Graph representation learning has been extensively studied in recent years. Despite its potential in generating continuous embeddings for various networks, both the effectiveness and efficiency to infer high-quality representations toward large corpus of nodes are still challenging. Sampling is a critical point to achieve the performance goals. Prior arts usually focus on sampling positive node pairs, while the strategy for negative sampling is left insufficiently explored. To bridge the gap, we systematically analyze the role of negative sampling from the perspectives of both objective and risk, theoretically demonstrating that negative sampling is as important as positive sampling in determining the optimization objective and the resulted variance. To the best of our knowledge, we are the first to derive the theory and quantify that the negative sampling distribution should be positively but sub-linearly correlated to their positive sampling distribution. With the guidance of the theory, we propose MCNS, approximating the positive distribution with self-contrast approximation and accelerating negative sampling by Metropolis-Hastings. We evaluate our method on 5 datasets that cover extensive downstream graph learning tasks, including link prediction, node classification and personalized recommendation, on a total of 19 experimental settings. These relatively comprehensive experimental results demonstrate its robustness and superiorities.
The objective of unsupervised graph representation learning (GRL) is to learn a low-dimensional space of node embeddings that reflect the structure of a given unlabeled graph. Existing algorithms for this task rely on negative sampling objectives that maximize the similarity in node embeddings at nearby nodes (referred to as "cohesion") by maintaining positive and negative corpus of node pairs. While positive samples are drawn from node pairs that co-occur in short random walks, conventional approaches construct negative corpus by uniformly sampling random pairs, thus ignoring valuable informa…
Tokyo Institute of Technology（东京工业大学）；Gunma University（群马大学）；RIKEN AIP（理化学研究所先进智能项目中心）
In knowledge graph embedding, the theoretical relationship between the softmax cross-entropy and negative sampling loss functions has not been investigated. This makes it difficult to fairly compare the results of the two different loss functions. We attempted to solve this problem by using the Bregman divergence to provide a unified interpretation of the softmax cross-entropy and negative sampling loss functions. Under this interpretation, we can derive theoretical findings for fair comparison. Experimental results on the FB15k-237 and WN18RR datasets show that the theoretical findings are va…
Knowledge graph (KG) embedding is widely used in many downstream applications using KGs. Generally, since KGs contain only ground truth triples, it is necessary to construct arbitrary negative samples for representation learning of KGs. Recently, various methods for sampling high-quality negatives have been studied because the quality of negative triples has great effect on KG embedding. In this paper, we propose a novel method called Entity Aware Negative Sampling (EANS), which is able to sample negative entities resemble to positive one by adopting Gaussian distribution to the aligned entity…
Knowledge graphs (KGs) are typically incomplete and we often wish to infer new facts given the existing ones. This can be thought of as a binary classification problem; we aim to predict if new facts are true or false. Unfortunately, we generally only have positive examples (the known facts) but we also need negative ones to train a classifier. To resolve this, it is usual to generate negative examples using a negative sampling strategy. However, this can produce false negatives which may reduce performance, is computationally expensive, and does not produce calibrated classification probabili…
Paradigm Inc.（第四范式公司）；Tsinghua University（清华大学）；Hong Kong University of Science and Technology（香港科技大学）
Negative sampling, which samples negative triplets from non-observed ones in knowledge graph (KG), is an essential step in KG embedding. Recently, generative adversarial network (GAN), has been introduced in negative sampling. By sampling negative triplets with large gradients, these methods avoid the problem of vanishing gradient and thus obtain better performance. However, they make the original model more complex and harder to train. In this paper, motivated by the observation that negative triplets with large gradients are important but rare, we propose to directly keep track of them with …
Layer-diverse Negative Sampling for Graph Neural Networks
Australian Artificial Intelligence Institute（澳大利亚人工智能研究所）；University of Technology Sydney（悉尼科技大学）；Institute of Natural Sciences（自然科学研究所）；School of Mathematical Sciences（数学科学学院）；Shanghai Jiao Tong University（上海交通大学）
The Hong Kong University of Science and Technology（香港科技大学）；Paradigm Inc.（第四范式有限公司）；Beijing University of Posts and Telecommunications（北京邮电大学）
Knowledge Graph (KG) embedding is a fundamental problem in data mining research with many real-world applications. It aims to encode the entities and relations in the graph into low dimensional vector space, which can be used for subsequent algorithms. Negative sampling, which samples negative triplets from non-observed ones in the training data, is an important step in KG embedding. Recently, generative adversarial network (GAN), has been introduced in negative sampling. By sampling negative triplets with large scores, these methods avoid the problem of vanishing gradient and thus obtain bett…
University of Bonn（波恩大学）；BMW Group（宝马集团）；Nature-Inspired Machine Intelligence-InfAI（自然启发机器智能-InfAI研究院）
Knowledge Graph Embedding models have become an important area of machine learning.Those models provide a latent representation of entities and relations in a knowledge graph which can then be used in downstream machine learning tasks such as link prediction. The learning process of such models can be performed by contrasting positive and negative triples. While all triples of a KG are considered positive, negative triples are usually not readily available. Therefore, the choice of the sampling method to obtain the negative triples play a crucial role in the performance and effectiveness of Kn…
Nara Institute of Science and Technology (NAIST)（奈良先端科学技术大学院大学）；Hokkaido University（北海道大学）
Negative sampling (NS) loss plays an important role in learning knowledge graph embedding (KGE) to handle a huge number of entities. However, the performance of KGE degrades without hyperparameters such as the margin term and number of negative samples in NS loss being appropriately selected. Currently, empirical hyperparameter tuning addresses this problem at the cost of computational time. To solve this problem, we theoretically analyzed NS loss to assist hyperparameter tuning and understand the better use of the NS loss in KGE learning. Our theoretical analysis showed that scoring methods w…
IBM Almaden Research Center（IBM阿尔马登研究中心）；IBM Thomas J. Watson Research Center（IBM托马斯·J·沃森研究中心）
This paper describes an end-to-end solution for the relationship prediction task in heterogeneous, multi-relational graphs. We particularly address two building blocks in the pipeline, namely heterogeneous graph representation learning and negative sampling. Existing message passing-based graph neural networks use edges either for graph traversal and/or selection of message encoding functions. Ignoring the edge semantics could have severe repercussions on the quality of embeddings, especially when dealing with two nodes having multiple relations. Furthermore, the expressivity of the learned re…
Rice University（莱斯大学）；University of Texas at Austin（德克萨斯大学奥斯汀分校）
We introduce Negative Sampling in Semi-Supervised Learning (NS3L), a simple, fast, easy to tune algorithm for semi-supervised learning (SSL). NS3L is motivated by the success of negative sampling/contrastive estimation. We demonstrate that adding the NS3L loss to state-of-the-art SSL algorithms, such as the Virtual Adversarial Training (VAT), significantly improves upon vanilla VAT and its variant, VAT with Entropy Minimization. By adding the NS3L loss to MixMatch, the current state-of-the-art approach on semi-supervised tasks, we observe significant improvements over vanilla MixMatch. We cond…
State-of-the-art approaches for Knowledge Base Completion (KBC) exploit deep neural networks trained with both false and true assertions: positive assertions are explicitly taken from the knowledge base, whereas negative ones are generated by random sampling of entities. In this paper, we argue that random sampling is not a good training strategy since it is highly likely to generate a huge number of nonsensical assertions during training, which does not provide relevant training signal to the system. Hence, it slows down the learning process and decreases accuracy. To address this issue, we p…
McGill University（麦吉尔大学）；Montreal Institute of Learning Algorithms (Mila)（蒙特利尔学习算法研究所（米拉））
Learning low-dimensional representations for entities and relations in knowledge graphs using contrastive estimation represents a scalable and effective method for inferring connectivity patterns. A crucial aspect of contrastive learning approaches is the choice of corruption distribution that generates hard negative samples, which force the embedding model to learn discriminative representations and find critical characteristics of observed data. While earlier methods either employ too simple corruption distributions, i.e. uniform, yielding easy uninformative negatives or sophisticated advers…
In recent years, the Word2Vec model trained with the Negative Sampling loss function has shown state-of-the-art results in a number of machine learning tasks, including language modeling tasks, such as word analogy and word similarity, and in recommendation tasks, through Prod2Vec, an extension that applies to modeling user shopping activity and user preferences. Several methods that aim to improve upon the standard Negative Sampling loss have been proposed. In our paper we pursue more sophisticated Negative Sampling, by leveraging ideas from the field of Generative Adversarial Networks (GANs)…
The problem of matching two sets of multiple elements, namely set-to-set matching, has received a great deal of attention in recent years. In particular, it has been reported that good experimental results can be obtained by preparing a neural network as a matching function, especially in complex cases where, for example, each element of the set is an image. However, theoretical analysis of set-to-set matching with such black-box functions is lacking. This paper aims to perform a generalization error analysis in set-to-set matching to reveal the behavior of the model in that task.
How can you sample good negative examples for contrastive learning? We argue that, as with metric learning, contrastive learning of representations benefits from hard negative samples (i.e., points that are difficult to distinguish from an anchor point). The key challenge toward using hard negatives is that contrastive methods must remain unsupervised, making it infeasible to adopt existing negative sampling strategies that use true similarity information. In response, we develop a new family of unsupervised sampling methods for selecting hard negative samples where the user can control the ha…
Huazhong University of Science and Technology (HUST)（华中科技大学）
How to sample high quality negative instances from unlabeled data, i.e., negative sampling, is important for training implicit collaborative filtering and contrastive learning models. Although previous studies have proposed some approaches to sample informative instances, few has been done to discriminating false negative from true negative for unbiased negative sampling. On the basis of our order relation analysis of negatives' scores, we first derive the class conditional density of true negatives and that of false negatives. We next design a Bayesian classifier for negative classification, …
Recent methods for learning unsupervised visual representations, dubbed contrastive learning, optimize the noise-contrastive estimation (NCE) bound on mutual information between two views of an image. NCE uses randomly sampled negative examples to normalize the objective. In this paper, we show that choosing difficult negatives, or those more similar to the current instance, can yield stronger representations. To do this, we introduce a family of mutual information estimators that sample negatives conditionally -- in a "ring" around each positive. We prove that these estimators lower-bound mut…
Negative sampling approaches are prevalent in implicit collaborative filtering for obtaining negative labels from massive unlabeled data. As two major concerns in negative sampling, efficiency and effectiveness are still not fully achieved by recent works that use complicate structures and overlook risk of false negative instances. In this paper, we first provide a novel understanding of negative instances by empirically observing that only a few instances are potentially important for model learning, and false negatives tend to have stable predictions over many training iterations. Above find…
University of Glagow（格拉斯哥大学）；Shanghai Jiao Tong University（上海交通大学）
Although the word-popularity based negative sampler has shown superb performance in the skip-gram model, the theoretical motivation behind oversampling popular (non-observed) words as negative samples is still not well understood. In this paper, we start from an investigation of the gradient vanishing issue in the skipgram model without a proper negative sampler. By performing an insightful analysis from the stochastic gradient descent (SGD) learning perspective, we demonstrate that, both theoretically and intuitively, negative samples with larger inner product scores are more informative than…
Alfréd Rényi Institute of Mathematics（阿尔弗雷德·雷尼数学研究所）；Eötvös Loránd University（厄特沃什·罗兰大学）
Modern deep artificial neural networks have achieved great success in the domain of computer vision and beyond. However, their application to many real-world tasks is undermined by certain limitations, such as overconfident uncertainty estimates on out-of-distribution data or performance deterioration under data distribution shifts. Several types of deep learning models used for density estimation through probabilistic generative modeling have been shown to fail to detect out-of-distribution samples by assigning higher likelihoods to anomalous data. We investigate this failure mode in Variatio…
One of the challenges in contrastive learning is the selection of appropriate \textit{hard negative} examples, in the absence of label information. Random sampling or importance sampling methods based on feature similarity often lead to sub-optimal performance. In this work, we introduce UnReMix, a hard negative sampling strategy that takes into account anchor similarity, model uncertainty and representativeness. Experimental results on several benchmarks show that UnReMix improves negative sample selection, and subsequently downstream performance when compared to state-of-the-art contrastive …
The word2vec software of Tomas Mikolov and colleagues (https://code.google.com/p/word2vec/ ) has gained a lot of traction lately, and provides state-of-the-art word embeddings. The learning models behind the software are described in two research papers. We found the description of the models in these papers to be somewhat cryptic and hard to follow. While the motivations and presentation may be obvious to the neural-networks language-modeling crowd, we had to struggle quite a bit to figure out the rationale behind the equations. This note is an attempt to explain equation (4) (negative sampli…
Institute of Information Engineering, Chinese Academy of Sciences（中国科学院信息工程研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）；Peng Cheng Laboratory（鹏城实验室）
The recently proposed Collaborative Metric Learning (CML) paradigm has aroused wide interest in the area of recommendation systems (RS) owing to its simplicity and effectiveness. Typically, the existing literature of CML depends largely on the \textit{negative sampling} strategy to alleviate the time-consuming burden of pairwise computation. However, in this work, by taking a theoretical analysis, we find that negative sampling would lead to a biased estimation of the generalization error. Specifically, we show that the sampling-based CML would introduce a bias term in the generalization bound…
Princeton University（普林斯顿大学）；University of California, Berkeley（加州大学伯克利分校）；Stanford University（斯坦福大学）
Imitation learning, followed by reinforcement learning algorithms, is a promising paradigm to solve complex control tasks sample-efficiently. However, learning from demonstrations often suffers from the covariate shift problem, which results in cascading errors of the learned policy. We introduce a notion of conservatively-extrapolated value functions, which provably lead to policies with self-correction. We design an algorithm Value Iteration with Negative Sampling (VINS) that practically learns such value functions with conservative extrapolation. We show that VINS can correct mistakes of th…
We revisit skip-gram negative sampling (SGNS), one of the most popular neural-network based approaches to learning distributed word representation. We first point out the ambiguity issue undermining the SGNS model, in the sense that the word vectors can be entirely distorted without changing the objective value. To resolve the issue, we investigate the intrinsic structures in solution that a good word embedding model should deliver. Motivated by this, we rectify the SGNS model with quadratic regularization, and show that this simple modification suffices to structure the solution in the desire…
National University of Singapore（新加坡国立大学）；Southeast University（东南大学）；University of Science and Technology of China（中国科学技术大学）；HeFei University of Technology（合肥工业大学）
Properly handling missing data is a fundamental challenge in recommendation. Most present works perform negative sampling from unobserved data to supply the training of recommender models with negative signals. Nevertheless, existing negative sampling strategies, either static or adaptive ones, are insufficient to yield high-quality negative samples --- both informative to model training and reflective of user real needs. In this work, we hypothesize that item knowledge graph (KG), which provides rich relations among items and KG entities, could be useful to infer informative and factual negat…
Softmax classifiers with a very large number of classes naturally occur in many applications such as natural language processing and information retrieval. The calculation of full softmax is costly from the computational and energy perspective. There have been various sampling approaches to overcome this challenge, popularly known as negative sampling (NS). Ideally, NS should sample negative classes from a distribution that is dependent on the input data, the current parameters, and the correct positive class. Unfortunately, due to the dynamically updated parameters and data samples, there is …
University of Connecticut（康涅狄格大学）；ByteDance Inc.（字节跳动）
We investigate the issue of parameter estimation with nonuniform negative sampling for imbalanced data. We first prove that, with imbalanced data, the available information about unknown parameters is only tied to the relatively small number of positive instances, which justifies the usage of negative sampling. However, if the negative instances are subsampled to the same level of the positive cases, there is information loss. To maintain more information, we derive the asymptotic distribution of a general inverse probability weighted (IPW) estimator and obtain the optimal sampling probability…
Estimating the parameters of probabilistic models of language such as maxent models and probabilistic neural models is computationally difficult since it involves evaluating partition functions by summing over an entire vocabulary, which may be millions of word types in size. Two closely related strategies---noise contrastive estimation (Mnih and Teh, 2012; Mnih and Kavukcuoglu, 2013; Vaswani et al., 2013) and negative sampling (Mikolov et al., 2012; Goldberg and Levy, 2014)---have emerged as popular solutions to this computational problem, but some confusion remains as to which is more approp…
Stanford University（斯坦福大学）；Mila - University of Montreal（米拉研究所 - 蒙特利尔大学）
Off-policy policy estimators that use importance sampling (IS) can suffer from high variance in long-horizon domains, and there has been particular excitement over new IS methods that leverage the structure of Markov decision processes. We analyze the variance of the most popular approaches through the viewpoint of conditional Monte Carlo. Surprisingly, we find that in finite horizon MDPs there is no strict variance reduction of per-decision importance sampling or stationary importance sampling, comparing with vanilla importance sampling. We then provide sufficient conditions under which the p…
Negative sampling schemes enable efficient training given a large number of classes, by offering a means to approximate a computationally expensive loss function that takes all labels into account. In this paper, we present a new connection between these schemes and loss modification techniques for countering label imbalance. We show that different negative sampling schemes implicitly trade-off performance on dominant versus rare labels. Further, we provide a unified means to explicitly tackle both sampling bias, arising from working with a subset of all labels, and labeling bias, which is inh…
Tsinghua University（清华大学）；Microsoft Research Asia（微软亚洲研究院）
InfoNCE loss is a widely used loss function for contrastive model training. It aims to estimate the mutual information between a pair of variables by discriminating between each positive pair and its associated $K$ negative pairs. It is proved that when the sample labels are clean, the lower bound of mutual information estimation is tighter when more negative samples are incorporated, which usually yields better model performance. However, in many real-world tasks the labels often contain noise, and incorporating too many noisy negative samples for model training may be suboptimal. In this pap…
Harbin Institute of Technology (Shenzhen)（哈尔滨工业大学（深圳））
Graph representation learning has long been an important yet challenging task for various real-world applications. However, their downstream tasks are mainly performed in the settings of supervised or semi-supervised learning. Inspired by recent advances in unsupervised contrastive learning, this paper is thus motivated to investigate how the node-wise contrastive learning could be performed. Particularly, we respectively resolve the class collision issue and the imbalanced negative data distribution issue. Extensive experiments are performed on three real-world datasets and the proposed appro…
Evaluating Negative Sampling Approaches for Neural Topic Models
School of Mathematical and Computational Sciences, Indian Association for the Cultivation of Science（印度科学促进会数学与计算科学学院）；Ashoka University（阿育王大学）；Indian Institute of Technology Kharagpur（印度理工学院卡拉格普尔分校）
On SkipGram Word Embedding Models with Negative Sampling: Unified Framework and Impact of Noise Distributions
School of Computer Science and Engineering, Beihang University（北京航空航天大学计算机科学与工程学院）；School of Computer Science and Technology, Tongji University（同济大学计算机科学与技术学院）
Institute of Computer Science & Technology, Peking University（北京大学计算机科学技术研究所）；IBM China Research Lab（IBM中国研究院）
Syntactic features play an essential role in identifying relationship in a sentence. Previous neural network models often suffer from irrelevant information introduced when subjects and objects are in a long distance. In this paper, we propose to learn more robust relation representations from the shortest dependency path through a convolution neural network. We further propose a straightforward negative sampling strategy to improve the assignment of subjects and objects. Experimental results show that our method outperforms the state-of-the-art methods on the SemEval-2010 Task 8 dataset.
Deezer Research & Development（Deezer研发部）；Paris（巴黎）
Distance metric learning based on triplet loss has been applied with success in a wide range of applications such as face recognition, image retrieval, speaker change detection and recently recommendation with the CML model. However, as we show in this article, CML requires large batches to work reasonably well because of a too simplistic uniform negative sampling strategy for selecting triplets. Due to memory limitations, this makes it difficult to scale in high-dimensional scenarios. To alleviate this problem, we propose here a 2-stage negative sampling strategy which finds triplets that are…
Northeastern University（东北大学）；University of Amsterdam（阿姆斯特丹大学）；Google Research（谷歌研究院）
World models trained by contrastive learning are a compelling alternative to autoencoder-based world models, which learn by reconstructing pixel states. In this paper, we describe three cases where small changes in how we sample negative states in the contrastive loss lead to drastic changes in model performance. In previously studied Atari datasets, we show that leveraging time step correlations can double the performance of the Contrastive Structured World Model. We also collect a full version of the datasets to study contrastive learning under a more diverse set of experiences.
Knowledge representation learning aims at modeling knowledge graph by encoding entities and relations into a low dimensional space. Most of the traditional works for knowledge embedding need negative sampling to minimize a margin-based ranking loss. However, those works construct negative samples through a random mode, by which the samples are often too trivial to fit the model efficiently. In this paper, we propose a novel knowledge representation learning framework based on Generative Adversarial Networks (GAN). In this GAN-based framework, we take advantage of a generator to obtain high-qua…
Beihang University（北京航空航天大学）；Capital Normal University（首都师范大学）
Extreme Multi-label text Classification (XMC) is a task of finding the most relevant labels from a large label set. Nowadays deep learning-based methods have shown significant success in XMC. However, the existing methods (e.g., AttentionXML and X-Transformer etc) still suffer from 1) combining several models to train and predict for one dataset, and 2) sampling negative labels statically during the process of training label ranking model, which reduces both the efficiency and accuracy of the model. To address the above problems, we proposed LightXML, which adopts end-to-end training and dynam…
