However, the log likelihood term is not analytical yet. The third view with radius 0.3 was further translated to make the points overlapping, We used 128 units as the hidden dimension. SNGP's GP layer: We followed the settings provided by its authors in their tutorial Our framework is based on GPflow [9]. The uncertainty surfaces of each view are shown in Figure 2. Implementation Details We used the same datasets of the TMC's datasets (Handwritten, CUB, In addition to the methods used in B.1, we implemented MC Dropout and DE(EF) MC Dropout: We used a dropout layer with the dropout rate of 0.2 and a fully connected During inference, 100 samples were used to make a prediction. Figure 4: Domain-shift test accuracy where Gaussian noise is added to half of the views.

Uncertainty estimation is essential to make neural networks trustworthy in real-world applications. Extensive research efforts have been made to quantify and reduce predictive uncertainty.

The relational representations relied upon by such methods, however, are abstract.

Uncertainty estimation is essential to make neural networks trustworthy in real-world applications. Extensive research efforts have been made to quantify and reduce predictive uncertainty.

Multi-view clustering (MVC) has emerged as a powerful technique for extracting valuable insights from data characterized by multiple perspectives or modalities. Despite significant advancements, existing MVC methods struggle with effectively quantifying the consistency and complementarity among views, and are particularly susceptible to the adverse effects of noisy views, known as the Noisy-View Drawback (NVD). To address these challenges, we propose CE-MVC, a novel framework that integrates an adaptive weighting algorithm with a parameter-decoupled deep model. Leveraging the concept of conditional entropy and normalized mutual information, CE-MVC quantitatively assesses and weights the informative contribution of each view, facilitating the construction of robust unified representations. The parameter-decoupled design enables independent processing of each view, effectively mitigating the influence of noise and enhancing overall clustering performance. Extensive experiments demonstrate that CE-MVC outperforms existing approaches, offering a more resilient and accurate solution for multi-view clustering tasks.

Graph Contrastive Learning (GCL) leverages data augmentation techniques to produce contrasting views, enhancing the accuracy of recommendation systems through learning the consistency between contrastive views. However, existing augmentation methods, such as directly perturbing interaction graph (e.g., node/edge dropout), may interfere with the original connections and generate poor contrasting views, resulting in sub-optimal performance. In this paper, we define the views that share only a small amount of information with the original graph due to poor data augmentation as noisy views (i.e., the last 20% of the views with a cosine similarity value less than 0.1 to the original view). We demonstrate through detailed experiments that noisy views will significantly degrade recommendation performance. Further, we propose a model-agnostic Symmetric Graph Contrastive Learning (SGCL) method with theoretical guarantees to address this issue. Specifically, we introduce symmetry theory into graph contrastive learning, based on which we propose a symmetric form and contrast loss resistant to noisy interference. We provide theoretical proof that our proposed SGCL method has a high tolerance to noisy views. Further demonstration is given by conducting extensive experiments on three real-world datasets. The experimental results demonstrate that our approach substantially increases recommendation accuracy, with relative improvements reaching as high as 12.25% over nine other competing models. These results highlight the efficacy of our method.

Multi-view clustering (MVC) aims at exploring category structures among multi-view data in self-supervised manners. Multiple views provide more information than single views and thus existing MVC methods can achieve satisfactory performance. However, their performance might seriously degenerate when the views are noisy in practical multi-view scenarios. In this paper, we first formally investigate the drawback of noisy views and then propose a theoretically grounded deep MVC method (namely MVCAN) to address this issue. Specifically, we propose a novel MVC objective that enables un-shared parameters and inconsistent clustering predictions across multiple views to reduce the side effects of noisy views. Furthermore, a two-level multi-view iterative optimization is designed to generate robust learning targets for refining individual views' representation learning. Theoretical analysis reveals that MVCAN works by achieving the multi-view consistency, complementarity, and noise robustness. Finally, experiments on extensive public datasets demonstrate that MVCAN outperforms state-of-the-art methods and is robust against the existence of noisy views.

Recent advances in fine-grained representation learning leverage local-to-global (emergent) relationships for achieving state-of-the-art results. The relational representations relied upon by such methods, however, are abstract. We aim to deconstruct this abstraction by expressing them as interpretable graphs over image views. We begin by theoretically showing that abstract relational representations are nothing but a way of recovering transitive relationships among local views. Based on this, we design Transitivity Recovering Decompositions (TRD), a graph-space search algorithm that identifies interpretable equivalents of abstract emergent relationships at both instance and class levels, and with no post-hoc computations. We additionally show that TRD is provably robust to noisy views, with empirical evidence also supporting this finding. The latter allows TRD to perform at par or even better than the state-of-the-art, while being fully interpretable. Implementation is available at https://github.com/abhrac/trd.