The main result is presented in Theorem 2. According to the definition of the Fiedler vector, we have ( L + L)( f + f) = ( λ + λ)( f + f). We outline the proof below for interested readers. The main result is presented in Theorem 2. We first present Stewart's theorem in Lemma 1 to assist Actual times may differ depending on hardware and environment. We also show the number of model parameters required for each method in Table S3. Hyper-parameters were selected based on a coarse search on the validation set.

Contrastive learning methods can be applied to deep regression by enforcing label distance relationships in feature space. However, these methods are limited to labeled data only unlike for classification, where unlabeled data can be used for contrastive pretraining. In this work, we extend contrastive regression methods to allow unlabeled data to be used in a semi-supervised setting, thereby reducing the reliance on manual annotations. We observe that the feature similarity matrix between unlabeled samples still reflect inter-sample relationships, and that an accurate ordinal relationship can be recovered through spectral seriation algorithms if the level of error is within certain bounds. By using the recovered ordinal relationship for contrastive learning on unlabeled samples, we can allow more data to be used for feature representation learning, thereby achieve more robust results. The ordinal rankings can also be used to supervise predictions on unlabeled samples, which can serve as an additional training signal. We provide theoretical guarantees and empirical support through experiments on different datasets, demonstrating that our method can surpass existing state-of-the-art semi-supervised deep regression methods. To the best of our knowledge, this work is the first to explore using unlabeled data to perform contrastive learning for regression.

Virtual Screening is an essential technique in the early phases of drug discovery, aimed at identifying promising drug candidates from vast molecular libraries. Recently, ligand-based virtual screening has garnered significant attention due to its efficacy in conducting extensive database screenings without relying on specific protein-binding site information.Obtaining binding affinity data for complexes is highly expensive, resulting in a limited amount of available data that covers a relatively small chemical space. Moreover, these datasets contain a significant amount of inconsistent noise. It is challenging to identify an inductive bias that consistently maintains the integrity of molecular activity during data augmentation. To tackle these challenges, we propose S-MolSearch, the first framework to our knowledge, that leverages molecular 3D information and affinity information in semi-supervised contrastive learning for ligand-based virtual screening.

Contrastive learning methods can be applied to deep regression by enforcing label distance relationships in feature space. However, these methods are limited to labeled data only unlike for classification, where unlabeled data can be used for contrastive pretraining. In this work, we extend contrastive regression methods to allow unlabeled data to be used in a semi-supervised setting, thereby reducing the reliance on manual annotations. We observe that the feature similarity matrix between unlabeled samples still reflect inter-sample relationships, and that an accurate ordinal relationship can be recovered through spectral seriation algorithms if the level of error is within certain bounds. By using the recovered ordinal relationship for contrastive learning on unlabeled samples, we can allow more data to be used for feature representation learning, thereby achieve more robust results.

Early detection of relevant locations in a piece of news is especially important in extreme events such as environmental disasters, war conflicts, disease outbreaks, or political turmoils. Additionally, this detection also helps recommender systems to promote relevant news based on user locations. Note that, when the relevant locations are not mentioned explicitly in the text, state-of-the-art methods typically fail to recognize them because these methods rely on syntactic recognition. In contrast, by incorporating a knowledge base and connecting entities with their locations, our system successfully infers the relevant locations even when they are not mentioned explicitly in the text. To evaluate the effectiveness of our approach, and due to the lack of datasets in this area, we also contribute to the research community with a gold-standard multilingual news-location dataset, NewsLOC. It contains the annotation of the relevant locations (and their WikiData IDs) of 600+ Wikinews articles in five different languages: English, French, German, Italian, and Spanish. Through experimental evaluations, we show that our proposed system outperforms the baselines and the fine-tuned version of the model using semi-supervised data that increases the classification rate. The source code and the NewsLOC dataset are publicly available for being used by the research community at https://github.com/vsuarezpaniagua/NewsLocation.