Regression is a fundamental task in machine learning that has garnered extensive attention over the past decades. The conventional approach for regression involves employing loss functions that primarily concentrate on aligning model prediction with the ground truth for each individual data sample. Recent research endeavors have introduced novel perspectives by incorporating label similarity into regression through the imposition of additional pairwise regularization or contrastive learning on the latent feature space, demonstrating their effectiveness. However, there are two drawbacks to these approaches: (i) their pairwise operations in the latent feature space are computationally more expensive than conventional regression losses; (ii) they lack theoretical insights behind these methods. In this work, we propose GAR (Gradient Aligned Regression) as a competitive alternative method in label space, which is constituted by a conventional regression loss and two pairwise label difference losses for gradient alignment including magnitude and direction. GAR enjoys: i) the same level efficiency as conventional regression loss because the quadratic complexity for the proposed pairwise losses can be reduced to linear complexity; ii) theoretical insights from learning the pairwise label difference to learning the gradient of the ground truth function. We limit our current scope as regression on the clean data setting without noises, outliers or distributional shifts, etc. We demonstrate the effectiveness of the proposed method practically on two synthetic datasets and on eight extensive real-world tasks from six benchmark datasets with other eight competitive baselines. Running time experiments demonstrate the superior efficiency of the proposed GAR compared to existing methods with pairwise regularization or contrastive learning in the latent feature space. Additionally, ablation studies confirm the effectiveness of each component of GAR. The code is open sourced at https://github.com/DixianZhu/GAR.

This paper considers a novel application of deep AUC maximization (DAM) for multi-instance learning (MIL), in which a single class label is assigned to a bag of instances (e.g., multiple 2D slices of a CT scan for a patient). We address a neglected yet non-negligible computational challenge of MIL in the context of DAM, i.e., bag size is too large to be loaded into GPU memory for backpropagation, which is required by the standard pooling methods of MIL. To tackle this challenge, we propose variance-reduced stochastic pooling methods in the spirit of stochastic optimization by formulating the loss function over the pooled prediction as a multi-level compositional function. By synthesizing techniques from stochastic compositional optimization and non-convex min-max optimization, we propose a unified and provable muli-instance DAM (MIDAM) algorithm with stochastic smoothed-max pooling or stochastic attention-based pooling, which only samples a few instances for each bag to compute a stochastic gradient estimator and to update the model parameter. We establish a similar convergence rate of the proposed MIDAM algorithm as the state-of-the-art DAM algorithms. Our extensive experiments on conventional MIL datasets and medical datasets demonstrate the superiority of our MIDAM algorithm. The method is open-sourced at https://libauc.org/.

We study a family of loss functions named label-distributionally robust (LDR) losses for multi-class classification that are formulated from distributionally robust optimization (DRO) perspective, where the uncertainty in the given label information are modeled and captured by taking the worse case of distributional weights. The benefits of this perspective are several fold: (i) it provides a unified framework to explain the classical cross-entropy (CE) loss and SVM loss and their variants, (ii) it includes a special family corresponding to the temperature-scaled CE loss, which is widely adopted but poorly understood; (iii) it allows us to achieve adaptivity to the uncertainty degree of label information at an instance level. Our contributions include: (1) we study both consistency and robustness by establishing top-$k$ ($\forall k\geq 1$) consistency of LDR losses for multi-class classification, and a negative result that a top-$1$ consistent and symmetric robust loss cannot achieve top-$k$ consistency simultaneously for all $k\geq 2$; (2) we propose a new adaptive LDR loss that automatically adapts the individualized temperature parameter to the noise degree of class label of each instance; (3) we demonstrate stable and competitive performance for the proposed adaptive LDR loss on 7 benchmark datasets under 6 noisy label and 1 clean settings against 13 loss functions, and on one real-world noisy dataset. The method is open-sourced at https://github.com/Optimization-AI/ICML2023_LDR.

This paper introduces the award-winning deep learning (DL) library called LibAUC for implementing state-of-the-art algorithms towards optimizing a family of risk functions named X-risks. X-risks refer to a family of compositional functions in which the loss function of each data point is defined in a way that contrasts the data point with a large number of others. They have broad applications in AI for solving classical and emerging problems, including but not limited to classification for imbalanced data (CID), learning to rank (LTR), and contrastive learning of representations (CLR). The motivation of developing LibAUC is to address the convergence issues of existing libraries for solving these problems. In particular, existing libraries may not converge or require very large mini-batch sizes in order to attain good performance for these problems, due to the usage of the standard mini-batch technique in the empirical risk minimization (ERM) framework. Our library is for deep X-risk optimization (DXO) that has achieved great success in solving a variety of tasks for CID, LTR and CLR. The contributions of this paper include: (1) It introduces a new mini-batch based pipeline for implementing DXO algorithms, which differs from existing DL pipeline in the design of controlled data samplers and dynamic mini-batch losses; (2) It provides extensive benchmarking experiments for ablation studies and comparison with existing libraries. The LibAUC library features scalable performance for millions of items to be contrasted, faster and better convergence than existing libraries for optimizing X-risks, seamless PyTorch deployment and versatile APIs for various loss optimization. Our library is available to the open source community at https://github.com/Optimization-AI/LibAUC, to facilitate further academic research and industrial applications.

This paper investigates new families of compositional optimization problems, called non-smooth weakly-convex finite-sum coupled compositional optimization (NSWC FCCO). There has been a growing interest in FCCO due to its wide-ranging applications in machine learning and AI, as well as its ability to address the shortcomings of stochastic algorithms based on empirical risk minimization. However, current research on FCCO presumes that both the inner and outer functions are smooth, limiting their potential to tackle a more diverse set of problems. Our research expands on this area by examining non-smooth weakly-convex FCCO, where the outer function is weakly convex and non-decreasing, and the inner function is weakly-convex. We analyze a single-loop algorithm and establish its complexity for finding an $\epsilon$-stationary point of the Moreau envelop of the objective function. Additionally, we also extend the algorithm for solving novel non-smooth weakly-convex tri-level finite-sum coupled compositional optimization problems, which feature a nested arrangement of three functions. Lastly, we explore the applications of our algorithms in deep learning for two-way partial AUC maximization and multi-instance two-way partial AUC maximization, using empirical studies to showcase the effectiveness of the proposed algorithms.

In this paper, we propose systematic and efficient gradient-based methods for both one-way and two-way partial AUC (pAUC) maximization that are applicable to deep learning. We propose new formulations of pAUC surrogate objectives by using the distributionally robust optimization (DRO) to define the loss for each individual positive data. We consider two formulations of DRO, one of which is based on conditional-value-at-risk (CVaR) that yields a non-smooth but exact estimator for pAUC, and another one is based on a KL divergence regularized DRO that yields an inexact but smooth (soft) estimator for pAUC. For both one-way and two-way pAUC maximization, we propose two algorithms and prove their convergence for optimizing their two formulations, respectively. Experiments demonstrate the effectiveness of the proposed algorithms for pAUC maximization for deep learning on various datasets.

Multivariate time series data are becoming increasingly ubiquitous in varies real-world applications such as smart city, power plant monitoring, wearable devices, etc. Given the current time series segment, how to retrieve similar segments within the historical data in an efficient and effective manner is becoming increasingly important. As it can facilitate underlying applications such as system status identification, anomaly detection, etc. Despite the fact that various binary coding techniques can be applied to this task, few of them are specially designed for multivariate time series data in an unsupervised setting. To this end, we present Deep Unsupervised Binary Coding Networks (DUBCNs) to perform multivariate time series retrieval. DUBCNs employ the Long Short-Term Memory (LSTM) encoder-decoder framework to capture the temporal dynamics within the input segment and consist of three key components, i.e., a temporal encoding mechanism to capture the temporal order of different segments within a mini-batch, a clustering loss on the hidden feature space to capture the hidden feature structure, and an adversarial loss based upon Generative Adversarial Networks (GANs) to enhance the generalization capability of the generated binary codes. Thoroughly empirical studies on three public datasets demonstrated that the proposed DUBCNs can outperform state-of-the-art unsupervised binary coding techniques.

In this paper, we present a novel robust zero- sum game framework for pool-based active learning grounded on advanced statistical learning theory. Pool-based active learning usually consists of two components, namely, learning of a classifier given labeled data and querying of unlabeled data for labeling. Most previous studies on active learning consider these as two separate tasks and propose various heuristics for selecting important unlabeled data for labeling, which may render the selection of unlabeled examples sub-optimal for minimizing the classification error. In contrast, the present work formulates active learning as a unified optimization framework for learning the classifier, i.e., the querying of labels and the learning of models are unified to minimize a common objective for statistical learning. In addition, the proposed method avoids the issues of many previous algorithms such as inefficiency, sampling bias and sensitivity to imbalanced data distribution. Besides theoretical analysis, we conduct extensive experiments on benchmark datasets and demonstrate the superior performance of the proposed active learning method compared with the state-of-the-art methods.

MOTIVATION: With the development of high-throughput sequencing, the number of assembled genomes continues to rise. It is critical to well organize and index many assembled genomes to promote future genomics studies. Burrows-Wheeler Transform (BWT) is an important data structure of genome indexing, which has many fundamental applications; however, it is still non-trivial to construct BWT for large collection of genomes, especially for highly similar or repetitive genomes. Moreover, the state-of-the-art approaches cannot well support scalable parallel computing owing to their incremental nature, which is a bottleneck to use modern computers to accelerate BWT construction. RESULTS: We propose de Bruijn branch-based BWT constructor (deBWT), a novel parallel BWT construction approach. DeBWT innovatively represents and organizes the suffixes of input sequence with a novel data structure, de Bruijn branch encoding. This data structure takes the advantage of de Bruijn graph to facilitate the comparison between the suffixes with long common prefix, which breaks the bottleneck of the BWT construction of repetitive genomic sequences. Meanwhile, deBWT also uses the structure of de Bruijn graph for reducing unnecessary comparisons between suffixes. The benchmarking suggests that, deBWT is efficient and scalable to construct BWT for large dataset by parallel computing. It is well-suited to index many genomes, such as a collection of individual human genomes, with multiple-core servers or clusters. AVAILABILITY AND IMPLEMENTATION: deBWT is implemented in C language, the source code is available at https://github.com/hitbc/deBWT or https://github.com/DixianZhu/deBWTContact: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.