This paper studies Ebert's hat problem for three and four players and two colors, where the probabilities of the colors may be different for each player. Our goal is to maximize the probability of winning the game and to describe winning strategies We use the concept of an adequate set. The construction of adequate sets is independent of underlying probabilities and we can use this fact in the analysis of our general case.
To fully understand the 3D context of a single image, a visual system must be able to segment both the visible and occluded regions of objects, while discerning their occlusion order. Ideally, the system should be able to handle any object and not be restricted to segmenting a limited set of object classes, especially in robotic applications. Addressing this need, we introduce a diffusion model with cumulative occlusion learning designed for sequential amodal segmentation of objects with uncertain categories. This model iteratively refines the prediction using the cumulative mask strategy during diffusion, effectively capturing the uncertainty of invisible regions and adeptly reproducing the complex distribution of shapes and occlusion orders of occluded objects. It is akin to the human capability for amodal perception, i.e., to decipher the spatial ordering among objects and accurately predict complete contours for occluded objects in densely layered visual scenes. Experimental results across three amodal datasets show that our method outperforms established baselines.
We introduce Probabilistic Regular Expressions (PRE), a probabilistic analogue of regular expressions denoting probabilistic languages in which every word is assigned a probability of being generated. We present and prove the completeness of an inference system for reasoning about probabilistic language equivalence of PRE based on Salomaa's axiomatisation of Kleene Algebra.
Pearson's correlation coefficient is a popular statistical measure to summarize the strength of association between two continuous variables. It is usually interpreted via its square as percentage of variance of one variable predicted by the other in a linear regression model. It can be generalized for multiple regression via the coefficient of determination, which is not straightforward to interpret in terms of prediction accuracy. In this paper, we propose to assess the prediction accuracy of a linear model via the prediction interval reduction (PIR) by comparing the width of the prediction interval derived from this model with the width of the prediction interval obtained without this model. At the population level, PIR is one-to-one related to the correlation and the coefficient of determination. In particular, a correlation of 0.5 corresponds to a PIR of only 13%. It is also the one's complement of the coefficient of alienation introduced at the beginning of last century. We argue that PIR is easily interpretable and useful to keep in mind how difficult it is to make accurate individual predictions, an important message in the era of precision medicine and artificial intelligence. Different estimates of PIR are compared in the context of a linear model and an extension of the PIR concept to non-linear models is outlined.
In Gaussian graphical model selection, noise-corrupted samples present significant challenges. It is known that even minimal amounts of noise can obscure the underlying structure, leading to fundamental identifiability issues. A recent line of work addressing this "robust model selection" problem narrows its focus to tree-structured graphical models. Even within this specific class of models, exact structure recovery is shown to be impossible. However, several algorithms have been developed that are known to provably recover the underlying tree-structure up to an (unavoidable) equivalence class. In this paper, we extend these results beyond tree-structured graphs. We first characterize the equivalence class up to which general graphs can be recovered in the presence of noise. Despite the inherent ambiguity (which we prove is unavoidable), the structure that can be recovered reveals local clustering information and global connectivity patterns in the underlying model. Such information is useful in a range of real-world problems, including power grids, social networks, protein-protein interactions, and neural structures. We then propose an algorithm which provably recovers the underlying graph up to the identified ambiguity. We further provide finite sample guarantees in the high-dimensional regime for our algorithm and validate our results through numerical simulations.
Entity disambiguation (ED), which links the mentions of ambiguous entities to their referent entities in a knowledge base, serves as a core component in entity linking (EL). Existing generative approaches demonstrate improved accuracy compared to classification approaches under the standardized ZELDA benchmark. Nevertheless, generative approaches suffer from the need for large-scale pre-training and inefficient generation. Most importantly, entity descriptions, which could contain crucial information to distinguish similar entities from each other, are often overlooked. We propose an encoder-decoder model to disambiguate entities with more detailed entity descriptions. Given text and candidate entities, the encoder learns interactions between the text and each candidate entity, producing representations for each entity candidate. The decoder then fuses the representations of entity candidates together and selects the correct entity. Our experiments, conducted on various entity disambiguation benchmarks, demonstrate the strong and robust performance of this model, particularly +1.5% in the ZELDA benchmark compared with GENRE. Furthermore, we integrate this approach into the retrieval/reader framework and observe +1.5% improvements in end-to-end entity linking in the GERBIL benchmark compared with EntQA.
With the rapid expansion of academic literature and the proliferation of preprints, researchers face growing challenges in manually organizing and labeling large volumes of articles. The NSLP 2024 FoRC Shared Task I addresses this challenge organized as a competition. The goal is to develop a classifier capable of predicting one of 123 predefined classes from the Open Research Knowledge Graph (ORKG) taxonomy of research fields for a given article.This paper presents our results. Initially, we enrich the dataset (containing English scholarly articles sourced from ORKG and arXiv), then leverage different pre-trained language Models (PLMs), specifically BERT, and explore their efficacy in transfer learning for this downstream task. Our experiments encompass feature-based and fine-tuned transfer learning approaches using diverse PLMs, optimized for scientific tasks, including SciBERT, SciNCL, and SPECTER2. We conduct hyperparameter tuning and investigate the impact of data augmentation from bibliographic databases such as OpenAlex, Semantic Scholar, and Crossref. Our results demonstrate that fine-tuning pre-trained models substantially enhances classification performance, with SPECTER2 emerging as the most accurate model. Moreover, enriching the dataset with additional metadata improves classification outcomes significantly, especially when integrating information from S2AG, OpenAlex and Crossref. Our best-performing approach achieves a weighted F1-score of 0.7415. Overall, our study contributes to the advancement of reliable automated systems for scholarly publication categorization, offering a potential solution to the laborious manual curation process, thereby facilitating researchers in efficiently locating relevant resources.
With the rapid development of deep learning, training Big Models (BMs) for multiple downstream tasks becomes a popular paradigm. Researchers have achieved various outcomes in the construction of BMs and the BM application in many fields. At present, there is a lack of research work that sorts out the overall progress of BMs and guides the follow-up research. In this paper, we cover not only the BM technologies themselves but also the prerequisites for BM training and applications with BMs, dividing the BM review into four parts: Resource, Models, Key Technologies and Application. We introduce 16 specific BM-related topics in those four parts, they are Data, Knowledge, Computing System, Parallel Training System, Language Model, Vision Model, Multi-modal Model, Theory&Interpretability, Commonsense Reasoning, Reliability&Security, Governance, Evaluation, Machine Translation, Text Generation, Dialogue and Protein Research. In each topic, we summarize clearly the current studies and propose some future research directions. At the end of this paper, we conclude the further development of BMs in a more general view.
Graph Convolutional Network (GCN) has achieved extraordinary success in learning effective task-specific representations of nodes in graphs. However, regarding Heterogeneous Information Network (HIN), existing HIN-oriented GCN methods still suffer from two deficiencies: (1) they cannot flexibly explore all possible meta-paths and extract the most useful ones for a target object, which hinders both effectiveness and interpretability; (2) they often need to generate intermediate meta-path based dense graphs, which leads to high computational complexity. To address the above issues, we propose an interpretable and efficient Heterogeneous Graph Convolutional Network (ie-HGCN) to learn the representations of objects in HINs. It is designed as a hierarchical aggregation architecture, i.e., object-level aggregation first, followed by type-level aggregation. The novel architecture can automatically extract useful meta-paths for each object from all possible meta-paths (within a length limit), which brings good model interpretability. It can also reduce the computational cost by avoiding intermediate HIN transformation and neighborhood attention. We provide theoretical analysis about the proposed ie-HGCN in terms of evaluating the usefulness of all possible meta-paths, its connection to the spectral graph convolution on HINs, and its quasi-linear time complexity. Extensive experiments on three real network datasets demonstrate the superiority of ie-HGCN over the state-of-the-art methods.
Contextual embeddings, such as ELMo and BERT, move beyond global word representations like Word2Vec and achieve ground-breaking performance on a wide range of natural language processing tasks. Contextual embeddings assign each word a representation based on its context, thereby capturing uses of words across varied contexts and encoding knowledge that transfers across languages. In this survey, we review existing contextual embedding models, cross-lingual polyglot pre-training, the application of contextual embeddings in downstream tasks, model compression, and model analyses.
Automatic KB completion for commonsense knowledge graphs (e.g., ATOMIC and ConceptNet) poses unique challenges compared to the much studied conventional knowledge bases (e.g., Freebase). Commonsense knowledge graphs use free-form text to represent nodes, resulting in orders of magnitude more nodes compared to conventional KBs (18x more nodes in ATOMIC compared to Freebase (FB15K-237)). Importantly, this implies significantly sparser graph structures - a major challenge for existing KB completion methods that assume densely connected graphs over a relatively smaller set of nodes. In this paper, we present novel KB completion models that can address these challenges by exploiting the structural and semantic context of nodes. Specifically, we investigate two key ideas: (1) learning from local graph structure, using graph convolutional networks and automatic graph densification and (2) transfer learning from pre-trained language models to knowledge graphs for enhanced contextual representation of knowledge. We describe our method to incorporate information from both these sources in a joint model and provide the first empirical results for KB completion on ATOMIC and evaluation with ranking metrics on ConceptNet. Our results demonstrate the effectiveness of language model representations in boosting link prediction performance and the advantages of learning from local graph structure (+1.5 points in MRR for ConceptNet) when training on subgraphs for computational efficiency. Further analysis on model predictions shines light on the types of commonsense knowledge that language models capture well.