al has become a standard approach for dealing with missing and long-tail labels in extreme multi-label classification (XMLC). In this paper, we critically revise this approach showing that despite its theoretical soundness, its application in contemporary XMLC works is debatable. We exhaustively discuss the flaws of the propensity-based approach, and present several recipes, some of them related to solutions used in search engines and recommender systems, that we believe constitute promising alternatives to be followed in XMLC.

Extreme multi-label classification (XMLC) refers to the task of tagging instances with small subsets of relevant labels coming from an extremely large set of all possible labels. Recently, XMLC has been widely applied to diverse web applications such as automatic content labeling, online advertising, or recommendation systems. In such environments, label distribution is often highly imbalanced, consisting mostly of very rare tail labels, and relevant labels can be missing. As a remedy to these problems, the propensity model has been introduced and applied within several XMLC algorithms. In this work, we focus on the problem of optimal predictions under this model for probabilistic label trees, a popular approach for XMLC problems. We introduce an inference procedure, based on the A*-search algorithm, that efficiently finds the optimal solution, assuming that all probabilities and propensities are known. We demonstrate the attractiveness of this approach in a wide empirical study on popular XMLC benchmark datasets.

Extreme Classification (XC) refers to supervised learning where each training/test instance is labeled with small subset of relevant labels that are chosen from a large set of possible target labels. The framework of XC has been widely employed in web applications such as automatic labeling of web-encyclopedia, prediction of related searches, and recommendation systems.

Extreme multi-label classification refers to supervised multi-label learning involving hundreds of thousands or even millions of labels. Datasets in extreme classification exhibit fit to power-law distribution, i.e. a large fraction of labels have very few positive instances in the data distribution. Most state-of-the-art approaches for extreme multi-label classification attempt to capture correlation among labels by embedding the label matrix to a low-dimensional linear sub-space. However, in the presence of power-law distributed extremely large and diverse label spaces, structural assumptions such as low rank can be easily violated.

For large-scale multi-class classification problems, consisting of tens of thousand target categories, recent works have emphasized the need to store billions of parameters. For instance, the classical l2-norm regularization employed by a state-of-the-art method results in the model size of 17GB for a training set whose size is only 129MB. To the contrary, by using a mixed-norm regularization approach, we show that around 99.5% of the stored parameters is dispensable noise. Using this strategy, we can extract the information relevant for classification, which is constituted in remaining 0.5% of the parameters, and hence demonstrate drastic reduction in model sizes. Furthermore, the proposed method leads to improvement in generalization performance compared to state-of-the-art methods, especially for under-represented categories. Lastly, our method enjoys easy parallelization, and scales well to tens of thousand target categories.

For large-scale category systems, such as Directory Mozilla, which consist of tens of thousand categories, it has been empirically verified in earlier studies that the distribution of documents among categories can be modeled as a power-law distribution. It implies that a significant fraction of categories, referred to as rare categories, have very few documents assigned to them. This characteristic of the data makes it harder for learning algorithms to learn effective decision boundaries which can correctly detect such categories in the test set. In this work, we exploit the distribution of documents among categories to (i) derive an upper bound on the accuracy of any classifier, and (ii) propose a ranking-based algorithm which aims to maximize this upper bound. The empirical evaluation on publicly available large-scale datasets demonstrate that the proposed method not only achieves higher accuracy but also much higher coverage of rare categories as compared to state-of-the-art methods.

While multi-class categorization of documents has been of research interest for over a decade, relatively fewer approaches have been proposed for large scale taxonomies in which the number of classes range from hundreds of thousand as in Directory Mozilla to over a million in Wikipedia. As a result of ever increasing number of text documents and images from various sources, there is an immense need for automatic classification of documents in such large hierarchies. In this paper, we analyze the tradeoffs between the important characteristics of different classifiers employed in the top down fashion. The properties for relative comparison of these classifiers include, (i) accuracy on test instance, (ii) training time (iii) size of the model and (iv) test time required for prediction. Our analysis is motivated by the well known error bounds from learning theory, which is also further reinforced by the empirical observations on the publicly available data from the Large Scale Hierarchical Text Classification Challenge. We show that by exploiting the data heterogenity across the large scale hierarchies, one can build an overall classification system which is approximately 4 times faster for prediction, 3 times faster to train, while sacrificing only 1% point in accuracy.