Consistent algorithms for multi-label classification with macro-at-$k$ metrics

We consider the optimization of complex performance metrics in multi-label classification under the population utility framework. We mainly focus on metrics linearly decomposable into a sum of binary classification utilities applied separately to each label with an additional requirement of exactly $k$ labels predicted for each instance. These "macro-at-$k$" metrics possess desired properties for extreme classification problems with long tail labels. Unfortunately, the at-$k$ constraint couples the otherwise independent binary classification tasks, leading to a much more challenging optimization problem than standard macro-averages. We provide a statistical framework to study this problem, prove the existence and the form of the optimal classifier, and propose a statistically consistent and practical learning algorithm based on the Frank-Wolfe method. Interestingly, our main results concern even more general metrics being non-linear functions of label-wise confusion matrices. Empirical results provide evidence for the competitive performance of the proposed approach.

Generalized test utilities for long-tail performance in extreme multi-label classification

Extreme multi-label classification (XMLC) is the task of selecting a small subset of relevant labels from a very large set of possible labels. As such, it is characterized by long-tail labels, i.e., most labels have very few positive instances. With standard performance measures such as precision@k, a classifier can ignore tail labels and still report good performance. However, it is often argued that correct predictions in the tail are more interesting or rewarding, but the community has not yet settled on a metric capturing this intuitive concept. The existing propensity-scored metrics fall short on this goal by confounding the problems of long-tail and missing labels. In this paper, we analyze generalized metrics budgeted "at k" as an alternative solution. To tackle the challenging problem of optimizing these metrics, we formulate it in the expected test utility (ETU) framework, which aims at optimizing the expected performance on a fixed test set. We derive optimal prediction rules and construct computationally efficient approximations with provable regret guarantees and robustness against model misspecification. Our algorithm, based on block coordinate ascent, scales effortlessly to XMLC problems and obtains promising results in terms of long-tail performance.

Towards Memory-Efficient Training for Extremely Large Output Spaces -- Learning with 500k Labels on a Single Commodity GPU

In classification problems with large output spaces (up to millions of labels), the last layer can require an enormous amount of memory. Using sparse connectivity would drastically reduce the memory requirements, but as we show below, it can result in much diminished predictive performance of the model. Fortunately, we found that this can be mitigated by introducing a penultimate layer of intermediate size. We further demonstrate that one can constrain the connectivity of the sparse layer to be uniform, in the sense that each output neuron will have the exact same number of incoming connections. This allows for efficient implementations of sparse matrix multiplication and connection redistribution on GPU hardware. Via a custom CUDA implementation, we show that the proposed approach can scale to datasets with 670,000 labels on a single commodity GPU with only 4GB memory.

CascadeXML: Rethinking Transformers for End-to-end Multi-resolution Training in Extreme Multi-label Classification

Extreme Multi-label Text Classification (XMC) involves learning a classifier that can assign an input with a subset of most relevant labels from millions of label choices. Recent approaches, such as XR-Transformer and LightXML, leverage a transformer instance to achieve state-of-the-art performance. However, in this process, these approaches need to make various trade-offs between performance and computational requirements. A major shortcoming, as compared to the Bi-LSTM based AttentionXML, is that they fail to keep separate feature representations for each resolution in a label tree. We thus propose CascadeXML, an end-to-end multi-resolution learning pipeline, which can harness the multi-layered architecture of a transformer model for attending to different label resolutions with separate feature representations. CascadeXML significantly outperforms all existing approaches with non-trivial gains obtained on benchmark datasets consisting of up to three million labels. Code for CascadeXML will be made publicly available at \url{https://github.com/xmc-aalto/cascadexml}.

On Missing Labels, Long-tails and Propensities in Extreme Multi-label Classification

The propensity model introduced by Jain et al. 2016 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.

Adversarial Examples for Extreme Multilabel Text Classification

Extreme Multilabel Text Classification (XMTC) is a text classification problem in which, (i) the output space is extremely large, (ii) each data point may have multiple positive labels, and (iii) the data follows a strongly imbalanced distribution. With applications in recommendation systems and automatic tagging of web-scale documents, the research on XMTC has been focused on improving prediction accuracy and dealing with imbalanced data. However, the robustness of deep learning based XMTC models against adversarial examples has been largely underexplored. In this paper, we investigate the behaviour of XMTC models under adversarial attacks. To this end, first, we define adversarial attacks in multilabel text classification problems. We categorize attacking multilabel text classifiers as (a) positive-targeted, where the target positive label should fall out of top-k predicted labels, and (b) negative-targeted, where the target negative label should be among the top-k predicted labels. Then, by experiments on APLC-XLNet and AttentionXML, we show that XMTC models are highly vulnerable to positive-targeted attacks but more robust to negative-targeted ones. Furthermore, our experiments show that the success rate of positive-targeted adversarial attacks has an imbalanced distribution. More precisely, tail classes are highly vulnerable to adversarial attacks for which an attacker can generate adversarial samples with high similarity to the actual data-points. To overcome this problem, we explore the effect of rebalanced loss functions in XMTC where not only do they increase accuracy on tail classes, but they also improve the robustness of these classes against adversarial attacks. The code for our experiments is available at https://github.com/xmc-aalto/adv-xmtc

Propensity-scored Probabilistic Label Trees

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.

Speeding-up One-vs-All Training for Extreme Classification via Smart Initialization

In this paper we show that a simple, data dependent way of setting the initial vector can be used to substantially speed up the training of linear one-versus-all (OVA) classifiers in extreme multi-label classification (XMC). We discuss the problem of choosing the initial weights from the perspective of three goals. We want to start in a region of weight space a) with low loss value, b) that is favourable for second-order optimization, and c) where the conjugate-gradient (CG) calculations can be performed quickly. For margin losses, such an initialization is achieved by selecting the initial vector such that it separates the mean of all positive (relevant for a label) instances from the mean of all negatives -- two quantities that can be calculated quickly for the highly imbalanced binary problems occurring in XMC. We demonstrate a speedup of $\approx 3\times$ for training with squared hinge loss on a variety of XMC datasets. This comes in part from the reduced number of iterations that need to be performed due to starting closer to the solution, and in part from an implicit negative mining effect that allows to ignore easy negatives in the CG step. Because of the convex nature of the optimization problem, the speedup is achieved without any degradation in classification accuracy.

Unbiased Loss Functions for Multilabel Classification with Missing Labels

This paper considers binary and multilabel classification problems in a setting where labels are missing independently and with a known rate. Missing labels are a ubiquitous phenomenon in extreme multi-label classification (XMC) tasks, such as matching Wikipedia articles to a small subset out of the hundreds of thousands of possible tags, where no human annotator can possibly check the validity of all the negative samples. For this reason, propensity-scored precision -- an unbiased estimate for precision-at-k under a known noise model -- has become one of the standard metrics in XMC. Few methods take this problem into account already during the training phase, and all are limited to loss functions that can be decomposed into a sum of contributions from each individual label. A typical approach to training is to reduce the multilabel problem into a series of binary or multiclass problems, and it has been shown that if the surrogate task should be consistent for optimizing recall, the resulting loss function is not decomposable over labels. Therefore, this paper derives the unique unbiased estimators for the different multilabel reductions, including the non-decomposable ones. These estimators suffer from increased variance and may lead to ill-posed optimization problems, which we address by switching to convex upper-bounds. The theoretical considerations are further supplemented by an experimental study showing that the switch to unbiased estimators significantly alters the bias-variance trade-off and may thus require stronger regularization, which in some cases can negate the benefits of unbiased estimation.

Embedding Convolutions for Short Text Extreme Classification with Millions of Labels

Automatic annotation of short-text data to a large number of target labels, referred to as Short Text Extreme Classification, has recently found numerous applications in prediction of related searches and product recommendation tasks. The conventional usage of Convolutional Neural Network (CNN) to capture n-grams in text-classification relies heavily on uniformity in word-ordering and the presence of long input sequences to convolve over. However, this is missing in short and unstructured text sequences encountered in search and recommendation. In order to tackle this, we propose an orthogonal approach by recasting the convolution operation to capture coupled semantics along the embedding dimensions, and develop a word-order agnostic embedding enhancement module to deal with the lack of structure in such queries. Benefitting from the computational efficiency of the convolution operation, Embedding Convolutions, when applied on the enriched word embeddings, result in a light-weight and yet powerful encoder (InceptionXML) that is robust to the inherent lack of structure in short-text extreme classification. Towards scaling our model to problems with millions of labels, we also propose InceptionXML+, which addresses the shortcomings of the dynamic hard-negative mining framework in the recently proposed LightXML by improving the alignment between the label-shortlister and extreme classifier. On popular benchmark datasets, we empirically demonstrate that the proposed method outperforms state-of-the-art deep extreme classifiers such as Astec by an average of 5% and 8% on the P@k and propensity-scored PSP@k metrics respectively.