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Social Aspects · Privacy-preserving Statistics and Machine Learning

Chendi Wang, Yuqing Zhu, Weijie Su, Yu-Xiang Wang

A recent study by De et al. (2022) shows that large-scale representation learning through pre-training on a public dataset significantly enhances differentially private (DP) learning in downstream tasks. To explain this, we consider a layer-peeled model in representation learning, resulting in Neural Collapse (NC) phenomena. Within NC, we establish that the misclassification error is independent of dimension when the distance between actual and ideal features is below a threshold. We empirically evaluate feature quality in the last layer under different pre-trained models, showing that a more powerful pre-trained model improves feature representation. Moreover, we show that DP fine-tuning is less robust compared to non-DP fine-tuning, especially with perturbations. Supported by theoretical analyses and experiments, we suggest strategies like feature normalization and dimension reduction methods such as PCA to enhance DP fine-tuning robustness. Conducting PCA on last-layer features significantly improves testing accuracy.

Miscellaneous Aspects of Machine Learning

Jing Wang, Miao Yu, Peng Zhao, Zhi-Hua Zhou

The study of machine learning under limited resources has gathered increasing attention, considering improving the learning efficiency and effectiveness with budgeted resources. However, previous efforts mainly focus on *single* learning task, and a common resource-limited scenario is less explored: to handle *multiple* time-constrained learning tasks concurrently with budgeted computational resources. In this paper, we point out that this is a very challenging task because it demands the learner to be concerned about not only the progress of the learning tasks but also the coordinative allocation of computational resources. We present the *Learning with Adaptive Resource Allocation* (LARA) approach, which comprises an efficient online estimator for learning progress prediction, an adaptive search method for computational resource allocation, and a balancing strategy for alleviating prediction-allocation compounding errors. Empirical studies validate the effectiveness of our proposed approach.

Miscellaneous Aspects of Machine Learning · Supervised Learning

Caixing Wang, Ziliang Shen

In this paper, we focus on distributed estimation and support recovery for high-dimensional linear quantile regression. Quantile regression is a popular alternative tool to the least squares regression for robustness against outliers and data heterogeneity. However, the non-smoothness of the check loss function poses big challenges to both computation and theory in the distributed setting. To tackle these problems, we transform the original quantile regression into the least-squares optimization. By applying a double-smoothing approach, we extend a previous Newton-type distributed approach without the restrictive independent assumption between the error term and covariates. An efficient algorithm is developed, which enjoys high computation and communication efficiency. Theoretically, the proposed distributed estimator achieves a near-oracle convergence rate and high support recovery accuracy after a constant number of iterations. Extensive experiments on synthetic examples and a real data application further demonstrate the effectiveness of the proposed method.

Miscellaneous Aspects of Machine Learning · Online Learning, Active Learning and Bandits

Zhou Wang, Xingye Qiao

Conformal prediction is a distribution-free method that wraps a given machine learning model and returns a set of plausible labels that contain the true label with a prescribed coverage rate. In practice, the empirical coverage achieved highly relies on fully observed label information from data both in the training phase for model fitting and the calibration phase for quantile estimation. This dependency poses a challenge in the context of online learning with bandit feedback, where a learner only has access to the correctness of actions (i.e., pulled an arm) but not the full information of the true label. In particular, when the pulled arm is incorrect, the learner only knows that the pulled one is not the true class label, but does not know which label is true. Additionally, bandit feedback further results in a smaller labeled dataset for calibration, limited to instances with correct actions, thereby affecting the accuracy of quantile estimation. To address these limitations, we propose Bandit Class-specific Conformal Prediction (BCCP), offering coverage guarantees on a class-specific granularity. Using an unbiased estimation of an estimand involving the true label, BCCP trains the model and makes set-valued inferences through stochastic gradient descent. Our approach overcomes the challenges of sparsely labeled data in each iteration and generalizes the reliability and applicability of conformal prediction to online decision-making environments.

Miscellaneous Aspects of Machine Learning · Supervised Learning

Ke Wang, Guillermo Ortiz-Jimenez, Rodolphe Jenatton, Mark Collier, Efi Kokiopoulou, Pascal Frossard

Label noise is a pervasive problem in deep learning that often compromises the generalization performance of trained models. Recently, leveraging privileged information (PI) -- information available only during training but not at test time -- has emerged as an effective approach to mitigate this issue. Yet, existing PI-based methods have failed to consistently outperform their no-PI counterparts in terms of preventing overfitting to label noise. To address this deficiency, we introduce Pi-DUAL, an architecture designed to harness PI to distinguish clean from wrong labels. Pi-DUAL decomposes the output logits into a prediction term, based on conventional input features, and a noise-fitting term influenced solely by PI. A gating mechanism steered by PI adaptively shifts focus between these terms, allowing the model to implicitly separate the learning paths of clean and wrong labels. Empirically, Pi-DUAL achieves significant performance improvements on key PI benchmarks (e.g., +6.8% on ImageNet-PI), establishing a new state-of-the-art test set accuracy. Additionally, Pi-DUAL is a potent method for identifying noisy samples post-training, outperforming other strong methods at this task. Overall, Pi-DUAL is a simple, scalable and practical approach for mitigating the effects of label noise in a variety of real-world scenarios with PI.

Miscellaneous Aspects of Machine Learning · Causality

Xin Wang, Shengfei Lyu, Lishan Yang, Yibing Zhan, Huanhuan Chen

Efficiently and effectively estimating counterfactuals over time is crucial for optimizing treatment strategies. We present the Adversarial Counterfactual Temporal Inference Network (ACTIN), a novel framework with dual modules to enhance counterfactual estimation. The balancing module employs a distribution-based adversarial method to learn balanced representations, extending beyond the limitations of current classification-based methods to mitigate confounding bias across various treatment types. The integrating module adopts a novel Temporal Integration Predicting (TIP) strategy, which has a wider receptive field of treatments and balanced representations from the beginning to the current time for a more profound level of analysis. TIP goes beyond the established Direct Predicting (DP) strategy, which only relies on current treatments and representations, by empowering the integrating module to effectively capture long-range dependencies and temporal treatment interactions. ACTIN exceeds the confines of specific base models, and when implemented with simple base models, consistently delivers state-of-the-art performance and efficiency across both synthetic and real-world datasets.

Miscellaneous Aspects of Machine Learning · Unsupervised and Semi-supervised Learning

Wei Wang, Takashi Ishida, Yu-Jie Zhang, Gang Niu, Masashi Sugiyama

Complementary-label learning is a weakly supervised learning problem in which each training example is associated with one or multiple complementary labels indicating the classes to which it does not belong. Existing consistent approaches have relied on the uniform distribution assumption to model the generation of complementary labels, or on an ordinary-label training set to estimate the transition matrix in non-uniform cases. However, either condition may not be satisfied in real-world scenarios. In this paper, we propose a novel consistent approach that does not rely on these conditions. Inspired by the positive-unlabeled (PU) learning literature, we propose an unbiased risk estimator based on the Selected-Completely-at-Random assumption for complementary-label learning. We then introduce a risk-correction approach to address overfitting problems. Furthermore, we find that complementary-label learning can be expressed as a set of negative-unlabeled binary classification problems when using the one-versus-rest strategy. Extensive experimental results on both synthetic and real-world benchmark datasets validate the superiority of our proposed approach over state-of-the-art methods.

Miscellaneous Aspects of Machine Learning · Causality

Wenjie Wang, Biwei Huang, Feng Liu, Xinge You, Tongliang Liu, Kun Zhang, Mingming Gong

Score-based methods have demonstrated their effectiveness in discovering causal relationships by scoring different causal structures based on their goodness of fit to the data. Recently, Huang et al. proposed a generalized score function that can handle general data distributions and causal relationships by modeling the relations in reproducing kernel Hilbert space (RKHS). The selection of an appropriate kernel within this score function is crucial for accurately characterizing causal relationships and ensuring precise causal discovery. However, the current method involves manual heuristic selection of kernel parameters, making the process tedious and less likely to ensure optimality. In this paper, we propose a kernel selection method within the generalized score function that automatically selects the optimal kernel that best fits the data. Specifically, we model the generative process of the variables involved in each step of the causal graph search procedure as a mixture of independent noise variables. Based on this model, we derive an automatic kernel selection method by maximizing the marginal likelihood of the variables involved in each search step. We conduct experiments on both synthetic data and real-world benchmarks, and the results demonstrate that our proposed method outperforms heuristic kernel selection methods.

Miscellaneous Aspects of Machine Learning · Causality

Tian-Zuo Wang, Wen-Bo Du, Zhi-Hua Zhou

Maximal ancestral graph (MAG) is a prevalent graphical model to characterize causal relations in the presence of *latent variables* including latent confounders and selection variables. Given observational data, only a Markov equivalence class (MEC) of MAGs is identifiable if without some additional assumptions. Due to this fact, MAG listing, listing all the MAGs in the MEC, is usually demanded in many downstream tasks. To the best of our knowledge, there are no relevant methods for MAG listing other than brute force in the literature. In this paper, we propose the first brute-force-free MAG listing method, by determining the local structures of each vertex recursively. We provide the graphical characterization for each valid local transformation of a vertex, and present sound and complete rules to incorporate the valid local transformation in the presence of latent confounders and selection variables. Based on these components, our method can efficiently output all the MAGs in the MEC with no redundance, that is, every intermediate graph in the recursive process is necessary for the MAG listing task. The empirical analysis demonstrates the superiority of our proposed method on efficiency and effectiveness.

Miscellaneous Aspects of Machine Learning · Causality

Vy Vo, He Zhao, Trung Le, Edwin V. Bonilla, Dinh Phung

Causal discovery in the presence of missing data introduces a chicken-and-egg dilemma. While the goal is to recover the true causal structure, robust imputation requires considering the dependencies or, preferably, causal relations among variables. Merely filling in missing values with existing imputation methods and subsequently applying structure learning on the complete data is empirically shown to be sub-optimal. To address this problem, we propose a score-based algorithm for learning causal structures from missing data based on optimal transport. This optimal transport viewpoint diverges from existing score-based approaches that are dominantly based on expectation maximization. We formulate structure learning as a density fitting problem, where the goal is to find the causal model that induces a distribution of minimum Wasserstein distance with the observed data distribution. Our framework is shown to recover the true causal graphs more effectively than competing methods in most simulations and real-data settings. Empirical evidence also shows the superior scalability of our approach, along with the flexibility to incorporate any off-the-shelf causal discovery methods for complete data.

Miscellaneous Aspects of Machine Learning · Causality

Allen Tran, Aurelien Bibaut, Nathan Kallus

We study inference on the long-term causal effect of a continual exposure to a novel intervention, which we term a long-term treatment, based on an experiment involving only short-term observations. Key examples include the long-term health effects of regularly-taken medicine or of environmental hazards and the long-term effects on users of changes to an online platform. This stands in contrast to short-term treatments or "shocks," whose long-term effect can reasonably be mediated by short-term observations, enabling the use of surrogate methods. Long-term treatments by definition have direct effects on long-term outcomes via continual exposure, so surrogacy conditions cannot reasonably hold. We connect the problem with offline reinforcement learning, leveraging doubly-robust estimators to estimate long-term causal effects for long-term treatments and construct confidence intervals.

Miscellaneous Aspects of Machine Learning · Online Learning, Active Learning and Bandits

Mo Tiwari, Ryan Kang, Jaeyong Lee, Donghyun Lee, Chris Piech, Sebastian Thrun, Ilan Shomorony, Martin Zhang

Maximum Inner Product Search (MIPS) is a ubiquitous task in machine learning applications. Given a query vector and $n$ other vectors in $d$ dimensions, the MIPS problem is to find the atom that has the highest inner product with the query vector. Existing MIPS algorithms scale at least as $O(\sqrt{d})$ with respect to $d$, which becomes computationally prohibitive in high-dimensional settings. In this work, we present BanditMIPS, a novel randomized algorithm that provably improves the state-of-the-art complexity from $O(\sqrt{d})$ to $O(1)$ with respect to $d$. We validate the scaling of BanditMIPS and demonstrate that BanditMIPS outperforms prior state-of-the-art MIPS algorithms in sample complexity, wall-clock time, and precision/speedup tradeoff across a variety of experimental settings. Furthermore, we propose a variant of our algorithm, named BanditMIPS-$\alpha$, which improves upon BanditMIPS by employing non-uniform sampling across coordinates. We also demonstrate the usefulness of BanditMIPS in problems for which MIPS is a subroutine, including Matching Pursuit and Fourier analysis. Finally, we demonstrate that BanditMIPS can be used in conjunction with preprocessing techniques to improve its complexity with respect to $n$. All of our experimental results are reproducible via a 1-line script at github.com/ThrunGroup/BanditMIPS.

Miscellaneous Aspects of Machine Learning · Kernel methods

Jinyue Tian, Hui Xue, Yanfang Xue, Pengfei Fang

Spectral Kernel Networks (SKNs) emerge as a promising approach in machine learning, melding solid theoretical foundations of spectral kernels with the representation power of hierarchical architectures. At its core, the spectral density function plays a pivotal role by revealing essential patterns in data distributions, thereby offering deep insights into the underlying framework in real-world tasks. Nevertheless, prevailing designs of spectral density often overlook the intricate interactions within data structures. This phenomenon consequently neglects expanses of the hypothesis space, thus curtailing the performance of SKNs. This paper addresses the issues through a novel approach, the **Co**pula-Nested Spectral **Ke**rnel **Net**work (**CokeNet**). Concretely, we first redefine the spectral density with the form of copulas to enhance the diversity of spectral densities. Next, the specific expression of the copula module is designed to allow the excavation of complex dependence structures. Finally, the unified kernel network is proposed by integrating the corresponding spectral kernel and the copula module. Through rigorous theoretical analysis and experimental verification, CokeNet demonstrates superior performance and significant advancements over SOTA algorithms in the field.

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Hongduan Tian, Feng Liu, Tongliang Liu, Bo Du, Yiu Ming Cheung, Bo Han

In cross-domain few-shot classification, _nearest centroid classifier_ (NCC) aims to learn representations to construct a metric space where few-shot classification can be performed by measuring the similarities between samples and the prototype of each class. An intuition behind NCC is that each sample is pulled closer to the class centroid it belongs to while pushed away from those of other classes. However, in this paper, we find that there exist high similarities between NCC-learned representations of two samples from different classes. In order to address this problem, we propose a bi-level optimization framework, _maximizing optimized kernel dependence_ (MOKD) to learn a set of class-specific representations that match the cluster structures indicated by labeled data of the given task. Specifically, MOKD first optimizes the kernel adopted in *Hilbert-Schmidt independence criterion* (HSIC) to obtain the optimized kernel HSIC (opt-HSIC) that can capture the dependence more precisely. Then, an optimization problem regarding the opt-HSIC is addressed to simultaneously maximize the dependence between representations and labels and minimize the dependence among all samples. Extensive experiments on Meta-Dataset demonstrate that MOKD can not only achieve better generalization performance on unseen domains in most cases but also learn better data representation clusters. The project repository of MOKD is available at: [https://github.com/tmlr-group/MOKD](https://github.com/tmlr-group/MOKD).

Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Anke Tang, Li Shen, Yong Luo, Nan Yin, Lefei Zhang, Dacheng Tao

Merging various task-specific Transformer-based vision models trained on different tasks into a single unified model can execute all the tasks concurrently. Previous methods, exemplified by task arithmetic, have been proven to be both effective and scalable. Existing methods have primarily focused on seeking a static optimal solution within the original model parameter space. A notable challenge is mitigating the interference between parameters of different models, which can substantially deteriorate performance. In this paper, we propose to merge most of the parameters while upscaling the MLP of the Transformer layers to a weight-ensembling mixture of experts (MoE) module, which can dynamically integrate shared and task-specific knowledge based on the input, thereby providing a more flexible solution that can adapt to the specific needs of each instance. Our key insight is that by identifying and separating shared knowledge and task-specific knowledge, and then dynamically integrating them, we can mitigate the parameter interference problem to a great extent. We conduct the conventional multi-task model merging experiments and evaluate the generalization and robustness of our method. The results demonstrate the effectiveness of our method and provide a comprehensive understanding of our method. The code is available at https://github.com/tanganke/weight-ensembling_MoE

Theory · Miscellaneous Aspects of Machine Learning

Yifan Sun, Grace Yi

Multivariate linear regression models are broadly used to facilitate relationships between outcomes and features. However, their effectiveness is compromised by the presence of missing observations, a ubiquitous challenge in real-world applications. Considering a scenario where learners access only limited components for both outcomes and features, we develop efficient algorithms tailored for the least squares ($L_2$) and least absolute ($L_1$) loss functions, each coupled with a ridge-like and Lasso-type penalty, respectively. Moreover, we establish rigorous error bounds for all proposed algorithms. Notably, our $L_2$ loss function algorithms are probably approximately correct (PAC), distinguishing them from their $L_1$ counterparts. Extensive numerical experiments show that our approach outperforms methods that apply existing algorithms for univariate outcome individually to each coordinate of multivariate outcomes in a naive manner. Further, utilizing the $L_1$ loss function or introducing a Lasso-type penalty can enhance predictions in the presence of outliers or high dimensional features. This research contributes valuable insights into addressing the challenges posed by incomplete data.

Miscellaneous Aspects of Machine Learning · Online Learning, Active Learning and Bandits

Sophia Sun, Abishek Sankararaman, Balakrishnan Narayanaswamy

Selecting appropriate thresholds for anomaly detection in online, unsupervised settings is a challenging task, especially in the presence of data distribution shifts. Addressing these challenges is critical in many practical large scale systems, such as infrastructure monitoring and network intrusion detection. This paper proposes an algorithm that connects online thresholding with constructing confidence sequences achieving (1) adaptive online threshold selection robust to distribution shifts, (2) statistical guarantees on false positive and false negative rates without any distributional assumptions, and (3) improved performance when given relevant offline data to warm-start the online algorithm, while having bounded degradation if the offline data is irrelevant. We complement our theoretical results by empirical evidence that our method outperforms commonly used baselines across synthetic and real world datasets.

Miscellaneous Aspects of Machine Learning · Supervised Learning

Jiang-Xin Shi, Tong Wei, Zhi Zhou, Jie-Jing Shao, Xin-Yan Han, Yu-Feng Li

The fine-tuning paradigm in addressing long-tail learning tasks has sparked significant interest since the emergence of foundation models. Nonetheless, how fine-tuning impacts performance in long-tail learning was not explicitly quantified. In this paper, we disclose that heavy fine-tuning may even lead to non-negligible performance deterioration on tail classes, and lightweight fine-tuning is more effective. The reason is attributed to inconsistent class conditions caused by heavy fine-tuning. With the observation above, we develop a low-complexity and accurate long-tail learning algorithms LIFT with the goal of facilitating fast prediction and compact models by adaptive lightweight fine-tuning. Experiments clearly verify that both the training time and the learned parameters are significantly reduced with more accurate predictive performance compared with state-of-the-art approaches. The implementation code is available at https://github.com/shijxcs/LIFT.

Miscellaneous Aspects of Machine Learning · Sequential, Network, and Time Series Modeling

Shubhanshu Shekhar, Aaditya Ramdas

We consider the problem of sequential change detection under minimal assumptions on the distribution generating the stream of observations. Formally, our goal is to design a scheme for detecting any changes in a parameter or functional $\theta$ of the data stream distribution that has small detection delay, but guarantees control on the frequency of false alarms in the absence of changes. We describe a simple reduction from sequential change detection to sequential estimation using confidence sequences (CSs): begin a new level-$(1-\alpha)$ CS at each time step, and proclaim a change as soon as the intersection of all active CSs becomes empty. We prove that the average run length of our scheme is at least $1/\alpha$, resulting in a change detection scheme with minimal structural assumptions (thus allowing for possibly dependent observations, and nonparametric distribution classes), but strong guarantees. We also describe an interesting parallel with Lorden's reduction from change detection to sequential testing and connections to the recent ''e-detector'' framework.

Miscellaneous Aspects of Machine Learning · Online Learning, Active Learning and Bandits

Yuming Shao, Zhixuan Fang

In this paper, we investigate a Multi-Armed Bandit (MAB) setting where an arm exits the game if the algorithm continuously neglects it. This setup is motivated by real-world scenarios, such as online advertising and crowdsourcing, where arms only gain benefits after being pulled by the algorithm. We identify the intrinsic hardness of this problem and limitations in existing approaches. We propose FC-SE algorithm with expected regret upper bounds as our solution to this problem. As an extension, we even allow new arms to enter after the game starts and design FC-Entry algorithm with performance guarantees for this setup. Finally, we conduct experiments to validate our theoretical results.