We propose a summation analog of the paradigm of parallel integration. Using this paradigm, we make some first steps towards an indefinite summation algorithm applicable to summands that rationally depend on the summation index and a P-recursive sequence and its shifts. Under the assumption that the corresponding difference field has no unnatural constants, we are able to compute a bound on the normal part of the denominator of a potential closed form. We can also handle the numerator. Our algorithm is incomplete so far as we cannot predict the special part of the denominator. However, we do have some structural results about special polynomials for the setting under consideration.
The concept of causality plays an important role in human cognition . In the past few decades, causal inference has been well developed in many fields, such as computer science, medicine, economics, and education. With the advancement of deep learning techniques, it has been increasingly used in causal inference against counterfactual data. Typically, deep causal models map the characteristics of covariates to a representation space and then design various objective optimization functions to estimate counterfactual data unbiasedly based on the different optimization methods. This paper focuses on the survey of the deep causal models, and its core contributions are as follows: 1) we provide relevant metrics under multiple treatments and continuous-dose treatment; 2) we incorporate a comprehensive overview of deep causal models from both temporal development and method classification perspectives; 3) we assist a detailed and comprehensive classification and analysis of relevant datasets and source code.
This manuscript portrays optimization as a process. In many practical applications the environment is so complex that it is infeasible to lay out a comprehensive theoretical model and use classical algorithmic theory and mathematical optimization. It is necessary as well as beneficial to take a robust approach, by applying an optimization method that learns as one goes along, learning from experience as more aspects of the problem are observed. This view of optimization as a process has become prominent in varied fields and has led to some spectacular success in modeling and systems that are now part of our daily lives.
In the era of deep learning, modeling for most NLP tasks has converged to several mainstream paradigms. For example, we usually adopt the sequence labeling paradigm to solve a bundle of tasks such as POS-tagging, NER, Chunking, and adopt the classification paradigm to solve tasks like sentiment analysis. With the rapid progress of pre-trained language models, recent years have observed a rising trend of Paradigm Shift, which is solving one NLP task by reformulating it as another one. Paradigm shift has achieved great success on many tasks, becoming a promising way to improve model performance. Moreover, some of these paradigms have shown great potential to unify a large number of NLP tasks, making it possible to build a single model to handle diverse tasks. In this paper, we review such phenomenon of paradigm shifts in recent years, highlighting several paradigms that have the potential to solve different NLP tasks.
Recently, a considerable literature has grown up around the theme of Graph Convolutional Network (GCN). How to effectively leverage the rich structural information in complex graphs, such as knowledge graphs with heterogeneous types of entities and relations, is a primary open challenge in the field. Most GCN methods are either restricted to graphs with a homogeneous type of edges (e.g., citation links only), or focusing on representation learning for nodes only instead of jointly propagating and updating the embeddings of both nodes and edges for target-driven objectives. This paper addresses these limitations by proposing a novel framework, namely the Knowledge Embedding based Graph Convolutional Network (KE-GCN), which combines the power of GCNs in graph-based belief propagation and the strengths of advanced knowledge embedding (a.k.a. knowledge graph embedding) methods, and goes beyond. Our theoretical analysis shows that KE-GCN offers an elegant unification of several well-known GCN methods as specific cases, with a new perspective of graph convolution. Experimental results on benchmark datasets show the advantageous performance of KE-GCN over strong baseline methods in the tasks of knowledge graph alignment and entity classification.
Data augmentation has been widely used to improve generalizability of machine learning models. However, comparatively little work studies data augmentation for graphs. This is largely due to the complex, non-Euclidean structure of graphs, which limits possible manipulation operations. Augmentation operations commonly used in vision and language have no analogs for graphs. Our work studies graph data augmentation for graph neural networks (GNNs) in the context of improving semi-supervised node-classification. We discuss practical and theoretical motivations, considerations and strategies for graph data augmentation. Our work shows that neural edge predictors can effectively encode class-homophilic structure to promote intra-class edges and demote inter-class edges in given graph structure, and our main contribution introduces the GAug graph data augmentation framework, which leverages these insights to improve performance in GNN-based node classification via edge prediction. Extensive experiments on multiple benchmarks show that augmentation via GAug improves performance across GNN architectures and datasets.
In this paper, we present an accurate and scalable approach to the face clustering task. We aim at grouping a set of faces by their potential identities. We formulate this task as a link prediction problem: a link exists between two faces if they are of the same identity. The key idea is that we find the local context in the feature space around an instance (face) contains rich information about the linkage relationship between this instance and its neighbors. By constructing sub-graphs around each instance as input data, which depict the local context, we utilize the graph convolution network (GCN) to perform reasoning and infer the likelihood of linkage between pairs in the sub-graphs. Experiments show that our method is more robust to the complex distribution of faces than conventional methods, yielding favorably comparable results to state-of-the-art methods on standard face clustering benchmarks, and is scalable to large datasets. Furthermore, we show that the proposed method does not need the number of clusters as prior, is aware of noises and outliers, and can be extended to a multi-view version for more accurate clustering accuracy.
Embedding models for deterministic Knowledge Graphs (KG) have been extensively studied, with the purpose of capturing latent semantic relations between entities and incorporating the structured knowledge into machine learning. However, there are many KGs that model uncertain knowledge, which typically model the inherent uncertainty of relations facts with a confidence score, and embedding such uncertain knowledge represents an unresolved challenge. The capturing of uncertain knowledge will benefit many knowledge-driven applications such as question answering and semantic search by providing more natural characterization of the knowledge. In this paper, we propose a novel uncertain KG embedding model UKGE, which aims to preserve both structural and uncertainty information of relation facts in the embedding space. Unlike previous models that characterize relation facts with binary classification techniques, UKGE learns embeddings according to the confidence scores of uncertain relation facts. To further enhance the precision of UKGE, we also introduce probabilistic soft logic to infer confidence scores for unseen relation facts during training. We propose and evaluate two variants of UKGE based on different learning objectives. Experiments are conducted on three real-world uncertain KGs via three tasks, i.e. confidence prediction, relation fact ranking, and relation fact classification. UKGE shows effectiveness in capturing uncertain knowledge by achieving promising results on these tasks, and consistently outperforms baselines on these tasks.
We study the problem of textual relation embedding with distant supervision. To combat the wrong labeling problem of distant supervision, we propose to embed textual relations with global statistics of relations, i.e., the co-occurrence statistics of textual and knowledge base relations collected from the entire corpus. This approach turns out to be more robust to the training noise introduced by distant supervision. On a popular relation extraction dataset, we show that the learned textual relation embedding can be used to augment existing relation extraction models and significantly improve their performance. Most remarkably, for the top 1,000 relational facts discovered by the best existing model, the precision can be improved from 83.9% to 89.3%.
Link prediction for knowledge graphs is the task of predicting missing relationships between entities. Previous work on link prediction has focused on shallow, fast models which can scale to large knowledge graphs. However, these models learn less expressive features than deep, multi-layer models -- which potentially limits performance. In this work, we introduce ConvE, a multi-layer convolutional network model for link prediction, and report state-of-the-art results for several established datasets. We also show that the model is highly parameter efficient, yielding the same performance as DistMult and R-GCN with 8x and 17x fewer parameters. Analysis of our model suggests that it is particularly effective at modelling nodes with high indegree -- which are common in highly-connected, complex knowledge graphs such as Freebase and YAGO3. In addition, it has been noted that the WN18 and FB15k datasets suffer from test set leakage, due to inverse relations from the training set being present in the test set -- however, the extent of this issue has so far not been quantified. We find this problem to be severe: a simple rule-based model can achieve state-of-the-art results on both WN18 and FB15k. To ensure that models are evaluated on datasets where simply exploiting inverse relations cannot yield competitive results, we investigate and validate several commonly used datasets -- deriving robust variants where necessary. We then perform experiments on these robust datasets for our own and several previously proposed models, and find that ConvE achieves state-of-the-art Mean Reciprocal Rank across all datasets.
In this paper, we propose a conceptually simple and geometrically interpretable objective function, i.e. additive margin Softmax (AM-Softmax), for deep face verification. In general, the face verification task can be viewed as a metric learning problem, so learning large-margin face features whose intra-class variation is small and inter-class difference is large is of great importance in order to achieve good performance. Recently, Large-margin Softmax and Angular Softmax have been proposed to incorporate the angular margin in a multiplicative manner. In this work, we introduce a novel additive angular margin for the Softmax loss, which is intuitively appealing and more interpretable than the existing works. We also emphasize and discuss the importance of feature normalization in the paper. Most importantly, our experiments on LFW BLUFR and MegaFace show that our additive margin softmax loss consistently performs better than the current state-of-the-art methods using the same network architecture and training dataset. Our code has also been made available at //github.com/happynear/AMSoftmax