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

Adam B Kashlak, Prachi Loliencar, Giseon Heo

The Hidden Markov Model is a classic modelling tool with a wide swath of applications. Its inception considered observations restricted to a finite alphabet, but it was quickly extended to multivariate continuous distributions. In this article, we further extend the Hidden Markov Model from mixtures of normal distributions in $d$-dimensional Euclidean space to general Gaussian measure mixtures in locally convex topological spaces, and hence, we christen this method the Topological Hidden Markov Model. The main innovation is the use of the Onsager-Machlup functional as a proxy for the probability density function in infinite dimensional spaces. This allows for choice of a Cameron-Martin space suitable for a given application. We demonstrate the versatility of this methodology by applying it to simulated diffusion processes such as Brownian and fractional Brownian sample paths as well as the Ornstein-Uhlenbeck process. Our methodology is applied to the identification of sleep states from overnight polysomnography time series data with the aim of diagnosing Obstructive Sleep Apnea in pediatric patients. It is also applied to a series of annual cumulative snowfall curves from 1940 to 1990 in the city of Edmonton, Alberta.

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

Hamid Mousavi, Jakob Drefs, Florian Hirschberger, Jörg Lücke

Latent variable models (LVMs) represent observed variables by parameterized functions of latent variables. Prominent examples of LVMs for unsupervised learning are probabilistic PCA or probabilistic sparse coding which both assume a weighted linear summation of the latents to determine the mean of a Gaussian distribution for the observables. In many cases, however, observables do not follow a Gaussian distribution. For unsupervised learning, LVMs which assume specific non-Gaussian observables (e.g., Bernoulli or Poisson) have therefore been considered. Already for specific choices of distributions, parameter optimization is challenging and only a few previous contributions considered LVMs with more generally defined observable distributions. In this contribution, we do consider LVMs that are defined for a range of different distributions, i.e., observables can follow any (regular) distribution of the exponential family. Furthermore, the novel class of LVMs presented here is defined for binary latents, and it uses maximization in place of summation to link the latents to observables. In order to derive an optimization procedure, we follow an expectation maximization approach for maximum likelihood parameter estimation. We then show, as our main result, that a set of very concise parameter update equations can be derived which feature the same functional form for all exponential family distributions. The derived generic optimization can consequently be applied (without further derivations) to different types of metric data (Gaussian and non-Gaussian) as well as to different types of discrete data. Moreover, the derived optimization equations can be combined with a recently suggested variational acceleration which is likewise generically applicable to the LVMs considered here. Thus, the combination maintains generic and direct applicability of the derived optimization procedure, but, crucially, enables efficient scalability. We numerically verify our analytical results using different observable distributions, and, furthermore, discuss some potential applications such as learning of variance structure, noise type estimation and denoising.

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

Nimita Shinde, Tianjiao Ding, Daniel Robinson, Rene Vidal

Manifold clustering is an important problem in motion and video segmentation, natural image clustering, and other applications where high-dimensional data lie on multiple, low-dimensional, nonlinear manifolds. While current state-of-the-art methods on large-scale datasets such as CIFAR provide good empirical performance, they do not have any proof of theoretical correctness. In this work, we propose a method that clusters data belonging to a union of nonlinear manifolds. Furthermore, for a given input data sample $y$ belonging to the $l$th manifold $\mathcal{M}_l$, we provide geometric conditions that guarantee a manifold-preserving representation of $y$ can be recovered from the solution to the proposed model. The geometric conditions require that (i) $\mathcal{M}_l$ is well-sampled in the neighborhood of $y$, with the sampling density given as a function of the curvature, and (ii) $\mathcal{M}_l$ is sufficiently separated from the other manifolds. In addition to providing proof of correctness in this setting, a numerical comparison with state-of-the-art methods on CIFAR datasets shows that our method performs competitively although marginally worse than methods without

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

Yuxuan Yin, Yu Wang, Peng Li

We introduce a novel semi-supervised learning approach, named Teacher-Student Bayesian Optimization ($\texttt{TSBO}$), integrating the teacher-student paradigm into BO to minimize expensive labeled data queries for the first time. $\texttt{TSBO}$ incorporates a teacher model, an unlabeled data sampler, and a student model. The student is trained on unlabeled data locations generated by the sampler, with pseudo labels predicted by the teacher. The interplay between these three components implements a unique *selective regularization* to the teacher in the form of student feedback. This scheme enables the teacher to predict high-quality pseudo labels, enhancing the generalization of the GP surrogate model in the search space. To fully exploit $\texttt{TSBO}$, we propose two optimized unlabeled data samplers to construct effective student feedback that well aligns with the objective of Bayesian optimization. Furthermore, we quantify and leverage the uncertainty of the teacher-student model for the provision of reliable feedback to the teacher in the presence of risky pseudo-label predictions. $\texttt{TSBO}$ demonstrates significantly improved sample-efficiency in several global optimization tasks under tight labeled data budgets. The implementation is available at https://github.com/reminiscenty/TSBO-Official.

Social Aspects · Privacy-preserving Statistics and Machine Learning

Weiming Zhuang, Jian Xu, Chen Chen, Jingtao Li, Lingjuan Lyu

We present COALA, a vision-centric Federated Learning (FL) platform, and a suite of benchmarks for practical FL scenarios, which we categorize as task, data, and model levels. At the task level, COALA extends support from simple classification to 15 computer vision tasks, including object detection, segmentation, pose estimation, and more. It also facilitates federated multiple-task learning, allowing clients to train on multiple tasks simultaneously. At the data level, COALA goes beyond supervised FL to benchmark both semi-supervised FL and unsupervised FL. It also benchmarks feature distribution shifts other than commonly considered label distribution shifts. In addition to dealing with static data, it supports federated continual learning for continuously changing data in real-world scenarios. At the model level, COALA benchmarks FL with split models and different models in different clients. COALA platform offers three degrees of customization for these practical FL scenarios, including configuration customization, components customization, and workflow customization. We conduct systematic benchmarking experiments for the practical FL scenarios and highlight potential opportunities for further advancements in FL.

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

Zhe Huang, Xiaowei Yu, Dajiang Zhu, Michael Hughes

Semi-supervised learning (SSL) seeks to enhance task performance by training on both labeled and unlabeled data. Mainstream SSL image classification methods mostly optimize a loss that additively combines a supervised classification objective with a regularization term derived *solely* from unlabeled data. This formulation often neglects the potential for interaction between labeled and unlabeled images. In this paper, we introduce InterLUDE, a new approach to enhance SSL made of two parts that each benefit from labeled-unlabeled interaction. The first part, embedding fusion, interpolates between labeled and unlabeled embeddings to improve representation learning. The second part is a new loss, grounded in the principle of consistency regularization, that aims to minimize discrepancies in the model's predictions between labeled versus unlabeled inputs. Experiments on standard closed-set SSL benchmarks and a medical SSL task with an uncurated unlabeled set show clear benefits to our approach. On the STL-10 dataset with only 40 labels, InterLUDE achieves **3.2%** error rate, while the best previous method reports 6.3%.

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

Ming-Kun Xie, Jia-Hao Xiao, Pei Peng, Gang Niu, Masashi Sugiyama, Sheng-Jun Huang

The key to multi-label image classification (MLC) is to improve model performance by leveraging label correlations. Unfortunately, it has been shown that overemphasizing co-occurrence relationships can cause the overfitting issue of the model, ultimately leading to performance degradation. In this paper, we provide a causal inference framework to show that the correlative features caused by the target object and its co-occurring objects can be regarded as a mediator, which has both positive and negative impacts on model predictions. On the positive side, the mediator enhances the recognition performance of the model by capturing co-occurrence relationships; on the negative side, it has the harmful causal effect that causes the model to make an incorrect prediction for the target object, even when only co-occurring objects are present in an image. To address this problem, we propose a counterfactual reasoning method to measure the total direct effect, achieved by enhancing the direct effect caused only by the target object. Due to the unknown location of the target object, we propose patching-based training and inference to accomplish this goal, which divides an image into multiple patches and identifies the pivot patch that contains the target object. Experimental results on multiple benchmark datasets with diverse configurations validate that the proposed method can achieve state-of-the-art performance.

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

Yangfan Liu, JIAQI LYU, Xin Geng, Ning Xu

One major challenge in weakly supervised learning is learning from inexact supervision, ranging from partial labels (PLs) with *redundant* information to the extreme of unlabeled data with *insufficient* information. While recent work has made significant strides in specific inexact supervision contexts, supervision forms typically *coexist* in complex combinations. This is exemplified in *semi-supervised partial label learning*, where PLs act as the exclusive supervision in a semi-supervised setting. Current strategies addressing combined inexact scenarios are usually composite, which can lead to incremental solutions that essentially replicate existing methods. In this paper, we propose a novel approach to *uniformly* tackle both label redundancy and insufficiency, derived from a mutual information-based perspective. We design a label channel that facilitates dynamic label exchange within the candidate label sets, which identifies potential true labels and filters out likely incorrect ones, thereby minimizing error accumulation. Experimental results demonstrate the superiority of our method over existing state-of-the-art PL and semi-supervised learning approaches by directly integrating them. Furthermore, our extended experiments on partial-complementary label learning underscore the flexibility of our uniform treatment in managing diverse supervision scenarios.

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

Shuo Wen, Maria Brbic

In many real-world applications, test data may commonly exhibit categorical shifts, characterized by the emergence of novel classes, as well as distribution shifts arising from feature distributions different from the ones the model was trained on. However, existing methods either discover novel classes in the open-world setting or assume domain shifts without the ability to discover novel classes. In this work, we consider a cross-domain open-world discovery setting, where the goal is to assign samples to seen classes and discover unseen classes under a domain shift. To address this challenging problem, we present CROW, a prototype-based approach that introduces a cluster-then-match strategy enabled by a well-structured representation space of foundation models. In this way, CROW discovers novel classes by robustly matching clusters with previously seen classes, followed by fine-tuning the representation space using an objective designed for cross-domain open-world discovery. Extensive experimental results on image classification benchmark datasets demonstrate that CROW outperforms alternative baselines, achieving an 8% average performance improvement across 75 experimental settings.

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

Xinhang Wan, Jiyuan Liu, Xinwang Liu, Yi Wen, Hao Yu, Siwei Wang, Shengju Yu, Tianjiao Wan, Jun Wang, En Zhu

Sample labeling is the most primary and fundamental step of semi-supervised learning. In literature, most existing methods randomly label samples with a given ratio, but achieve unpromising and unstable results due to the randomness, especially in multi-view settings. To address this issue, we propose a Dynamic Multi-view Labeling Strategy with Shared and Specific Information. To be brief, by building two classifiers with existing labels to utilize decoupled shared and specific information, we select the samples of low classification confidence and label them in high priorities. The newly generated labels are also integrated to update the classifiers adaptively. The two processes are executed alternatively until a satisfying classification performance. To validate the effectiveness of the proposed method, we conduct extensive experiments on popular benchmarks, achieving promising performance. The code is publicly available at https://github.com/wanxinhang/ICML2024_decouple_then_classify.

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

Shengju Yu, Dong Zhibin, Siwei Wang, Xinhang Wan, Yue Liu, Weixuan Liang, Pei Zhang, Wenxuan Tu, Xinwang Liu

Incomplete multi-view clustering (IMVC) methods typically encounter three drawbacks: (1) intense time and/or space overheads; (2) intractable hyper-parameters; (3) non-zero variance results. With these concerns in mind, we give a simple yet effective IMVC scheme, termed as ToRES. Concretely, instead of self-expression affinity, we manage to construct prototype-sample affinity for incomplete data so as to decrease the memory requirements. To eliminate hyper-parameters, besides mining complementary features among views by view-wise prototypes, we also attempt to devise cross-view prototypes to capture consensus features for jointly forming high-quality clustering representation. To avoid the variance, we successfully unify representation learning and clustering operation, and directly optimize the discrete cluster indicators from incomplete data. Then, for the resulting objective function, we provide two equivalent solutions from perspectives of feasible region partitioning and objective transformation. Many results suggest that ToRES exhibits advantages against 20 SOTA algorithms, even in scenarios with a higher ratio of incomplete data.

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

Chaoqun Du, Yizeng Han, Gao Huang

Recent advancements in semi-supervised learning have focused on a more realistic yet challenging task: addressing imbalances in labeled data while the class distribution of unlabeled data remains both unknown and potentially mismatched. Current approaches in this sphere often presuppose rigid assumptions regarding the class distribution of unlabeled data, thereby limiting the adaptability of models to only certain distribution ranges. In this study, we propose a novel approach, introducing a highly adaptable framework, designated as **SimPro**, which does not rely on any predefined assumptions about the distribution of unlabeled data. Our framework, grounded in a probabilistic model, innovatively refines the expectation-maximization (EM) method by separating the modeling of conditional and marginal class distributions. This separation facilitates a closed-form solution for class distribution estimation during the maximization phase, leading to the formulation of a Bayes classifier. The Bayes classifier, in turn, enhances the quality of pseudo-labels in the expectation phase. Remarkably, the SimPro framework is not only straightforward to implement but also comes with theoretical guarantees. Moreover, we introduce two novel class distributions broadening the scope of the evaluation. Our method showcases consistent state-of-the-art performance across diverse benchmarks and data distribution scenarios. benchmarks and data distribution scenarios. Our code is available at https://github.com/LeapLabTHU/SimPro.

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

Qinghua Tao, Francesco Tonin, Alex Lambert, Yingyi Chen, Panagiotis Patrinos, Johan Suykens

In contrast with Mercer kernel-based approaches as used e.g. in Kernel Principal Component Analysis (KPCA), it was previously shown that Singular Value Decomposition (SVD) inherently relates to asymmetric kernels and Asymmetric Kernel Singular Value Decomposition (KSVD) has been proposed. However, the existing formulation to KSVD cannot work with infinite-dimensional feature mappings, the variational objective can be unbounded, and needs further numerical evaluation and exploration towards machine learning. In this work, i) we introduce a new asymmetric learning paradigm based on coupled covariance eigenproblem (CCE) through covariance operators, allowing infinite-dimensional feature maps. The solution to CCE is ultimately obtained from the SVD of the induced asymmetric kernel matrix, providing links to KSVD. ii) Starting from the integral equations corresponding to a pair of coupled adjoint eigenfunctions, we formalize the asymmetric Nyström method through a finite sample approximation to speed up training. iii) We provide the first empirical evaluations verifying the practical utility and benefits of KSVD and compare with methods resorting to symmetrization or linear SVD across multiple tasks.

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

Steinar Laenen, He Sun

This paper studies clustering algorithms for dynamically evolving graphs $\{G_t\}$, in which new edges (and potential new vertices) are added into a graph, and the underlying cluster structure of the graph can gradually change. The paper proves that, under some mild condition on the cluster-structure, the clusters of the final graph $G_T$ of $n_T$ vertices at time $T$ can be well approximated by a dynamic variant of the spectral clustering algorithm. The algorithm runs in amortised update time $O(1)$ and query time $o(n_T)$. Experimental studies on both synthetic and real-world datasets further confirm the practicality of our designed algorithm.

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

Zhangyu Wang, Gengchen Mai, Krzysztof Janowicz, Ni Lao

A wide range of (multivariate) temporal (1D) and spatial (2D) data analysis tasks, such as grouping vehicle sensor trajectories, can be formulated as clustering with given metric constraints. Existing metric-constrained clustering algorithms overlook the rich correlation between feature similarity and metric distance, i.e., metric autocorrelation. The model-based variations of these clustering algorithms (e.g. TICC and STICC) achieve SOTA performance, yet suffer from computational instability and complexity by using a metric-constrained Expectation-Maximization procedure. In order to address these two problems, we propose a novel clustering algorithm, MC-GTA (**M**odel-based **C**lustering via **G**oodness-of-fit **T**ests with **A**utocorrelations). Its objective is only composed of pairwise weighted sums of feature similarity terms (square Wasserstein-2 distance) and metric autocorrelation terms (a novel multivariate generalization of classic semivariogram). We show that MC-GTA is effectively minimizing the total hinge loss for intra-cluster observation pairs not passing goodness-of-fit tests, i.e., statistically not originating from the same distribution. Experiments on 1D/2D synthetic and real-world datasets demonstrate that MC-GTA successfully incorporates metric autocorrelation. It outperforms strong baselines by large margins (up to 14.3% in ARI and 32.1% in NMI) with faster and stabler optimization (>10x speedup).

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

Xi Han, Fei Hou, Hong Qin

Numerical solvers of Partial Differential Equations (PDEs) are of fundamental significance to science and engineering. To date, the historical reliance on legacy techniques has circumscribed possible integration of big data knowledge and exhibits sub-optimal efficiency for certain PDE formulations, while data-driven neural methods typically lack mathematical guarantee of convergence and correctness. This paper articulates a mathematically rigorous neural solver for linear PDEs. The proposed UGrid solver, built upon the principled integration of U-Net and MultiGrid, manifests a mathematically rigorous proof of both convergence and correctness, and showcases high numerical accuracy, as well as strong generalization power to various input geometry/values and multiple PDE formulations. In addition, we devise a new residual loss metric, which enables unsupervised training and affords more stability and a larger solution space over the legacy losses.

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

Yulong Zhang, Yuan Yao, Shuhao Chen, Pengrong Jin, Yu Zhang, Jian Jin, Jiangang Lu

Empirical Risk Minimization (ERM) is fragile in scenarios with insufficient labeled samples. A vanilla extension of ERM to unlabeled samples is Entropy Minimization (EntMin), which employs the soft-labels of unlabeled samples to guide their learning. However, EntMin emphasizes prediction discriminability while neglecting prediction diversity. To alleviate this issue, in this paper, we rethink the guidance information to utilize unlabeled samples. By analyzing the learning objective of ERM, we find that the guidance information for labeled samples in a specific category is the corresponding *label encoding*. Inspired by this finding, we propose a Label-Encoding Risk Minimization (LERM). It first estimates the label encodings through prediction means of unlabeled samples and then aligns them with their corresponding ground-truth label encodings. As a result, the LERM ensures both prediction discriminability and diversity, and it can be integrated into existing methods as a plugin. Theoretically, we analyze the relationships between LERM and ERM as well as EntMin. Empirically, we verify the superiority of the LERM under several label insufficient scenarios. The codes are available at https://github.com/zhangyl660/LERM.

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

Sascha Xu, Nils Philipp Walter, Janis Kalofolias, Jilles Vreeken

Finding and describing sub-populations that are exceptional in terms of a target property has important applications in many scientific disciplines, from identifying disadvantaged demographic groups in census data to finding conductive molecules within gold nanoparticles. Current approaches to finding such subgroups require pre-discretized predictive variables, do not permit non-trivial target distributions, do not scale to large datasets, and struggle to find diverse results. To address these limitations, we propose SYFLOW, an end-to-end optimizable approach in which we leverage normalizing flows to model arbitrary target distributions and introduce a novel neural layer that results in easily interpretable subgroup descriptions. We demonstrate on synthetic data, real-world data, and via a case study, that SYFLOW reliably finds highly exceptional subgroups accompanied by insightful descriptions.

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

Jie Wen, Shijie Deng, Waikeung Wong, Guoqing Chao, Chao Huang, Lunke Fei, Yong Xu

As a branch of clustering, multi-view clustering has received much attention in recent years. In practical applications, a common phenomenon is that partial views of some samples may be missing in the collected multi-view data, which poses a severe challenge to design the multi-view learning model and explore complementary and consistent information. Currently, most of the incomplete multi-view clustering methods only focus on exploring the information of available views while few works study the missing view recovery for incomplete multi-view learning. To this end, we propose an innovative diffusion-based missing view generation (DMVG) network. Moreover, for the scenarios with high missing rates, we further propose an incomplete multi-view data augmentation strategy to enhance the recovery quality for the missing views. Extensive experimental results show that the proposed DMVG can not only accurately predict missing views, but also further enhance the subsequent clustering performance in comparison with several state-of-the-art incomplete multi-view clustering methods.

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.