Semi-Supervised Learning

When modeling class-imbalanced data, it is crucial to address the imbalance, as models trained on such data tend to be biased towards the majority classes. This problem is amplified under partial supervision, where pseudo-labels for unlabeled data are predicted based on imbalanced labeled data, propagating the bias. While recent semi-supervised models address class imbalance, they typically assume single-modal input data. However, with the growing availability of multimodal data, it is essential to leverage complementary modalities. In this article, we propose a multimodal deep generative model for semi-supervised learning under class imbalance. Our approach uses separate encoders for each modality, sharing latent variables across modalities, and simplifies joint posterior computation with a product-of-experts method. To further address class imbalance, we replace typical Gaussian distributions with Student's t-distributions for the prior, encoder, and decoder, better capturing the heavy-tailed latent distributions in imbalanced data. We derive a new objective function for training the proposed model on both labeled and unlabeled data using $γ$-power divergence. Empirical results on benchmark and real-world datasets demonstrate that our model outperforms baseline methods in generalization, achieving superior classification performance for partially labeled multimodal data with imbalanced class distributions.

We develop graph-based methods for semi-supervised learning based on label propagation on a data similarity graph. When data is abundant or arrive in a stream, the problems of computation and data storage arise for any graph-based method. We propose a fast approximate online algorithm that solves for the harmonic solution on an approximate graph. We show, both empirically and theoretically, that good behavior can be achieved by collapsing nearby points into a set of local representative points that minimize distortion. Moreover, we regularize the harmonic solution to achieve better stability properties. We also present graph-based methods for detecting conditional anomalies and apply them to the identification of unusual clinical actions in hospitals. Our hypothesis is that patient-management actions that are unusual with respect to the past patients may be due to errors and that it is worthwhile to raise an alert if such a condition is encountered. Conditional anomaly detection extends standard unconditional anomaly framework but also faces new problems known as fringe and isolated points. We devise novel nonparametric graph-based methods to tackle these problems. Our methods rely on graph connectivity analysis and soft harmonic solution. Finally, we conduct an extensive human evaluation study of our conditional anomaly methods by 15 experts in critical care.

Capturing semantic consistency among nodes is crucial for effective graph representation learning. Existing approaches typically rely on $k$-nearest neighbors ($k$NN) or other node-level full search algorithms (FSA) to mine semantic relationships via exhaustive pairwise similarity computation, which suffer from high computational complexity and rigid neighbor selection, limiting scalability and introducing noisy connections. In this paper, we propose the Semantic Consistency enhanced Graph Neural Network (SCGNN), a novel plug-and-play framework that leverages granular-ball computing (GBC) to efficiently capture semantic consistency in a scalable manner. Unlike node-level FSA methods, SCGNN models group-level semantic structure by adaptively partitioning nodes into granular balls, significantly reducing computational cost while improving robustness to noise. To effectively utilize the discovered group-level semantic consistency, we design a dual enhancement strategy. Specifically, (1) a structure enhancement module constructs an anchor-based graph structure, where each anchor is a virtual node representing the group-level semantic carried by a granular ball, then injecting group-level semantic information into the graph structure; and (2) a supervision enhancement module performs label consistency checking (LCC) by combining GBC predictions with model-generated pseudo-labels, thereby producing more reliable supervision signals. SCGNN is compatible with various GNN backbones. During the forward propagation of SCGNN, the vanilla graph and the augment graph are jointly encoded, and their predictions are fused; during the backpropagation, the supervision enhancement module provides enhanced supervision signals to guide parameter updates.

We consider the problem of two-sample testing in a semi-supervised setting with abundant unlabeled covariate data. Standard two-sample tests neglect covariate information, which has the potential to significantly boost performance. However, incorporating covariates potentially breaks the exchangeability assumption under the null, which further complicates a calibration procedure. To address these issues, we propose a semi-supervised method that produces a test statistic with asymptotic normality, while effectively integrating additional information from covariates. Our test is straightforward to calibrate due to the asymptotic normality under the null and achieves asymptotic power that is often much higher than existing kernel tests without covariates. Furthermore, we formally show that the proposed method is consistent in power against fixed and local alternatives. Simulations confirm the practical and theoretical strengths of our approach.

The rapidly expanding artificial intelligence (AI) industry has produced diverse yet powerful prediction tools, each with its own network architecture, training strategy, data-processing pipeline, and domain-specific strengths. These tools create new opportunities for semi-supervised inference, in which labeled data are limited and expensive to obtain, whereas unlabeled data are abundant and widely available. Given a collection of predictors, we treat them as a mixture of experts (MOE) and introduce an MOE-powered semi-supervised inference framework built upon prediction-powered inference (PPI). Motivated by the variance reduction principle underlying PPI, the proposed framework seeks the mixture of experts that achieves the smallest possible variance. Compared with standard PPI, the MOE-powered inference framework adapts to the unknown performance of individual predictors, benefits from their collective predictive power, and enjoys a best-expert guarantee. The framework is flexible and applies to mean estimation, linear regression, quantile estimation, and general M-estimation. We develop non-asymptotic theory for the MOE-powered inference framework and establish upper bounds on the coverage error of the resulting confidence intervals. Numerical experiments demonstrate the practical effectiveness of MOE-powered inference and corroborate our theoretical findings.

In open-world semi-supervised learning (OWSSL), a model learns from labeled data and unlabeled data containing both known and novel classes. In practical OWSSL applications, models are expected to perform rigorous classification by directly selecting the most semantically relevant label from a candidate set for each sample. Existing OWSSL methods fail to achieve this because novel samples are trained without explicit supervision, and these methods lack mechanisms to extract latent semantic information, resulting in predicted labels that have no semantic correspondence to candidate textual labels. To address this, we introduce SEmantic Capture for Open-world Semi-supervised learning (SECOS), which directly predicts textual labels from the candidate set without post-processing, meeting the requirements of practical OWSSL applications. SECOS leverages external knowledge to extract and align semantic representations across modalities for both known and novel classes, providing explicit supervisory signals for training novel classes. Extensive experiments demonstrate that even when existing OWSSL methods are evaluated under the more lenient post-hoc matching setting, SECOS still surpasses them by up to 5.4% without such assistance, highlighting its superior effectiveness. Code is available at https://github.com/ganchi-huanggua/OSSL-Classification.

This paper proposes an algorithm for real-time learning without explicit feedback. The algorithm combines the ideas of semi-supervised learning on graphs and online learning. In particular, it iteratively builds a graphical representation of its world and updates it with observed examples. Labeled examples constitute the initial bias of the algorithm and are provided offline, and a stream of unlabeled examples is collected online to update this bias. We motivate the algorithm, discuss how to implement it efficiently, prove a regret bound on the quality of its solutions, and apply it to the problem of real-time face recognition. Our recognizer runs in real time, and achieves superior precision and recall on 3 challenging video datasets.

This paper proposes a novel algorithm for semisupervised learning. This algorithm learns graph cuts that maximize the margin with respect to the labels induced by the harmonic function solution. We motivate the approach, compare it to existing work, and prove a bound on its generalization error. The quality of our solutions is evaluated on a synthetic problem and three UCI ML repository datasets. In most cases, we outperform manifold regularization of support vector machines, which is a state-of-the-art approach to semi-supervised max-margin learning.

We introduce Sparse-HFS, a scalable algorithm that can compute solutions to SSL problems using only O(n polylog(n)) space and O(m polylog(n)) time.

I developed a new version of Latent Semantic Scaling (LSS) employing word2vec as a masked language model. Unlike original spatial models, it assigns polarity scores to words and documents as predicted probabilities of seed words to occur in given contexts. These probabilistic polarity scores are more accurate, interpretable and consistent than those spatial polarity models can produce in text analysis. I demonstrate these advantages by applying both probabilistic and spatial models to China Daily's coverage of China and other countries during the coronavirus disease (COVID) pandemic in terms of achievement in health issues. The result suggests that more advanced masked language models would further improve the semisupervised machine learning technique.

Human visual preferences are inherently multi-dimensional, encompassing aesthetics, detail fidelity, and semantic alignment. However, existing datasets provide only single, holistic annotations, resulting in severe label noise: images that excel in some dimensions but are deficient in others are simply marked as winner or loser. We theoretically demonstrate that compressing multi-dimensional preferences into binary labels generates conflicting gradient signals that misguide Diffusion Direct Preference Optimization (DPO). To address this, we propose Semi-DPO, a semi-supervised approach that treats consistent pairs as clean labeled data and conflicting ones as noisy unlabeled data. Our method starts by training on a consensus-filtered clean subset, then uses this model as an implicit classifier to generate pseudo-labels for the noisy set for iterative refinement. Experimental results demonstrate that Semi-DPO achieves state-of-the-art performance and significantly improves alignment with complex human preferences, without requiring additional human annotation or explicit reward models during training. We will release our code and models at: https://github.com/L-CodingSpace/semi-dpo

Semi-supervised learning (SSL) has become a promising solution to alleviate the annotation burden of deep learning-based medical image segmentation models. While recent advances in foundation model-driven SSL have pushed the boundary to extremely limited annotation scenarios, they fail to maintain robust competitive performance in complex imaging modalities. In this paper, we propose SemiSAM-O1, an annotation-efficient framework using only one annotated template image for segmentation. SemiSAM-O1 extends the specialist-generalist collaborative learning framework to the extreme one-label setting by fully exploiting the foundation model's feature representation capability beyond its prompting interface. SemiSAM-O1 operates in two stages. In the first stage, the foundation model's encoder extracts dense features from all volumes, and class prototypes derived from the single annotated template are propagated to the unlabeled pool via feature similarity to produce coarse initial pseudo-labels. In the second stage, an iterative training-and-refinement loop progressively improves both the segmentation model and the pseudo-labels over multiple rounds, where each round trains the model from scratch on current pseudo-labels and generates updated predictions with voxel-wise uncertainty estimates. An uncertainty-guided refinement step further leverages the foundation model's global feature space to correct high-uncertainty regions by aggregating labels from their most similar confident neighbors, establishing a virtuous cycle of mutual improvement. Extensive experiments on a wide range of segmentation tasks across different modalities and anatomical targets demonstrate that SemiSAM-O1 significantly narrows the performance gap between one-label semi-supervised learning and full supervision, while significantly reducing the computational overhead of online foundation model inference.

Semi-supervised classification, where unlabeled data are massive but labeled data are limited, often arises in machine learning applications. We address this challenge under high-dimensional data by leveraging the manifold and cluster assumptions. Based on the Fermat distance, a density-sensitive metric that naturally encodes the cluster assumption, we propose the weighted $k$-nearest neighbors (NN) classifier and multidimensional scaling (MDS)-induced classifiers. The use of MDS with a large target dimension allows the effective application of linear classifiers to complex manifold data. Theoretically, we derive a sharp lower bound for the expected excess risk within clusters and prove that the weighted $k$-NN classifier utilizing the true Fermat distance is minimax optimal. Furthermore, we explicitly quantify the utility of unlabeled data by showing that the error arising from estimating the Fermat distance decays exponentially with the pooled sample size. Such a rate is much faster than the related rates in the literature. Extensive experiments on synthetic and real datasets demonstrate competitive or superior performance of our approaches compared to state-of-the-art graph-based semi-supervised classifiers.

Knee osteoarthritis (KOA) is a degenerative joint disease that can lead to chronic pain, reduced mobility, and long-term disability. Automated severity grading from knee radiographs can support early assessment, but current methods heavily depend on large labeled datasets and remain sensitive to class imbalance, noisy samples, and variability in clinical annotations. To alleviate these limitations, we propose a Hierarchical fusion of Semi-Supervised framework with Self-Supervision (H-SemiS) for KOA severity grading in knee X-ray samples using limited annotated data. Rather than treating severity grading as a flat multi-class problem, H-SemiS decomposes the task into a sequence of binary sub-tasks within a semi-supervised teacher-student architecture, directly mitigating the impact of class imbalance. To further enhance feature learning from unlabeled data, the framework integrates an adversarial self-supervised reconstruction module that encourages the network to capture robust anatomical structures. In parallel, a teacher-student design with quantum-inspired feature mixing improves discrimination boundaries between adjacent grades when pseudo-labels are noisy. We comprehensively evaluate H-SemiS on two challenging multi-class datasets and assess its generalizability on two binary-class datasets. Our experimental results demonstrate the superiority of the proposed H-SemiS framework across multiple evaluation metrics, consistently outperforming several competing baselines and state-of-the-art methods. The code is publicly available at https://github.com/chandravardhan-singh-raghaw/H-SemiS.

Semi-supervised learning addresses label scarcity and high annotation costs in medical image segmentation by exploiting the latent information in unlabeled data to enhance model performance. Traditional discriminative segmentation relies on segmentation masks, neglecting feature-level distribution constraints. This limits robust semantic representation learning and adaptive modeling of unlabeled data in scenarios with few labels. To address these limitations, we propose SemiGDA, a novel Generative Dual-distribution Alignment framework for semi-supervised medical image segmentation. Our SemiGDA overcomes the reliance of discriminative methods on large labeled datasets by aligning feature and semantic distributions to boost semantic learning and scene adaptability. Specifically, we propose a Dual-distribution Alignment Module (DAM), which employs two structurally distinct encoders to model image and mask feature distributions. It enforces their alignment in the latent space via distributional constraints, establishing structured feature consistency. Moreover, we design a Consistency-Driven Skip Adapter (CDSA) strategy, which introduces dual skip adapters (Image and Mask) to fuse multi-scale features via skip connections. Using a consistency loss, CDSA enhances cross-branch semantic alignment and reinforces fine-grained semantic consistency. Experimental results on diverse medical datasets show that our method outperforms other state-of-the-art semi-supervised segmentation methods. Code is released at: https://github.com/taozh2017/SemiGDA.

Semi-supervised learning has emerged as a powerful paradigm for leveraging large amounts of unlabeled data to improve the performance of machine learning models when labeled data are scarce. Among existing approaches, methods derived from FixMatch have achieved state-of-the-art results in image classification by combining weak and strong data augmentations with confidence-based pseudo-labeling. Despite their strong empirical performance, these methods typically struggle with two critical bottlenecks: majority classes tend to dominate the learning process, which is amplified by incorrect pseudo-labels, leading to biased models. Furthermore, noisy early pseudo-labels prevent the model from forming clear decision boundaries, requiring prolonged training to learn informative representation. In this paper, we introduce a paradigm shift from conventional logical output threshold base, toward an explicit shaping of geometric representations. Our approach is inspired by the recently proposed Latent-Euclidean Joint-Embedding Predictive Architectures (LeJEPA), a theoretically grounded framework asserting that meaningful representations should exhibit an isotropic Gaussian structure in latent space. Building on this principle, we propose a new training objective that combines the classical semi-supervised loss used in FlexMatch, an adaptive extension of FixMatch, with a latent-space regularization term derived from LeJEPA. Our proposed approach, encourages well-structured representations while preserving the advantages of pseudo-labeling strategies. Through extensive experiments on CIFAR-100, STL-10 and Tiny-ImageNet, we demonstrate that the proposed method consistently outperforms existing baselines. In addition, our method significantly accelerates the convergence, drastically reducing the overall computational cost compared to standard FixMatch-based pipelines.

Semi-supervised node classification is a foundational task in graph machine learning, yet state-of-the-art Graph Neural Networks (GNNs) are hindered by significant computational overhead and reliance on strong homophily assumptions. Traditional GNNs require expensive iterative training and multi-layer message passing, while existing training-free methods, such as Label Propagation, lack adaptability to heterophilo-us graph structures. This paper presents \textbf{F$^2$LP-AP} (Fast and Flexible Label Propagation with Adaptive Propagation Kernel), a training-free, computationally efficient framework that adapts to local graph topology. Our method constructs robust class prototypes via the geometric median and dynamically adjusts propagation parameters based on the Local Clustering Coefficient (LCC), enabling effective modeling of both homophilous and heterophilous graphs without gradient-based training. Extensive experiments across diverse benchmark datasets demonstrate that \textbf{F$^2$LP-AP} achieves competitive or superior accuracy compared to trained GNNs, while significantly outperforming existing baselines in computational efficiency.

Multi-task learning is effective for related applications, but its performance can deteriorate when the target sample size is small. Transfer learning can borrow strength from related studies; yet, many existing methods rely on restrictive bounded-difference assumptions between the source and target models. We propose SMART, a spectral transfer method for multi-task linear regression that instead assumes spectral similarity: the target left and right singular subspaces lie within the corresponding source subspaces and are sparsely aligned with the source singular bases. Such an assumption is natural when studies share latent structures and enables transfer beyond the bounded-difference settings. SMART estimates the target coefficient matrix through structured regularization that incorporates spectral information from a source study. Importantly, it requires only a fitted source model rather than the raw source data, making it useful when data sharing is limited. Although the optimization problem is nonconvex, we develop a practical ADMM-based algorithm. We establish general, non-asymptotic error bounds and a minimax lower bound in the noiseless-source regime. Under additional regularity conditions, these results yield near-minimax Frobenius error rates up to logarithmic factors. Simulations confirm improved estimation accuracy and robustness to negative transfer, and analysis of multi-modal single-cell data demonstrates better predictive performance. The Python implementation of SMART, along with the code to reproduce all experiments in this paper, is publicly available at https://github.com/boxinz17/smart.

Semi-supervised learning with manifold regularization is a classical framework for jointly learning from both labeled and unlabeled data, where the key requirement is that the support of the unknown marginal distribution has the geometric structure of a Riemannian manifold. Typically, the Laplace-Beltrami operator-based manifold regularization can be approximated empirically by the Laplacian regularization associated with the entire training data and its corresponding graph Laplacian matrix. However, the graph Laplacian matrix depends heavily on the prespecified similarity metric and may lead to inappropriate penalties when dealing with redundant or noisy input variables. To address the above issues, this paper proposes a new Semi-Supervised Meta Additive Model (S$^2$MAM) based on a bilevel optimization scheme that automatically identifies informative variables, updates the similarity matrix, and simultaneously achieves interpretable predictions. Theoretical guarantees are provided for S$^2$MAM, including the computing convergence and the statistical generalization bound. Experimental assessments across 4 synthetic and 12 real-world datasets, with varying levels and categories of corruption, validate the robustness and interpretability of the proposed approach.

In gradient-based learning, a step size chosen in parameter units does not produce a predictable per-step change in function output. This often leads to instability in the streaming setting (i.e., batch size=1), where stochasticity is not averaged out and update magnitudes can momentarily become arbitrarily big or small. Instead, we propose intentional updates: first specify the intended outcome of an update and then solve for the step size that approximately achieves it. This strategy has precedent in online supervised linear regression via Normalized Least Mean Squares algorithm, which selects a step size to yield a specified change in the function output proportional to the current error. We extend this principle to streaming deep reinforcement learning by defining appropriate intended outcomes: Intentional TD aims for a fixed fractional reduction of the TD error, and Intentional Policy Gradient aims for a bounded per-step change in the policy, limiting local KL divergence. We propose practical algorithms combining eligibility traces and diagonal scaling. Empirically, these methods yield state-of-the-art streaming performance, frequently performing on par with batch and replay-buffer approaches.

Principal Component Analysis (PCA) is a fundamental tool for representation learning, but its global linear formulation fails to capture the structure of data supported on curved manifolds. In contrast, manifold learning methods model nonlinearity but often sacrifice the spectral structure and stability of PCA. We propose \emph{Geodesic Tangent Space Aggregation PCA (GTSA-PCA)}, a geometric extension of PCA that integrates curvature awareness and geodesic consistency within a unified spectral framework. Our approach replaces the global covariance operator with curvature-weighted local covariance operators defined over a $k$-nearest neighbor graph, yielding local tangent subspaces that adapt to the manifold while suppressing high-curvature distortions. We then introduce a geodesic alignment operator that combines intrinsic graph distances with subspace affinities to globally synchronize these local representations. The resulting operator admits a spectral decomposition whose leading components define a geometry-aware embedding. We further incorporate semi-supervised information to guide the alignment, improving discriminative structure with minimal supervision. Experiments on real datasets show consistent improvements over PCA, Kernel PCA, Supervised PCA and strong graph-based baselines such as UMAP, particularly in small sample size and high-curvature regimes. Our results position GTSA-PCA as a principled bridge between statistical and geometric approaches to dimensionality reduction.

Smooth functions on graphs have wide applications in manifold and semi-supervised learning. In this paper, we study a bandit problem where the payoffs of arms are smooth on a graph. This framework is suitable for solving online learning problems that involve graphs, such as content-based recommendation. In this problem, each item we can recommend is a node and its expected rating is similar to its neighbors. The goal is to recommend items that have high expected ratings. We aim for the algorithms where the cumulative regret with respect to the optimal policy would not scale poorly with the number of nodes. In particular, we introduce the notion of an effective dimension, which is small in real-world graphs, and propose two algorithms for solving our problem that scale linearly and sublinearly in this dimension. Our experiments on real-world content recommendation problem show that a good estimator of user preferences for thousands of items can be learned from just tens of nodes evaluations.

Hyperspectral tree species classification is challenging due to limited and imbalanced class labels, spectral mixing (overlapping light signatures from multiple species), and ecological heterogeneity (variability among ecological systems). Addressing these challenges requires methods that integrate biological and structural characteristics of vegetation, such as canopy architecture and interspecific interactions, rather than relying solely on spectral signatures. This paper presents a biologically informed, semi-supervised deep learning method that integrates multi-sensor Earth observation data, specifically hyperspectral imaging (HSI) and airborne laser scanning (ALS), with expert, ecological knowledge. The approach relies on biologically inspired pseudo-labelling over a precomputed canopy graph, yielding accurate classification at low training cost. In addition, ecological priors on species cohabitation are automatically derived from reliable sources using large language models (LLMs) and encoded as a cohabitation matrix with likelihoods of species occurring together. These priors are incorporated into the pseudo-labelling strategy, effectively introducing expert knowledge into the model. Experiments on a real-world forest dataset demonstrate 5.6% improvement over the best reference method. Expert evaluation of cohabitation priors reveals high accuracy with differences no larger than 15%.

We revisit the framework of Smart PAC learning, which seeks supervised learners which compete with semi-supervised learners that are provided full knowledge of the marginal distribution on unlabeled data. Prior work has shown that such marginal-by-marginal guarantees are possible for "most" marginals, with respect to an arbitrary fixed and known measure, but not more generally. We discover that this failure can be attributed to an "indistinguishability" phenomenon: There are marginals which cannot be statistically distinguished from other marginals that require different learning approaches. In such settings, semi-supervised learning cannot certify its guarantees from unlabeled data, rendering them arguably non-actionable. We propose relatively smart learning, a new framework which demands that a supervised learner compete only with the best "certifiable" semi-supervised guarantee. We show that such modest relaxation suffices to bypass the impossibility results from prior work. In the distribution-free setting, we show that the One-Inclusion Graph learner is relatively smart up to squaring the sample complexity, and show that no supervised learning algorithm can do better. For distribution-family settings, we show that relatively smart learning can be impossible or can require idiosyncratic learning approaches, and its difficulty can be non-monotone in the inclusion order on distribution families.

The problem of corrupted data, missing features, or missing modalities continues to plague the modern machine learning landscape. To address this issue, a class of regularization methods that enforce consistency between imputed and fully observed data has emerged as a promising approach for improving model generalization, particularly in partially observed settings. We refer to this class of methods as Measure Consistency Regularization (MCR). Despite its empirical success in various applications, such as image inpainting, data imputation and semi-supervised learning, a fundamental understanding of the theoretical underpinnings of MCR remains limited. This paper bridges this gap by offering theoretical insights into when MCR yields a more favorable finite-sample estimation-error upper bound, viewed through the lens of neural network distance. Under ideal interpolation and compatibility conditions, we show that the MCR estimation-error upper bound is no larger than vanilla supervised training and becomes strictly smaller when the mixed-sample alternative is favorable. We then extend the analysis to the non-ideal regime, where optimization and compatibility residuals can potentially offset this finite-sample advantage. Guided by these insights, we propose a novel practical diagnostic that leverages the duality gap and a calibrated drift estimator to infer the potential benefit of MCR training. We present detailed empirical evidence to support our theoretical claims and to show the effectiveness and accuracy of our practical diagnostic. We further provide simulations on real-world datasets to show the versatility of MCR under different model architectures designed for different data sources.

High-level Computer-Aided Process Planning (CAPP) generates manufacturing process plans from part specifications. It suffers from limited dataset availability in industry, reducing model generalization. We propose a semi-supervised learning approach to improve transformer-based CAPP transformer models without manual labeling. An oracle, trained on available transformer behaviour data, filters correct predictions from unseen parts, which are then used for one-shot retraining. Experiments on small-scale datasets with simulated ground truth across the full data distribution show consistent accuracy gains over baselines, demonstrating the method's effectiveness in data-scarce manufacturing environments.

Semi-supervised few-shot learning (SSFSL) resembles real-world applications such as auto-annotation, as it aims to learn a model from a few labeled and abundant unlabeled task-specific examples to annotate the unlabeled ones. Despite the availability of powerful open-source Vision-Language Models (VLMs) and open-world data, existing SSFSL literature largely neglects these resources. In contrast, the related area few-shot learning (FSL) has already exploited them to boost performance. Arguably, to solve real-world auto-annotation, SSFSL should leverage such open resources. To bridge this gap, we explore established SSL methods to finetune a VLM. Unexpectedly, they significantly underperform FSL baselines that do not use unlabeled data. Our in-depth analysis reveals the root cause of failure: VLMs produce flat distributions of softmax probabilities, resulting in zero utilization of unlabeled data and weak supervision signals. To address this challenge, we propose an embarrassingly simple solution that uses temperatures to sharpen the softmax output, which not only increases the confidence scores of pseudo-labels to improve the utilization of unlabeled data, but also strengthens training supervision for effective finetuning. Furthermore, we exploit task-relevant open data, e.g., those retrieved from VLMs' publicly available pretraining set. To mitigate the imbalance and domain gaps in retrieved data, we employ a stage-wise training strategy. Building on the successful finetuning of VLMs and the exploitation of open data, we present a simple yet effective SSFSL method, Stage-Wise Finetuning with Temperatures (SWIFT). Across five benchmarks, SWIFT outperforms recent FSL and SSL methods by $\sim$5 accuracy points. SWIFT even rivals supervised learning, which finetunes a VLM assuming unlabeled data having ground-truth labels!

Multi-view learning is widely applied to real-life datasets, but it often suffers from both missing views and missing labels. Prior probabilistic approaches addressed the missing view problem by using a product-of-experts scheme to aggregate representations from present views and achieved superior performance over deterministic classifiers, using the information bottleneck (IB) principle. However, the IB framework is inherently fully supervised and cannot leverage unlabeled data. In this work, we propose a semi-supervised generative model that utilizes both labeled and unlabeled samples in a unified framework. Our method maximizes the likelihood of unlabeled samples to learn a latent space shared with the IB on labeled data. We also include modality-specific information in likelihood modeling and perform cross-view mutual information maximization in the shared latent space to enhance the extraction of shared information across views. Compared to existing approaches, our model achieves better predictive and generation performance on complex datasets with missing views and limited labeled samples.

Uncertainty quantification is crucial in machine learning, yet most (axiomatic) studies of uncertainty measures focus on classification, leaving a gap in regression settings with limited formal justification and evaluations. In this work, we provide a formal way of representing uncertainty in continuous space, using a general parametric formulation, allowing for tractable analysis and evaluation of uncertainty measures. Within this framework, we propose a set of axioms that enable rigorous assessment of total, aleatoric, and epistemic uncertainty measures. Together, this allows for a theoretical examination of uncertainty measures and their corresponding properties. As a specific example, we compare the widely used entropy- and variance-based measures with respect to established predictive models and analyze their limitations and challenges in uncertainty quantification. Our work provides a principled way to understand and develop uncertainty measures in supervised regression, offering theoretical insights and practical guidelines for reliable uncertainty assessment.

In the era of information explosion, efficiently leveraging large-scale unlabeled data while minimizing the reliance on high-quality pixel-level annotations remains a critical challenge in the field of medical imaging. Semi-supervised learning (SSL) enhances the utilization of unlabeled data by facilitating knowledge transfer, significantly improving the performance of fully supervised models and emerging as a highly promising research direction in medical image analysis. Inspired by the ability of Vision Foundation Models (e.g., SAM-2) to provide rich prior knowledge, we propose SSS (Semi-Supervised SAM-2), a novel approach that leverages SAM-2's robust feature extraction capabilities to uncover latent knowledge in unlabeled medical images, thus effectively enhancing feature support for fully supervised medical image segmentation. Specifically, building upon the single-stream "weak-to-strong" consistency regularization framework, this paper introduces a Discriminative Feature Enhancement (DFE) mechanism to further explore the feature discrepancies introduced by various data augmentation strategies across multiple views. By leveraging feature similarity and dissimilarity across multi-scale augmentation techniques, the method reconstructs and models the features, thereby effectively optimizing the salient regions. Furthermore, a prompt generator is developed that integrates Physical Constraints with a Sliding Window (PCSW) mechanism to generate input prompts for unlabeled data, fulfilling SAM-2's requirement for additional prompts. Extensive experiments demonstrate the superiority of the proposed method for semi-supervised medical image segmentation on two multi-label datasets, i.e., ACDC and BHSD. Notably, SSS achieves an average Dice score of 53.15 on BHSD, surpassing the previous state-of-the-art method by +3.65 Dice. Code will be available at https://github.com/AIGeeksGroup/SSS.