This paper presents SVAM (Sequential Variance-Altered MLE), a unified framework for learning generalized linear models under adversarial label corruption in training data. SVAM extends to tasks such as least squares regression, logistic regression, and gamma regression, whereas many existing works on learning with label corruptions focus only on least squares regression. SVAM is based on a novel variance reduction technique that may be of independent interest and works by iteratively solving weighted MLEs over variance-altered versions of the GLM objective. SVAM offers provable model recovery guarantees superior to the state-of-the-art for robust regression even when a constant fraction of training labels are adversarially corrupted. SVAM also empirically outperforms several existing problem-specific techniques for robust regression and classification. Code for SVAM is available at https://github.com/purushottamkar/svam/

The task of annotating a data point with labels most relevant to it from a large universe of labels is referred to as Extreme Classification (XC). State-of-the-art XC methods have applications in ranking, recommendation, and tagging and mostly employ a combination architecture comprised of a deep encoder and a high-capacity classifier. These two components are often trained in a modular fashion to conserve compute. This paper shows that in XC settings where data paucity and semantic gap issues abound, this can lead to suboptimal encoder training which negatively affects the performance of the overall architecture. The paper then proposes a lightweight alternative DEXA that augments encoder training with auxiliary parameters. Incorporating DEXA into existing XC architectures requires minimal modifications and the method can scale to datasets with 40 million labels and offer predictions that are up to 6% and 15% more accurate than embeddings offered by existing deep XC methods on benchmark and proprietary datasets, respectively. The paper also analyzes DEXA theoretically and shows that it offers provably superior encoder training than existing Siamese training strategies in certain realizable settings. Code for DEXA is available at https://github.com/Extreme-classification/dexa.

Personalized retrieval seeks to retrieve items relevant to a user event (e.g. a page visit or a query) that are adapted to the user's personal preferences. For example, two users who happen to perform the same event such as visiting the same product page or asking the same query should receive potentially distinct recommendations adapted to their individual tastes. Personalization is seldom attempted over catalogs of millions of items since the cost of existing personalization routines scale linearly in the number of candidate items. For example, performing two-sided personalized retrieval (with both event and item embeddings personalized to the user) incurs prohibitive storage and compute costs. Instead, it is common to use non-personalized retrieval to obtain a small shortlist of items over which personalized re-ranking can be done quickly. Despite being scalable, this strategy risks losing items uniquely relevant to a user that fail to get shortlisted during non-personalized retrieval. This paper bridges this gap by developing the XPERT algorithm that identifies a form of two-sided personalization that can be scalably implemented over millions of items and hundreds of millions of users. Key to overcoming the computational challenges of personalized retrieval is a novel concept of morph operators that can be used with arbitrary encoder architectures, completely avoids the steep memory overheads of two-sided personalization, provides millisecond-time inference and offers multi-intent retrieval. On multiple public and proprietary datasets, XPERT offered upto 5% superior recall and AUC than state-of-the-art techniques. Code for XPERT is available at https://github.com/personalizedretrieval/xpert.

Extreme Classification (XC) seeks to tag data points with the most relevant subset of labels from an extremely large label set. Performing deep XC with dense, learnt representations for data points and labels has attracted much attention due to its superiority over earlier XC methods that used sparse, hand-crafted features. Negative mining techniques have emerged as a critical component of all deep XC methods, allowing them to scale to millions of labels. However, despite recent advances, training deep XC models with large encoder architectures such as transformers remains challenging. This paper notices that memory overheads of popular negative mining techniques often force mini-batch sizes to remain small and slow training down. In response, this paper introduces NGAME, a light-weight mini-batch creation technique that offers provably accurate in-batch negative samples. This allows training with larger mini-batches offering significantly faster convergence and higher accuracies than existing negative sampling techniques. NGAME was found to be up to 16% more accurate than state-of-the-art methods on a wide array of benchmark datasets for extreme classification, as well as 3% more accurate at retrieving search engine queries in response to a user webpage visit to show personalized ads. In live A/B tests on a popular search engine, NGAME yielded up to 23% gains in click-through-rates. Code for NGAME is available at https://github.com/Extreme-classification/ngame

This paper develops the MUFIN technique for extreme classification (XC) tasks with millions of labels where data-points and labels are endowed with visual and textual de-scriptors. Applications of MUFIN to product-to-product recommendation and bid query prediction over several mil-lions of products are presented. Contemporary multi-modal methods frequently rely on purely embedding-based meth-ods. On the other hand, XC methods utilize classifier ar-chitectures to offer superior accuracies than embedding-only methods but mostly focus on text-based categorization tasks. MUFIN bridges this gap by reformulating multi-modal categorization as an XC problem with several mil-lions of labels. This presents the twin challenges of devel-oping multi-modal architectures that can offer embeddings sufficiently expressive to allow accurate categorization over millions of labels; and training and inference routines that scale logarithmically in the number of labels. MUFIN de-velops an architecture based on cross-modal attention and trains it in a modular fashion using pre-training and positive and negative mining. A novel product-to-product rec-ommendation dataset MM-AmazonTitles-300K containing over 300K products was curated from publicly available amazon.com listings with each product endowed with a title and multiple images. On the MM-AmazonTitles-300K and Polyvore datasets, and a dataset with over 4 million labels curated from click logs of the Bing search engine, MUFIN offered at least 3% higher accuracy than leading text-based, image-based and multi-modal techniques.

Deep extreme multi-label learning (XML) requires training deep architectures that can tag a data point with its most relevant subset of labels from an extremely large label set. XML applications such as ad and product recommendation involve labels rarely seen during training but which nevertheless hold the key to recommendations that delight users. Effective utilization of label metadata and high quality predictions for rare labels at the scale of millions of labels are thus key challenges in contemporary XML research. To address these, this paper develops the SiameseXML framework based on a novel probabilistic model that naturally motivates a modular approach melding Siamese architectures with high-capacity extreme classifiers, and a training pipeline that effortlessly scales to tasks with 100 million labels. SiameseXML offers predictions 2–13% more accurate than leading XML methods on public benchmark datasets, as well as in live A/B tests on the Bing search engine, it offers significant gains in click-through-rates, coverage, revenue and other online metrics over state-of-the-art techniques currently in production. Code for SiameseXML is available at https://github.com/Extreme-classification/siamesexml

Extreme multi-label classification (XML) involves tagging a data point with its most relevant subset of labels from an extremely large label set, with several applications such as product-to-product recommendation with millions of products. Although leading XML algorithms scale to millions of labels, they largely ignore label metadata such as textual descriptions of the labels. On the other hand, classical techniques that can utilize label metadata via representation learning using deep networks struggle in extreme settings. This paper develops the DECAF algorithm that addresses these challenges by learning models enriched by label metadata that jointly learn model parameters and feature representations using deep networks and offer accurate classification at the scale of millions of labels. DECAF makes specific contributions to model architecture design, initialization, and training, enabling it to offer up to 2-6% more accurate prediction than leading extreme classifiers on publicly available benchmark product-to-product recommendation datasets, such as LF-AmazonTitles-1.3M. At the same time, DECAF was found to be up to 22x faster at inference than leading deep extreme classifiers, which makes it suitable for real-time applications that require predictions within a few milliseconds. The code for DECAF is available at the following URL: https://github.com/Extreme-classification/DECAF

Deep extreme classification (XC) seeks to train deep architectures that can tag a data point with its most relevant subset of labels from an extremely large label set. The core utility of XC comes from predicting labels that are rarely seen during training. Such rare labels hold the key to personalized recommendations that can delight and surprise a user. However, the large number of rare labels and small amount of training data per rare label offer significant statistical and computational challenges. State-of-the-art deep XC methods attempt to remedy this by incorporating textual descriptions of labels but do not adequately address the problem. This paper presents ECLARE, a scalable deep learning architecture that incorporates not only label text, but also label correlations, to offer accurate real-time predictions within a few milliseconds. Core contributions of ECLARE include a frugal architecture and scalable techniques to train deep models along with label correlation graphs at the scale of millions of labels. In particular, ECLARE offers predictions that are 2–14% more accurate on both publicly available benchmark datasets as well as proprietary datasets for a related products recommendation task sourced from the Bing search engine. Code for ECLARE is available at https://github.com/Extreme-classification/ECLARE

We provide the first global model recovery results for the IRLS (iteratively reweighted least squares) heuristic for robust regression problems. IRLS is known to offer excellent performance, despite bad initializations and data corruption, for several parameter estimation problems. Existing analyses of IRLS frequently require careful initialization, thus offering only local convergence guarantees. We remedy this by proposing augmentations to the basic IRLS routine that not only offer guaranteed global recovery, but in practice also outperform state-of-the-art algorithms for robust regression. Our routines are more immune to hyperparameter misspecification in basic regression tasks, as well as applied tasks such as linear-armed bandit problems. Our theoretical analyses rely on a novel extension of the notions of strong convexity and smoothness to weighted strong convexity and smoothness, and establishing that sub-Gaussian designs offer bounded weighted condition numbers. These notions may be useful in analyzing other algorithms as well.

Extreme classification seeks to assign each data point, the most relevant labels from a universe of a million or more labels. This task is faced with the dual challenge of high precision and scalability, with millisecond level prediction times being a benchmark. We propose DEFRAG, an adaptive feature agglomeration technique to accelerate extreme classification algorithms. Despite past works on feature clustering and selection, DEFRAG distinguishes itself in being able to scale to millions of features, and is especially beneficial when feature sets are sparse, which is typical of recommendation and multi-label datasets. The method comes with provable performance guarantees and performs efficient task-driven agglomeration to reduce feature dimensionalities by an order of magnitude or more. Experiments show that DEFRAG can not only reduce training and prediction times of several leading extreme classification algorithms by as much as 40%, but also be used for feature reconstruction to address the problem of missing features, as well as offer superior coverage on rare labels.

The problem of multi-instance multi-label learning (MIML) requires a bag of instances to be assigned a set of labels most relevant to the bag as a whole. The problem finds numerous applications in machine learning, computer vision, and natural language processing settings where only partial or distant supervision is available. We present a novel method for optimizing multivariate performance measures in the MIML setting. Our approach MIML-perf uses a novel plug-in technique and offers a seamless way to optimize a vast variety of performance measures such as macro and micro-F measure, average precision, which are performance measures of choice in multi-label learning domains. MIML-perf offers two key benefits over the state of the art. Firstly, across a diverse range of benchmark tasks, ranging from relation extraction to text categorization and scene classification, MIML-perf offers superior performance as compared to state of the art methods designed specifically for these tasks. Secondly, MIML-perf operates with significantly reduced running times as compared to other methods, often by an order of magnitude or more.

We investigate a novel cluster-of-bandit algorithm CAB for collaborative recommendation tasks that implements the underlying feedback sharing mechanism by estimating user neighborhoods in a context-dependent manner. CAB makes sharp departures from the state of the art by incorporating collaborative effects into inference, as well as learning processes in a manner that seamlessly interleaves explore-exploit tradeoffs and collaborative steps. We prove regret bounds for CAB under various data-dependent assumptions which exhibit a crisp dependence on the expected number of clusters over the users, a natural measure of the statistical difficulty of the learning task. Experiments on production and real-world datasets show that CAB offers significantly increased prediction performance against a representative pool of state-of-the-art methods.

We present the first efficient and provably consistent estimator for the robust regression problem. The area of robust learning and optimization has generated a significant amount of interest in the learning and statistics communities in recent years owing to its applicability in scenarios with corrupted data, as well as in handling model mis-specifications. In particular, special interest has been devoted to the fundamental problem of robust linear regression where estimators that can tolerate corruption in up to a constant fraction of the response variables are widely studied. Surprisingly however, to this date, we are not aware of a polynomial time estimator that offers a consistent estimate in the presence of dense, unbounded corruptions. In this work we present such an estimator, called CRR. This solves an open problem put forward in the work of (Bhatia et al, 2015). Our consistency analysis requires a novel two-stage proof technique involving a careful analysis of the stability of ordered lists which may be of independent interest. We show that CRR not only offers consistent estimates, but is empirically far superior to several other recently proposed algorithms for the robust regression problem, including extended Lasso and the TORRENT algorithm. In comparison, CRR offers comparable or better model recovery but with runtimes that are faster by an order of magnitude.

The F-measure and its variants are performance measures of choice for evaluating classification and retrieval tasks in the presence of severe class imbalance. It is thus highly desirable to be able to directly optimize these performance measures on large-scale data. Recent advances have shown that this is possible in the simple binary classification setting. However, scant progress exists in multiclass settings with a large number of classes where, in addition, class-imbalance is much more severe. The lack of progress is especially conspicuous for the macro-averaged F-measure, which is the widely preferred F-measure variant in multiclass settings due to its equal emphasis on rare classes. Known methods of optimization scale poorly for macro F-measure, often requiring run times that are exponential in the number of classes. We develop BEAM-F, the first efficient method for directly optimizing the macro F-measure in multiclass settings. The challenge here is the intractability of optimizing a sum of fractional-linear functions over the space of confusion matrices. We overcome this difficulty by formulating the problem as a biconcave maximization program and solve it using an efficient alternating maximization approach that involves a Frank-Wolfe based iterative solver. Our approach offers guaranteed convergence to a stationary point and experiments show that, for a range synthetic data sets and real-world applications, our method offers superior performance on problems exhibiting large class imbalance.

The estimation of class prevalence, i.e., of the fraction of a population that belongs to a certain class, is an important task in data analytics, and finds applications in many domains such as the social sciences, market research, epidemiology, and others. For example, in sentiment analysis the goal is often not to estimate whether a specific text conveys a positive or a negative sentiment, but rather to estimate the overall distribution of positive and negative sentiments, e.g., in a certain time frame. A popular way of performing the above task, often dubbed quantification, is to use supervised learning in order to train a prevalence estimator from labeled data.

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.

Modern classification problems frequently present mild to severe label imbalance as well as specific requirements on classification characteristics, and require optimizing performance measures that are non-decomposable over the dataset, such as F-measure. Such measures have spurred much interest and pose specific challenges to learning algorithms since their non-additive nature precludes a direct application of well-studied large scale optimization methods such as stochastic gradient descent. In this paper we reveal that for two large families of performance measures that can be expressed as functions of true positive/negative rates, it is indeed possible to implement point stochastic updates. The families we consider are concave and pseudo-linear functions of TPR, TNR which cover several popularly used performance measures such as F-measure, G-mean and H-mean. Our core contribution is an adaptive linearization scheme for these families, using which we develop optimization techniques that enable truly point-based stochastic updates. For concave performance measures we propose SPADE, a stochastic primal dual solver; for pseudo-linear measures we propose STAMP, a stochastic alternate maximization procedure. Both methods have crisp convergence guarantees, demonstrate significant speedups over existing methods - often by an order of magnitude or more, and give similar or more accurate predictions on test data.

We study the problem of Robust Least Squares Regression (RLSR) where several response variables can be adversarially corrupted. More specifically, for a data matrix X \in \R^{p x n} and an underlying model w*, the response vector is generated as y = X'w* + b where b \in n is the corruption vector supported over at most C.n coordinates. Existing exact recovery results for RLSR focus solely on L1-penalty based convex formulations and impose relatively strict model assumptions such as requiring the corruptions b to be selected independently of X.In this work, we study a simple hard-thresholding algorithm called TORRENT which, under mild conditions on X, can recover w* exactly even if b corrupts the response variables in an adversarial manner, i.e. both the support and entries of b are selected adversarially after observing X and w*. Our results hold under deterministic assumptions which are satisfied if X is sampled from any sub-Gaussian distribution. Finally unlike existing results that apply only to a fixed w*, generated independently of X, our results are universal and hold for any w* \in \R^p.Next, we propose gradient descent-based extensions of TORRENT that can scale efficiently to large scale problems, such as high dimensional sparse recovery. and prove similar recovery guarantees for these extensions. Empirically we find TORRENT, and more so its extensions, offering significantly faster recovery than the state-of-the-art L1 solvers. For instance, even on moderate-sized datasets (with p = 50K) with around 40% corrupted responses, a variant of our proposed method called TORRENT-HYB is more than 20x faster than the best L1 solver.

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 SLEEC classifier to address both limitations. The main technical contribution in SLEEC is a formulation for learning a small ensemble of local distance preserving embeddings which can accurately predict infrequently occurring (tail) labels. This allows SLEEC 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 compare our method against state-of-the-art methods for extreme multi-label classification. Experiments reveal that SLEEC 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%). SLEEC can also scale efficiently to data sets with a million labels which are beyond the pale of leading embedding methods.

The multi-label classification problem has generated significant interest in recent years. However, existing approaches do not adequately address two key challenges: (a) scaling up to problems with a large number (say millions) of labels, and (b) handling data with missing labels. In this paper, we directly address both these problems by studying the multi-label problem in a generic empirical risk minimization (ERM) framework. Our framework, despite being simple, is surprisingly able to encompass several recent label-compression based methods which can be derived as special cases of our method. To optimize the ERM problem, we develop techniques that exploit the structure of specific loss functions - such as the squared loss function - to obtain efficient algorithms. We further show that our learning framework admits excess risk bounds even in the presence of missing labels. Our bounds are tight and demonstrate better generalization performance for low-rank promoting trace-norm regularization when compared to (rank insensitive) Frobenius norm regularization. Finally, we present extensive empirical results on a variety of benchmark datasets and show that our methods perform significantly better than existing label compression based methods and can scale up to very large datasets such as a Wikipedia dataset that has more than 200,000 labels.

In this paper, we study the generalization properties of online learning based stochastic methods for supervised learning problems where the loss function is dependent on more than one training sample (e.g., metric learning, ranking). We present a generic decoupling technique that enables us to provide Rademacher complexity-based generalization error bounds. Our bounds are in general tighter than those obtained by Wang et al. (COLT 2012) for the same problem. Using our decoupling technique, we are further able to obtain fast convergence rates for strongly con-vex pairwise loss functions. We are also able to analyze a class of memory efficient on-line learning algorithms for pairwise learning problems that use only a bounded subset of past training samples to update the hypothesis at each step. Finally, in order to complement our generalization bounds, we propose a novel memory efficient online learning algorithm for higher order learning problems with bounded regret guarantees.

We address the problem of general supervised learning when data can only be accessed through an (indefinite) similarity function between data points. Existing work on learning with indefinite kernels has concentrated solely on binary/multiclass classification problems. We propose a model that is generic enough to handle any supervised learning task and also subsumes the model previously proposed for classification. We give a ''goodness'' criterion for similarity functions w.r.t. a given supervised learning task and then adapt a well-known landmarking technique to provide efficient algorithms for supervised learning using ''good'' similarity functions. We demonstrate the effectiveness of our model on three important supervised learning problems: a) real-valued regression, b) ordinal regression and c) ranking where we show that our method guarantees bounded generalization error. Furthermore, for the case of real-valued regression, we give a natural goodness definition that, when used in conjunction with a recent result in sparse vector recovery, guarantees a sparse predictor with bounded generalization error. Finally, we report results of our learning algorithms on regression and ordinal regression tasks using non-PSD similarity functions and demonstrate the effectiveness of our algorithms, especially that of the sparse landmark selection algorithm that achieves significantly higher accuracies than the baseline methods while offering reduced computational costs.

We consider the problem of classification using similarity/distance functions over data. Specifically, we propose a framework for defining the goodness of a (dis)similarity function with respect to a given learning task and propose algorithms that have guaranteed generalization properties when working with such good functions. Our framework unifies and generalizes the frameworks proposed by (Balcan-Blum 2006) and (Wang et al 2007). An attractive feature of our framework is its adaptability to data - we do not promote a fixed notion of goodness but rather let data dictate it. We show, by giving theoretical guarantees that the goodness criterion best suited to a problem can itself be learned which makes our approach applicable to a variety of domains and problems. We propose a landmarking-based approach to obtaining a classifier from such learned goodness criteria. We then provide a novel diversity based heuristic to perform task-driven selection of landmark points instead of random selection. We demonstrate the effectiveness of our goodness criteria learning method as well as the landmark selection heuristic on a variety of similarity-based learning datasets and benchmark UCI datasets on which our method consistently outperforms existing approaches by a significant margin.

The Random Projection Tree (RPTree) structures proposed in [Dasgupta-Freund-STOC-08] are space partitioning data structures that automatically adapt to various notions of intrinsic dimensionality of data. We prove new results for both the RPTree-Max and the RPTree-Mean data structures. Our result for RPTree-Max gives a near-optimal bound on the number of levels required by this data structure to reduce the size of its cells by a factor s >= 2. We also prove a packing lemma for this data structure. Our final result shows that low-dimensional manifolds possess bounded Local Covariance Dimension. As a consequence we show that RPTree-Mean adapts to manifold dimension as well.