Diffusion models are increasingly used as powerful conditional generators, yet real deployments often involve multiple target distributions arising from different tasks, e.g., diverse prompt domains in text-to-image generation, or multiple environments in robotics with diffusion policies. This naturally leads to a multi-objective learning (MOL) problem. A key challenge is that achieving good Pareto trade-offs can require a generalist model class with substantially larger capacity than what suffices for solving any individual task, thereby increasing statistical cost since sample complexity typically scales with the model complexity. To reconcile this, we develop a principled MOL framework for diffusion models with limited data: a semi-supervised regime where paired (labeled) samples are scarce, but (unlabeled) condition data are abundant. We propose a two-stage training procedure that first fits lightweight specialist models from limited paired data, and then distills them into a generalist model by generating pseudo-samples. We establish generalization bounds showing that the required number of paired samples only depends on the complexity of the specialist model classes. We further extend the theory to diffusion policies for sequential decision making to account for distribution shift in on-policy rollouts. Extensive experiments on robotic control and image restoration tasks are conducted to verify our theoretical results.

In many prediction problems, we have extra information during training (for example, measurements that are expensive or slow to collect) that will not be available when the model is deployed. A common strategy is to first train a model that uses all training information, then use its predictions on unlabeled examples to train a second model that only uses the inputs available at test time. However, when the extra training-only information is weak or noisy, this Two-Stage approach can mislead the deployment model and even hurt accuracy. We propose a joint training method that learns the two models together, so the deployment model can benefit from the extra information only when it actually helps, instead of inheriting its mistakes. We provide guarantees that describe when joint training improves prediction accuracy and analyze a simple alternating training algorithm for large, high-dimensional models. Experiments on synthetic data and real-world prediction tasks show that our approach avoids these failures and robustly outperforms standard Two-Stage baselines.

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.

Regionalization aims to partition a spatial domain into contiguous regions that share similar characteristics, enabling more effective spatial analysis, policy making, and resource management. Existing approaches for spatial regionalization typically rely on static spatial snapshots rather than evolving time series. Meanwhile, most time series clustering methods ignore spatial structure or enforce spatial continuity through ad hoc regularization, constraining the number of inferred regions a priori either explicitly or implicitly. Utilizing the minimum description length principle from information theory, here we propose an efficient and fully nonparametric framework for the regionalization of spatial time series. Our method jointly infers a spatial partition along with a set of representative time series archetypes ("drivers") that best compress a spatiotemporal dataset, with a runtime log-linear in the number of time series. We demonstrate that this method can accurately recover planted regional structure and drivers in synthetic time series, and can extract meaningful structural regularities in large-scale empirical air quality and vegetation index records. Our method provides a principled and scalable framework for spatially contiguous partitioning, allowing interpretable temporal patterns and homogeneous regions to emerge directly from the data itself.

Graph-based semi-supervised learning (GSSL) serves as a powerful tool to model the underlying manifold structures of samples in high-dimensional spaces. It involves two phases: constructing an affinity graph from available data and inferring labels for unlabeled nodes on this graph. While numerous algorithms have been developed for label inference, the crucial graph construction phase has received comparatively less attention, despite its significant influence on the subsequent phase. In this paper, we present an optimal asymmetric graph structure for the label inference phase with theoretical motivations. Unlike existing graph construction methods, we differentiate the distinct roles that labeled nodes and unlabeled nodes could play.

Learning binary classifiers from positive and unlabeled data (PUL) is vital in many real-world applications, especially when verifying negative examples is difficult. Despite the impressive empirical performance of recent PUL methods, challenges like accumulated errors and increased estimation bias persist due to the absence of negative labels. In this paper, we unveil an intriguing yet long-overlooked observation in PUL: resampling the positive data in each training iteration to ensure a balanced distribution between positive and unlabeled examples results in strong early-stage performance. Furthermore, predictive trends for positive and negative classes display distinctly different patterns. Specifically, the scores (output probability) of unlabeled negative examples consistently decrease, while those of unlabeled positive examples show largely chaotic trends. Instead of focusing on classification within individual time frames, we innovatively adopt a holistic approach, interpreting the scores of each example as a temporal point process (TPP).

Semi-supervised learning aims to leverage a large amount of unlabeled data for performance boosting. Existing works primarily focus on image classification. In this paper, we delve into semi-supervised learning for object detection, where labeled data are more labor-intensive to collect. Current methods are easily distracted by noisy regions generated by pseudo labels. To combat the noisy labeling, we propose noise-resistant semi-supervised learning by quantifying the region uncertainty. We first investigate the adverse effects brought by different forms of noise associated with pseudo labels. Then we propose to quantify the uncertainty of regions by identifying the noise-resistant properties of regions over different strengths. By importing the region uncertainty quantification and promoting multipeak probability distribution output, we introduce uncertainty into training and further achieve noise-resistant learning. Experiments on both PASCALVOC and MSCOCO demonstrate the extraordinary performance of our method.

Existing semi-supervised learning (SSL) algorithms typically assume classbalanced datasets, although the class distributions of many real-world datasets are imbalanced. In general, classifiers trained on a class-imbalanced dataset are biased toward the majority classes. This issue becomes more problematic for SSL algorithms because they utilize the biased prediction of unlabeled data for training. However, traditional class-imbalanced learning techniques, which are designed for labeled data, cannot be readily combined with SSL algorithms. We propose a scalable class-imbalanced SSL algorithm that can effectively use unlabeled data, while mitigating class imbalance by introducing an auxiliary balanced classifier (ABC) of a single layer, which is attached to a representation layer of an existing SSL algorithm. The ABC is trained with a class-balanced loss of a minibatch, while using high-quality representations learned from all data points in the minibatch using the backbone SSL algorithm to avoid overfitting and information loss. Moreover, we use consistency regularization, a recent SSL technique for utilizing unlabeled data in a modified way, to train the ABC to be balanced among the classes by selecting unlabeled data with the same probability for each class. The proposed algorithm achieves state-of-the-art performance in various class-imbalanced SSL experiments using four benchmark datasets.

All experiments were conducted on a Linux server with a Tesla P40 GPU. Our Contrastive Graph Poisson Network (CGPN) was implemented via PyTorch 1.4.0 [1]. We adopted the Adam optimizer [2] for training. The number of GAT layers was set as two. Other hyperparameters were adjusted based on the corresponding datasets. Tables 1, 2, 3, and 4 provide the details of the important hyperparameters.

Semi-supervised learning (SSL) provides a powerful framework for leveraging unlabeled data. Existing SSL typically requires all classes have labels. However, in many real-world applications, there may exist some classes that are difficult to label or newly occurred classes that cannot be labeled in time, resulting in there are unseen classes in unlabeled data. Unseen classes will be misclassified as seen classes, causing poor classification performance. The performance of seen classes is also harmed by the existence of unseen classes.