LGOct 29, 2022Code
CascadeXML: Rethinking Transformers for End-to-end Multi-resolution Training in Extreme Multi-label ClassificationSiddhant Kharbanda, Atmadeep Banerjee, Erik Schultheis et al. · microsoft-research
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}.
LGMay 31
HASTE: Hardware-Aware Dynamic Sparse Training for Large Output SpacesNasib Ullah, Jinbin Zhang, Jean Lucien Randrianantenaina et al.
Extreme multi-label classification (XMC) involves learning models over large output spaces with millions of labels, making the output layer a memory-compute bottleneck. While sparsity-based methods reduce arithmetic complexity, they often fail to yield proportional speedups due to irregular memory access, poor hardware utilization, or reliance on auxiliary architectural components in long-tailed regimes. We introduce group-shared fixed fan-in sparsity, a semi-structured output-layer design in which semantically related labels share a sparse input pattern while retaining independent weights. This grouping introduces a task-aligned inductive bias -- encouraging related labels to share feature subsets -- while reducing index memory overhead, increasing feature reuse across labels, and enabling efficient GPU execution via custom CUDA kernels that leverage modern accelerator primitives. As an alternative to auxiliary objectives, we exploit the long-tailed structure of XMC by decomposing the output layer into a small dense head over frequent labels and a group-shared sparse tail over the remainder, providing an informative gradient pathway while preserving the memory benefits of sparsity. Through kernel-level microbenchmarking, we show that group-shared fixed fan-in translates arithmetic reductions into practical wall-clock gains, achieving up to $4.4\times$ speedup in the forward pass and up to $25\times$ speedup in backward passes over standard fixed fan-in sparsity, while operating within a few percent of a FLOPs-matched dense bottleneck. Across large-scale XMC benchmarks, our approach matches or improves precision@k over prior sparse baselines, while narrowing the performance gap to dense.
LGJul 26, 2022
On Missing Labels, Long-tails and Propensities in Extreme Multi-label ClassificationErik Schultheis, Marek Wydmuch, Rohit Babbar et al.
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.
LGNov 9, 2023
Generalized test utilities for long-tail performance in extreme multi-label classificationErik Schultheis, Marek Wydmuch, Wojciech Kotłowski et al.
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 to optimize 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.
LGJun 6, 2023
Towards Memory-Efficient Training for Extremely Large Output Spaces -- Learning with 500k Labels on a Single Commodity GPUErik Schultheis, Rohit Babbar
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.
LGMay 4, 2024Code
UniDEC : Unified Dual Encoder and Classifier Training for Extreme Multi-Label ClassificationSiddhant Kharbanda, Devaansh Gupta, Gururaj K et al. · microsoft-research
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 4-16x. 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.
LGDec 14, 2021Code
Adversarial Examples for Extreme Multilabel Text ClassificationMohammadreza Qaraei, Rohit Babbar
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
CLSep 13, 2021Code
InceptionXML: A Lightweight Framework with Synchronized Negative Sampling for Short Text Extreme ClassificationSiddhant Kharbanda, Atmadeep Banerjee, Devaansh Gupta et al.
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 short-listing 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/inceptionxml.
LGApr 17, 2019Code
Bonsai -- Diverse and Shallow Trees for Extreme Multi-label ClassificationSujay Khandagale, Han Xiao, Rohit Babbar
Extreme multi-label classification (XMC) refers to supervised multi-label learning involving hundreds of thousand or even millions of labels. In this paper, we develop a suite of algorithms, called Bonsai, which generalizes the notion of label representation in XMC, and partitions the labels in the representation space to learn shallow trees. We show three concrete realizations of this label representation space including : (i) the input space which is spanned by the input features, (ii) the output space spanned by label vectors based on their co-occurrence with other labels, and (iii) the joint space by combining the input and output representations. Furthermore, the constraint-free multi-way partitions learnt iteratively in these spaces lead to shallow trees. By combining the effect of shallow trees and generalized label representation, Bonsai achieves the best of both worlds - fast training which is comparable to state-of-the-art tree-based methods in XMC, and much better prediction accuracy, particularly on tail-labels. On a benchmark Amazon-3M dataset with 3 million labels, \bonsai outperforms a state-of-the-art one-vs-rest method in terms of prediction accuracy, while being approximately 200 times faster to train. The code for Bonsai is available at \url{https://github.com/xmc-aalto/bonsai}
LGMay 3, 2024
Learning label-label correlations in Extreme Multi-label Classification via Label FeaturesSiddhant Kharbanda, Devaansh Gupta, Erik Schultheis et al. · microsoft-research
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 works in this domain have increasingly focused on a symmetric problem setting where both input instances and label features are short-text in nature. Short-text XMC with label features has found numerous applications in areas such as query-to-ad-phrase matching in search ads, title-based product recommendation, prediction of related searches. In this paper, we propose Gandalf, a novel approach which makes use of a label co-occurrence graph to leverage label features as additional data points to supplement the training distribution. By exploiting the characteristics of the short-text XMC problem, it leverages the label features to construct valid training instances, and uses the label graph for generating the corresponding soft-label targets, hence effectively capturing the label-label correlations. Surprisingly, models trained on these new training instances, although being less than half of the original dataset, can outperform models trained on the original dataset, particularly on the PSP@k metric for tail labels. With this insight, we aim to train existing XMC algorithms on both, the original and new training instances, leading to an average 5% relative improvements for 6 state-of-the-art algorithms across 4 benchmark datasets consisting of up to 1.3M labels. Gandalf can be applied in a plug-and-play manner to various methods and thus forwards the state-of-the-art in the domain, without incurring any additional computational overheads.
LGJan 29, 2024
Consistent algorithms for multi-label classification with macro-at-$k$ metricsErik Schultheis, Wojciech Kotłowski, Marek Wydmuch et al.
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.
LGNov 5, 2024
Navigating Extremes: Dynamic Sparsity in Large Output SpacesNasib Ullah, Erik Schultheis, Mike Lasby et al.
In recent years, Dynamic Sparse Training (DST) has emerged as an alternative to post-training pruning for generating efficient models. In principle, DST allows for a more memory efficient training process, as it maintains sparsity throughout the entire training run. However, current DST implementations fail to capitalize on this in practice. Because sparse matrix multiplication is much less efficient than dense matrix multiplication on GPUs, most implementations simulate sparsity by masking weights. In this paper, we leverage recent advances in semi-structured sparse training to apply DST in the domain of classification with large output spaces, where memory-efficiency is paramount. With a label space of possibly millions of candidates, the classification layer alone will consume several gigabytes of memory. Switching from a dense to a fixed fan-in sparse layer updated with sparse evolutionary training (SET); however, severely hampers training convergence, especially at the largest label spaces. We find that poor gradient flow from the sparse classifier to the dense text encoder make it difficult to learn good input representations. By employing an intermediate layer or adding an auxiliary training objective, we recover most of the generalisation performance of the dense model. Overall, we demonstrate the applicability and practical benefits of DST in a challenging domain -- characterized by a highly skewed label distribution that differs substantially from typical DST benchmark datasets -- which enables end-to-end training with millions of labels on commodity hardware.
LGNov 6, 2024
Labels in Extremes: How Well Calibrated are Extreme Multi-label Classifiers?Nasib Ullah, Erik Schultheis, Jinbin Zhang et al.
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: \emph{Evaluating} each potential label for its expected worth, and then \emph{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 \emph{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 \emph{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.
LGOct 13, 2025
ELMO: Efficiency via Low-precision and Peak Memory Optimization in Large Output SpacesJinbin Zhang, Nasib Ullah, Erik Schultheis et al.
Large output spaces, also referred to as Extreme multilabel classification (XMC), is a setting that arises, e.g., in large-scale tagging and product-to-product recommendation, and is characterized by the number of labels ranging from hundreds of thousands to millions. This means that the linear classification head, usually only a tiny fraction of the overall model, turns into the main driver for compute and memory demand. Current state-of-the-art XMC methods predominantly rely on FP16-FP32 mixed-precision training, which we show can be unstable, and inefficient in terms of memory usage and computational overhead. Meanwhile, existing low-precision methods typically retain higher precision for the classification layer. In this work, we propose ELMO, a pure low-precision training framework for XMC models using BFloat16 and Float8 data types. By leveraging Kahan summation and stochastic rounding, we demonstrate that XMC models can be effectively trained entirely in Float8, without relying on single-precision master weights or tensor scaling. Low-precision training, combined with our proposed memory optimizations -- gradient fusion and chunking -- enables significant reductions in GPU memory usage. For example, we train a 3-million-label XMC model with only 6.6 GiB of GPU memory, compared to the 39.7 GiB required by the optimized SOTA method, Renee without compromising accuracy.
CLOct 11, 2025
DynaSpec: Context-aware Dynamic Speculative Sampling for Large-Vocabulary Language ModelsJinbin Zhang, Nasib Ullah, Erik Schultheis et al.
Speculative decoding has become a standard way to accelerate LLM inference: a small drafter proposes multiple tokens and a large target model verifies them once per speculation length. Recently, scaling of the LLM vocabulary has pushed the number of tokens to grow substantially. While verification over the full vocabulary leaves the target model largely unaffected, the O(|V|d) parameters in the drafter's output head become a latency bottleneck, slowing the entire pipeline. Contemporary methods (e.g., FR-Spec, VocabTrim) restrict the drafter's vocabulary to a fixed top frequent subset of the target model's vocabulary. Although this reduces draft-time compute, it is brittle, since: (i) frequency lists are corpus-dependent and require retuning to generalize, and (ii) static shortlists suppress rare or domain-specific tokens, lowering the expected number of tokens per verification step. We propose DynaSpec, a context-dependent dynamic shortlisting mechanism that is robust, speeds up drafting, and generalizes across diverse tasks. Concretely, we introduce lightweight, coarse-grained meta-classifiers that route contexts to a small number of token clusters; the union of the top-k selected clusters forms the drafter's shortlist, while verification retains the full vocabulary and exactness. The meta-classifier finishes its computation earlier than the drafter's hidden state generation by exploiting parallel execution of draft encoding and meta shortlisting on separate streams. Across standard speculative decoding benchmarks, DynaSpec delivers consistent improvements in mean accepted length, for Llama-3-8B, reaching upto 98.2% of full-vocabulary performance, while fixed-shortlist baselines attain only 84.4%. By leveraging context-dependent selection, DynaSpec achieves up to a 2.18 times increase in generated tokens compared to 1.91 times for fixed-vocabulary approaches.
LGJun 20, 2024
A General Online Algorithm for Optimizing Complex Performance MetricsWojciech Kotłowski, Marek Wydmuch, Erik Schultheis et al.
We consider sequential maximization of performance metrics that are general functions of a confusion matrix of a classifier (such as precision, F-measure, or G-mean). Such metrics are, in general, non-decomposable over individual instances, making their optimization very challenging. While they have been extensively studied under different frameworks in the batch setting, their analysis in the online learning regime is very limited, with only a few distinguished exceptions. In this paper, we introduce and analyze a general online algorithm that can be used in a straightforward way with a variety of complex performance metrics in binary, multi-class, and multi-label classification problems. The algorithm's update and prediction rules are appealingly simple and computationally efficient without the need to store any past data. We show the algorithm attains $\mathcal{O}(\frac{\ln n}{n})$ regret for concave and smooth metrics and verify the efficiency of the proposed algorithm in empirical studies.
LGJun 13, 2024
Large Language Model as a Teacher for Zero-shot Tagging at Extreme ScalesJinbin Zhang, Nasib Ullah, Rohit Babbar
Extreme Multi-label Text Classification (XMC) entails selecting the most relevant labels for an instance from a vast label set. Extreme Zero-shot XMC (EZ-XMC) extends this challenge by operating without annotated data, relying only on raw text instances and a predefined label set, making it particularly critical for addressing cold-start problems in large-scale recommendation and categorization systems. State-of-the-art methods, such as MACLR and RTS, leverage lightweight bi-encoders but rely on suboptimal pseudo labels for training, such as document titles (MACLR) or document segments (RTS), which may not align well with the intended tagging or categorization tasks. On the other hand, LLM-based approaches, like ICXML, achieve better label-instance alignment but are computationally expensive and impractical for real-world EZ-XMC applications due to their heavy inference costs. In this paper, we introduce LMTX (Large language Model as Teacher for eXtreme classification), a novel framework that bridges the gap between these two approaches. LMTX utilizes an LLM to identify high-quality pseudo labels during training, while employing a lightweight bi-encoder for efficient inference. This design eliminates the need for LLMs at inference time, offering the benefits of improved label alignment without sacrificing computational efficiency. Our approach achieves superior performance and efficiency over both LLM and non-LLM based approaches, establishing a new state-of-the-art in EZ-XMC.
LGOct 20, 2021
Propensity-scored Probabilistic Label TreesMarek Wydmuch, Kalina Jasinska-Kobus, Rohit Babbar et al.
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.
LGSep 27, 2021
Speeding-up One-vs-All Training for Extreme Classification via Smart InitializationErik Schultheis, Rohit Babbar
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.
LGSep 23, 2021
Unbiased Loss Functions for Multilabel Classification with Missing LabelsErik Schultheis, Rohit Babbar
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.
MLJul 1, 2020
Unbiased Loss Functions for Extreme Classification With Missing LabelsErik Schultheis, Mohammadreza Qaraei, Priyanshu Gupta et al.
The goal in extreme multi-label classification (XMC) is to tag an instance with a small subset of relevant labels from an extremely large set of possible labels. In addition to the computational burden arising from large number of training instances, features and labels, problems in XMC are faced with two statistical challenges, (i) large number of 'tail-labels' -- those which occur very infrequently, and (ii) missing labels as it is virtually impossible to manually assign every relevant label to an instance. In this work, we derive an unbiased estimator for general formulation of loss functions which decompose over labels, and then infer the forms for commonly used loss functions such as hinge- and squared-hinge-loss and binary cross-entropy loss. We show that the derived unbiased estimators, in the form of appropriate weighting factors, can be easily incorporated in state-of-the-art algorithms for extreme classification, thereby scaling to datasets with hundreds of thousand labels. However, empirically, we find a slightly altered version that gives more relative weight to tail labels to perform even better. We suspect is due to the label imbalance in the dataset, which is not explicitly addressed by our theoretically derived estimator. Minimizing the proposed loss functions leads to significant improvement over existing methods (up to 20% in some cases) on benchmark datasets in XMC.
MLMar 5, 2018
Adversarial Extreme Multi-label ClassificationRohit Babbar, Bernhard Schölkopf
The goal in extreme multi-label classification is to learn a classifier which can assign a small subset of relevant labels to an instance from an extremely large set of target labels. Datasets in extreme classification exhibit a long tail of labels which have small number of positive training instances. In this work, we pose the learning task in extreme classification with large number of tail-labels as learning in the presence of adversarial perturbations. This view motivates a robust optimization framework and equivalence to a corresponding regularized objective. Under the proposed robustness framework, we demonstrate efficacy of Hamming loss for tail-label detection in extreme classification. The equivalent regularized objective, in combination with proximal gradient based optimization, performs better than state-of-the-art methods on propensity scored versions of precision@k and nDCG@k(upto 20% relative improvement over PFastreXML - a leading tree-based approach and 60% relative improvement over SLEEC - a leading label-embedding approach). Furthermore, we also highlight the sub-optimality of a sparse solver in a widely used package for large-scale linear classification, which is interesting in its own right. We also investigate the spectral properties of label graphs for providing novel insights towards understanding the conditions governing the performance of Hamming loss based one-vs-rest scheme vis-à-vis label embedding methods.
MLSep 8, 2016
DiSMEC - Distributed Sparse Machines for Extreme Multi-label ClassificationRohit Babbar, Bernhard Shoelkopf
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. In this work, we present DiSMEC, which is a large-scale distributed framework for learning one-versus-rest linear classifiers coupled with explicit capacity control to control model size. Unlike most state-of-the-art methods, DiSMEC does not make any low rank assumptions on the label matrix. Using double layer of parallelization, DiSMEC can learn classifiers for datasets consisting hundreds of thousands labels within few hours. The explicit capacity control mechanism filters out spurious parameters which keep the model compact in size, without losing prediction accuracy. We conduct extensive empirical evaluation on publicly available real-world datasets consisting upto 670,000 labels. We compare DiSMEC with recent state-of-the-art approaches, including - SLEEC which is a leading approach for learning sparse local embeddings, and FastXML which is a tree-based approach optimizing ranking based loss function. On some of the datasets, DiSMEC can significantly boost prediction accuracies - 10% better compared to SLECC and 15% better compared to FastXML, in absolute terms.