论文检索

Miscellaneous Aspects of Machine Learning/Supervised Learning

Jiaming Qiu, Xiongtao Dai

We extend metric learning by studying the Riemannian manifold structure of the underlying data space induced by similarity measures between data points. The key quantity of interest here is the Riemannian metric, which characterizes the Riemannian geometry and defines straight lines and derivatives on the manifold. Being able to estimate the Riemannian metric allows us to gain insights into the underlying manifold and compute geometric features such as the geodesic curves. We model the observed similarity measures as noisy responses generated from a function of the intrinsic geodesic distance between data points. A new local regression approach is proposed to learn the Riemannian metric tensor and its derivatives based on a Taylor expansion for the squared geodesic distances, accommodating different types of data such as continuous, binary, or comparative responses. We develop theoretical foundation for our method by deriving the rates of convergence for the asymptotic bias and variance of the estimated metric tensor. The proposed method is shown to be versatile in simulation studies and real data applications involving taxi trip time in New York City and MNIST digits.

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

Liyuan Wang, Jingyi Xie, Xingxing Zhang, Mingyi Huang, Hang Su, Jun Zhu

Prompt-based continual learning is an emerging direction in leveraging pre-trained knowledge for downstream continual learning, and has almost reached the performance pinnacle under supervised pre-training. However, our empirical research reveals that the current strategies fall short of their full potential under the more realistic self-supervised pre-training, which is essential for handling vast quantities of unlabeled data in practice. This is largely due to the difficulty of task-specific knowledge being incorporated into instructed representations via prompt parameters and predicted by uninstructed representations at test time. To overcome the exposed sub-optimality, we conduct a theoretical analysis of the continual learning objective in the context of pre-training, and decompose it into hierarchical components: within-task prediction, task-identity inference, and task-adaptive prediction. Following these empirical and theoretical insights, we propose Hierarchical Decomposition (HiDe-)Prompt, an innovative approach that explicitly optimizes the hierarchical components with an ensemble of task-specific prompts and statistics of both uninstructed and instructed representations, further with the coordination of a contrastive regularization strategy. Our extensive experiments demonstrate the superior performance of HiDe-Prompt and its robustness to pre-training paradigms in continual learning (e.g., up to 15.01% and 9.61% lead on Split CIFAR-100 and Split ImageNet-R, respectively).

Miscellaneous Aspects of Machine Learning/General Machine Learning Techniques

Khai Nguyen, Tongzheng Ren, Nhat Ho

Sliced Wasserstein (SW) distance suffers from redundant projections due to independent uniform random projecting directions. To partially overcome the issue, max K sliced Wasserstein (Max-K-SW) distance ($K\geq 1$), seeks the best discriminative orthogonal projecting directions. Despite being able to reduce the number of projections, the metricity of the Max-K-SW cannot be guaranteed in practice due to the non-optimality of the optimization. Moreover, the orthogonality constraint is also computationally expensive and might not be effective. To address the problem, we introduce a new family of SW distances, named Markovian sliced Wasserstein (MSW) distance, which imposes a first-order Markov structure on projecting directions. We discuss various members of the MSW by specifying the Markov structure including the prior distribution, the transition distribution, and the burning and thinning technique. Moreover, we investigate the theoretical properties of MSW including topological properties (metricity, weak convergence, and connection to other distances), statistical properties (sample complexity, and Monte Carlo estimation error), and computational properties (computational complexity and memory complexity). Finally, we compare MSW distances with previous SW variants in various applications such as gradient flows, color transfer, and deep generative modeling to demonstrate the favorable performance of the MSW.

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

Yilin Lyu, Liyuan Wang, Xingxing Zhang, Zicheng Sun, Hang Su, Jun Zhu, Liping Jing

Continual learning entails learning a sequence of tasks and balancing their knowledge appropriately. With limited access to old training samples, much of the current work in deep neural networks has focused on overcoming catastrophic forgetting of old tasks in gradient-based optimization. However, the normalization layers provide an exception, as they are updated interdependently by the gradient and statistics of currently observed training samples, which require specialized strategies to mitigate recency bias. In this work, we focus on the most popular Batch Normalization (BN) and provide an in-depth theoretical analysis of its sub-optimality in continual learning. Our analysis demonstrates the dilemma between balance and adaptation of BN statistics for incremental tasks, which potentially affects training stability and generalization. Targeting on these particular challenges, we propose Adaptive Balance of BN (AdaB$^2$N), which incorporates appropriately a Bayesian-based strategy to adapt task-wise contributions and a modified momentum to balance BN statistics, corresponding to the training and testing stages. By implementing BN in a continual learning fashion, our approach achieves significant performance gains across a wide range of benchmarks, particularly for the challenging yet realistic online scenarios (e.g., up to 7.68\%, 6.86\% and 4.26\% on Split CIFAR-10, Split CIFAR-100 and Split Mini-ImageNet, respectively). Our code is available at https://github.com/lvyilin/AdaB2N.

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

Tian Zhou, Peisong Niu, xue wang, Liang Sun, Rong Jin

Although we have witnessed great success of pre-trained models in natural language processing (NLP) and computer vision (CV), limited progress has been made for general time series analysis. Unlike NLP and CV where a unified model can be used to perform different tasks, specially designed approach still dominates in each time series analysis task such as classification, anomaly detection, forecasting, and few-shot learning. The main challenge that blocks the development of pre-trained model for time series analysis is the lack of a large amount of data for training. In this work, we address this challenge by leveraging language or CV models, pre-trained from billions of tokens, for time series analysis. Specifically, we refrain from altering the self-attention and feedforward layers of the residual blocks in the pre-trained language or image model. This model, known as the Frozen Pretrained Transformer (FPT), is evaluated through fine-tuning on all major types of tasks involving time series. Our results demonstrate that pre-trained models on natural language or images can lead to a comparable or state-of-the-art performance in all main time series analysis tasks, as illustrated in Figure1. We also found both theoretically and empirically that the self-attention module behaviors similarly to principle component analysis (PCA), an observation that helps explains how transformer bridges the domain gap and a crucial step towards understanding the universality of a pre-trained transformer. The code is publicly available at https://anonymous.4open.science/r/Pretrained-LM-for-TSForcasting-C561.

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

Yu Wang, Zhun Zhong, Pengchong Qiao, Xuxin Cheng, Xiawu Zheng, Chang Liu, Nicu Sebe, Rongrong Ji, Jie Chen

Open-world Semi-Supervised Learning (OSSL) is a realistic and challenging task, aiming to classify unlabeled samples from both seen and novel classes using partially labeled samples from the seen classes. Previous works typically explore the relationship of samples as priors on the pre-defined single-granularity labels to help novel class recognition. In fact, classes follow a taxonomy and samples can be classified at multiple levels of granularity, which contains more underlying relationships for supervision. We thus argue that learning with single-granularity labels results in sub-optimal representation learning and inaccurate pseudo labels, especially with unknown classes. In this paper, we take the initiative to explore and propose a uniformed framework, called Taxonomic context prIors Discovering and Aligning (TIDA), which exploits the relationship of samples under various granularity. It allows us to discover multi-granularity semantic concepts as taxonomic context priors (i.e., sub-class, target-class, and super-class), and then collaboratively leverage them to enhance representation learning and improve the quality of pseudo labels.Specifically, TIDA comprises two components: i) A taxonomic context discovery module that constructs a set of hierarchical prototypes in the latent space to discover the underlying taxonomic context priors; ii) A taxonomic context-based prediction alignment module that enforces consistency across hierarchical predictions to build the reliable relationship between classes among various granularity and provide additions supervision. We demonstrate that these two components are mutually beneficial for an effective OSSL framework, which is theoretically explained from the perspective of the EM algorithm. Extensive experiments on seven commonly used datasets show that TIDA can significantly improve the performance and achieve a new state of the art. The source codes are publicly available at https://github.com/rain305f/TIDA.

Miscellaneous Aspects of Machine Learning/Causality

Junhyung Park, Simon Buchholz, Bernhard Schölkopf, Krikamol Muandet

Causality is a central concept in a wide range of research areas, yet there is still no universally agreed axiomatisation of causality. We view causality both as an extension of probability theory and as a study of what happens when one intervenes on a system, and argue in favour of taking Kolmogorov's measure-theoretic axiomatisation of probability as the starting point towards an axiomatisation of causality. To that end, we propose the notion of a causal space, consisting of a probability space along with a collection of transition probability kernels, called causal kernels, that encode the causal information of the space. Our proposed framework is not only rigorously grounded in measure theory, but it also sheds light on long-standing limitations of existing frameworks including, for example, cycles, latent variables and stochastic processes.

Miscellaneous Aspects of Machine Learning/Everything Else

Simon Schrodi, Danny Stoll, Binxin Ru, Rhea Sukthanker, Thomas Brox, Frank Hutter

The discovery of neural architectures from simple building blocks is a long-standing goal of Neural Architecture Search (NAS). Hierarchical search spaces are a promising step towards this goal but lack a unifying search space design framework and typically only search over some limited aspect of architectures. In this work, we introduce a unifying search space design framework based on context-free grammars that can naturally and compactly generate expressive hierarchical search spaces that are 100s of orders of magnitude larger than common spaces from the literature. By enhancing and using their properties, we effectively enable search over the complete architecture and can foster regularity. Further, we propose an efficient hierarchical kernel design for a Bayesian Optimization search strategy to efficiently search over such huge spaces. We demonstrate the versatility of our search space design framework and show that our search strategy can be superior to existing NAS approaches. Code is available at https://github.com/automl/hierarchical_nas_construction.

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

Siyuan Xu, Minghui Zhu

Meta-learning has attracted attention due to its strong ability to learn experiences from known tasks, which can speed up and enhance the learning process for new tasks. However, most existing meta-learning approaches only can learn from tasks without any constraint. This paper proposes an online constrained meta-learning framework, which continuously learns meta-knowledge from sequential learning tasks, and the learning tasks are subject to hard constraints. Beyond existing meta-learning analyses, we provide the upper bounds of optimality gaps and constraint violations produced by the proposed framework, which considers the dynamic regret of online learning, as well as the generalization ability of the task-specific models. Moreover, we provide a practical algorithm for the framework, and validate its superior effectiveness through experiments conducted on meta-imitation learning and few-shot image classification.

Miscellaneous Aspects of Machine Learning/Representation Learning

Md Ashiqur Rahman, Raymond A. Yeh

In computer vision, models must be able to adapt to changes in image resolution to effectively carry out tasks such as image segmentation; This is known as scale-equivariance. Recent works have made progress in developing scale-equivariant convolutional neural networks, e.g., through weight-sharing and kernel resizing. However, these networks are not truly scale-equivariant in practice. Specifically, they do not consider anti-aliasing as they formulate the down-scaling operation in the continuous domain. To address this shortcoming, we directly formulate down-scaling in the discrete domain with consideration of anti-aliasing. We then propose a novel architecture based on Fourier layers to achieve truly scale-equivariant deep nets, i.e., absolute zero equivariance-error. Following prior works, we test this model on MNIST-scale and STL-10 datasets. Our proposed model achieves competitive classification performance while maintaining zero equivariance-error.

Miscellaneous Aspects of Machine Learning/Causality

Chang Deng, Kevin Bello, Pradeep Ravikumar, Bryon Aragam

Recently, a new class of non-convex optimization problems motivated by the statistical problem of learning an acyclic directed graphical model from data has attracted significant interest. While existing work uses standard first-order optimization schemes to solve this problem, proving the global optimality of such approaches has proven elusive. The difficulty lies in the fact that unlike other non-convex problems in the literature, this problem is not "benign", and possesses multiple spurious solutions that standard approaches can easily get trapped in. In this paper, we prove that a simple path-following optimization scheme globally converges to the global minimum of the population loss in the bivariate setting.

Miscellaneous Aspects of Machine Learning/Causality

Tianyu Chen, Kevin Bello, Bryon Aragam, Pradeep Ravikumar

Structural causal models (SCMs) are widely used in various disciplines to represent causal relationships among variables in complex systems.Unfortunately, the underlying causal structure is often unknown, and estimating it from data remains a challenging task. In many situations, however, the end goal is to localize the changes (shifts) in the causal mechanisms between related datasets instead of learning the full causal structure of the individual datasets. Some applications include root cause analysis, analyzing gene regulatory network structure changes between healthy and cancerous individuals, or explaining distribution shifts. This paper focuses on identifying the causal mechanism shifts in two or more related datasets over the same set of variables---*without estimating the entire DAG structure of each SCM*.Prior work under this setting assumed linear models with Gaussian noises; instead, in this work we assume that each SCM belongs to the more general class of *nonlinear* additive noise models (ANMs).A key technical contribution of this work is to show that the Jacobian of the score function for the *mixture distribution* allows for the identification of shifts under general non-parametric functional mechanisms.Once the shifted variables are identified, we leverage recent work to estimate the structural differences, if any, for the shifted variables.Experiments on synthetic and real-world data are provided to showcase the applicability of this approach.Code implementing the proposed method is open-source and publicly available at https://github.com/kevinsbello/iSCAN.

Miscellaneous Aspects of Machine Learning/Causality

Tao Shen, Yifan Cui

A common concern when a policymaker draws causal inferences from and makes decisions based on observational data is that the measured covariates are insufficiently rich to account for all sources of confounding, i.e., the standard no confoundedness assumption fails to hold. The recently proposed proximal causal inference framework shows that proxy variables that abound in real-life scenarios can be leveraged to identify causal effects and therefore facilitate decision-making. Building upon this line of work, we propose a novel optimal individualized treatment regime based on so-called outcome and treatment confounding bridges. We then show that the value function of this new optimal treatment regime is superior to that of existing ones in the literature. Theoretical guarantees, including identification, superiority, excess value bound, and consistency of the estimated regime, are established. Furthermore, we demonstrate the proposed optimal regime via numerical experiments and a real data application.

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

Zihan Chen, Howard Yang, Tony Quek, Kai Fong Ernest Chong

Personalized federated learning (PFL) has been widely investigated to address the challenge of data heterogeneity, especially when a single generic model is inadequate in satisfying the diverse performance requirements of local clients simultaneously. Existing PFL methods are inherently based on the idea that the relations between the generic global and personalized local models are captured by the similarity of model weights. Such a similarity is primarily based on either partitioning the model architecture into generic versus personalized components or modeling client relationships via model weights. To better capture similar (yet distinct) generic versus personalized model representations, we propose $\textit{spectral distillation}$, a novel distillation method based on model spectrum information. Building upon spectral distillation, we also introduce a co-distillation framework that establishes a two-way bridge between generic and personalized model training. Moreover, to utilize the local idle time in conventional PFL, we propose a wait-free local training protocol. Through extensive experiments on multiple datasets over diverse heterogeneous data settings, we demonstrate the outperformance and efficacy of our proposed spectral co-distillation method, as well as our wait-free training protocol.

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

Zeshuai Deng, Zhuokun Chen, Shuaicheng Niu, Thomas Li, Bohan Zhuang, Mingkui Tan

Image super-resolution (SR) aims to learn a mapping from low-resolution (LR) to high-resolution (HR) using paired HR-LR training images. Conventional SR methods typically gather the paired training data by synthesizing LR images from HR images using a predetermined degradation model, e.g., Bicubic down-sampling. However, the realistic degradation type of test images may mismatch with the training-time degradation type due to the dynamic changes of the real-world scenarios, resulting in inferior-quality SR images. To address this, existing methods attempt to estimate the degradation model and train an image-specific model, which, however, is quite time-consuming and impracticable to handle rapidly changing domain shifts. Moreover, these methods largely concentrate on the estimation of one degradation type (e.g., blur degradation), overlooking other degradation types like noise and JPEG in real-world test-time scenarios, thus limiting their practicality. To tackle these problems, we present an efficient test-time adaptation framework for SR, named SRTTA, which is able to quickly adapt SR models to test domains with different/unknown degradation types. Specifically, we design a second-order degradation scheme to construct paired data based on the degradation type of the test image, which is predicted by a pre-trained degradation classifier. Then, we adapt the SR model by implementing feature-level reconstruction learning from the initial test image to its second-order degraded counterparts, which helps the SR model generate plausible HR images. Extensive experiments are conducted on newly synthesized corrupted DIV2K datasets with 8 different degradations and several real-world datasets, demonstrating that our SRTTA framework achieves an impressive improvement over existing methods with satisfying speed. The source code is available at https://github.com/DengZeshuai/SRTTA.

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

Junguang Jiang, Baixu Chen, Junwei Pan, Ximei Wang, Dapeng Liu, Jie Jiang, Mingsheng Long

Auxiliary-Task Learning (ATL) aims to improve the performance of the target task by leveraging the knowledge obtained from related tasks. Occasionally, learning multiple tasks simultaneously results in lower accuracy than learning only the target task, which is known as negative transfer. This problem is often attributed to the gradient conflicts among tasks, and is frequently tackled by coordinating the task gradients in previous works. However, these optimization-based methods largely overlook the auxiliary-target generalization capability. To better understand the root cause of negative transfer, we experimentally investigate it from both optimization and generalization perspectives. Based on our findings, we introduce ForkMerge, a novel approach that periodically forks the model into multiple branches, automatically searches the varying task weights by minimizing target validation errors, and dynamically merges all branches to filter out detrimental task-parameter updates. On a series of auxiliary-task learning benchmarks, ForkMerge outperforms existing methods and effectively mitigates negative transfer.

Miscellaneous Aspects of Machine Learning/Everything Else

Jia-Qi Yang, De-Chuan Zhan, Le Gan

Research has shown that deep networks tend to be overly optimistic about their predictions, leading to an underestimation of prediction errors. Due to the limited nature of data, existing studies have proposed various methods based on model prediction probabilities to bin the data and evaluate calibration error. We propose a more generalized definition of calibration error called Partitioned Calibration Error (PCE), revealing that the key difference among these calibration error metrics lies in how the data space is partitioned. We put forth an intuitive proposition that an accurate model should be calibrated across any partition, suggesting that the input space partitioning can extend beyond just the partitioning of prediction probabilities, and include partitions directly related to the input. Through semantic-related partitioning functions, we demonstrate that the relationship between model accuracy and calibration lies in the granularity of the partitioning function. This highlights the importance of partitioning criteria for training a calibrated and accurate model. To validate the aforementioned analysis, we propose a method that involves jointly learning a semantic aware grouping function based on deep model features and logits to partition the data space into subsets. Subsequently, a separate calibration function is learned for each subset. Experimental results demonstrate that our approach achieves significant performance improvements across multiple datasets and network architectures, thus highlighting the importance of the partitioning function for calibration.

Miscellaneous Aspects of Machine Learning/Scalable Algorithms

Aditya Bhaskara, Sepideh Mahabadi, Ali Vakilian

Given a set of points of interest, a volumetric spanner is a subset of the points using which all the points can be expressed using "small" coefficients (measured in an appropriate norm). Formally, given a set of vectors $X = [v_1, v_2, \dots, v_n]$, the goal is to find $T \subseteq [n]$ such that every $v \in X$ can be expressed as $\sum_{i\in T} \alpha_i v_i$, with $\Vert \alpha \Vert$ being small. This notion, which has also been referred to as a well-conditioned basis, has found several applications, including bandit linear optimization, determinant maximization, and matrix low rank approximation. In this paper, we give almost optimal bounds on the size of volumetric spanners for all $\ell_p$ norms, and show that they can be constructed using a simple local search procedure. We then show the applications of our result to other tasks and in particular the problem of finding coresets for the Minimum Volume Enclosing Ellipsoid (MVEE) problem.

Miscellaneous Aspects of Machine Learning/Representation Learning

Yiyou Sun, Zhenmei Shi, Yixuan Li

Open-world semi-supervised learning aims at inferring both known and novel classes in unlabeled data, by harnessing prior knowledge from a labeled set with known classes. Despite its importance, there is a lack of theoretical foundations for this problem. This paper bridges the gap by formalizing a graph-theoretic framework tailored for the open-world setting, where the clustering can be theoretically characterized by graph factorization. Our graph-theoretic framework illuminates practical algorithms and provides guarantees. In particular, based on our graph formulation, we apply the algorithm called Spectral Open-world Representation Learning (SORL), and show that minimizing our loss is equivalent to performing spectral decomposition on the graph. Such equivalence allows us to derive a provable error bound on the clustering performance for both known and novel classes, and analyze rigorously when labeled data helps. Empirically, SORL can match or outperform several strong baselines on common benchmark datasets, which is appealing for practical usage while enjoying theoretical guarantees.

Miscellaneous Aspects of Machine Learning/General Machine Learning Techniques

Alexandre Blain, Bertrand Thirion, Olivier Grisel, Pierre Neuvial

Controlled variable selection is an important analytical step in various scientific fields, such as brain imaging or genomics. In these high-dimensional data settings, considering too many variables leads to poor models and high costs, hence the need for statistical guarantees on false positives. Knockoffs are a popular statistical tool for conditional variable selection in high dimension. However, they control for the expected proportion of false discoveries (FDR) and not the actual proportion of false discoveries (FDP). We present a new method, KOPI, that controls the proportion of false discoveries for Knockoff-based inference. The proposed method also relies on a new type of aggregation to address the undesirable randomness associated with classical Knockoff inference. We demonstrate FDP control and substantial power gains over existing Knockoff-based methods in various simulation settings and achieve good sensitivity/specificity tradeoffs on brain imaging data.