Recently, metric learning and similarity learning have attracted a large amount of interest. Many models and optimisation algorithms have been proposed. However, there is relatively little work on the generalization analysis of such methods. In this paper, we derive novel generalization bounds of metric and similarity learning. In particular, we first show that the generalization analysis reduces to the estimation of the Rademacher average over "sums-of-i.i.d." sample-blocks related to the specific matrix norm. Then, we derive generalization bounds for metric/similarity learning with different matrix-norm regularisers by estimating their specific Rademacher complexities. Our analysis indicates that sparse metric/similarity learning with $L^1$-norm regularisation could lead to significantly better bounds than those with Frobenius-norm regularisation. Our novel generalization analysis develops and refines the techniques of U-statistics and Rademacher complexity analysis.
Shanghai University of Finance and Economics（上海财经大学）
Deep semi-supervised learning has been widely implemented in the real-world due to the rapid development of deep learning. Recently, attention has shifted to the approaches such as Mean-Teacher to penalize the inconsistency between two perturbed input sets. Although these methods may achieve positive results, they ignore the relationship information between data instances. To solve this problem, we propose a novel method named Metric Learning by Similarity Network (MLSN), which aims to learn a distance metric adaptively on different domains. By co-training with the classification network, simi…
Discriminative Similarity for Clustering and Semi-Supervised Learning
Snap Research（Snap 研究院）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Microsoft Research（微软研究院）；National University of Singapore（新加坡国立大学）；Beckman Institute, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校贝克曼研究所）
Google Inc.（谷歌公司）；Information Sciences Institute, University of Southern California（南加州大学信息科学研究所）；INRIA（法国国家信息与自动化研究所）
Similarity and metric learning provides a principled approach to construct a task-specific similarity from weakly supervised data. However, these methods are subject to the curse of dimensionality: as the number of features grows large, poor generalization is to be expected and training becomes intractable due to high computational and memory costs. In this paper, we propose a similarity learning method that can efficiently deal with high-dimensional sparse data. This is achieved through a parameterization of similarity functions by convex combinations of sparse rank-one matrices, together wit…
School of Computing and Augmented Intelligence（计算与增强智能学院）；Arizona State University（亚利桑那州立大学）；Baidu Research（百度研究院）
Similarity-based clustering methods separate data into clusters according to the pairwise similarity between the data, and the pairwise similarity is crucial for their performance. In this paper, we propose {\em Clustering by Discriminative Similarity (CDS)}, a novel method which learns discriminative similarity for data clustering. CDS learns an unsupervised similarity-based classifier from each data partition, and searches for the optimal partition of the data by minimizing the generalization error of the learnt classifiers associated with the data partitions. By generalization analysis via …
Pennsylvania State University（宾夕法尼亚州立大学）；University of California San Diego（加利福尼亚大学圣迭戈分校）；Scripps Institute of Oceanography（斯克里普斯海洋研究所）
The Analog Ensemble (AnEn) technique has been shown effective on several weather problems. Unlike previous weather analogs that are sought within a large spatial domain and an extended temporal window, AnEn strictly confines space and time, and independently generates results at each grid point within a short time window. AnEn can find similar forecasts that lead to accurate and calibrated ensemble forecasts. The central core of the AnEn technique is a similarity metric that sorts historical forecasts with respect to a new target prediction. A commonly used metric is Euclidean distance. Howeve…
Laval University（拉瓦尔大学）；Beijing University of Posts and Telecommunications（北京邮电大学）；University of Western Ontario（西安大略大学）
Generalizing knowledge to unseen domains, where data and labels are unavailable, is crucial for machine learning models. We tackle the domain generalization problem to learn from multiple source domains and generalize to a target domain with unknown statistics. The crucial idea is to extract the underlying invariant features across all the domains. Previous domain generalization approaches mainly focused on learning invariant features and stacking the learned features from each source domain to generalize to a new target domain while ignoring the label information, which will lead to indisting…
Google Research（谷歌研究院）；Mila（米拉研究所）；Université de Montréal（蒙特利尔大学）；DeepMind（深度思维公司）
Reinforcement learning methods trained on few environments rarely learn policies that generalize to unseen environments. To improve generalization, we incorporate the inherent sequential structure in reinforcement learning into the representation learning process. This approach is orthogonal to recent approaches, which rarely exploit this structure explicitly. Specifically, we introduce a theoretically motivated policy similarity metric (PSM) for measuring behavioral similarity between states. PSM assigns high similarity to states for which the optimal policies in those states as well as in fu…
RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）；Tohoku University（东北大学）；Osaka University（大阪大学）
Explaining the predictions made by complex machine learning models helps users to understand and accept the predicted outputs with confidence. One promising way is to use similarity-based explanation that provides similar instances as evidence to support model predictions. Several relevance metrics are used for this purpose. In this study, we investigated relevance metrics that can provide reasonable explanations to users. Specifically, we adopted three tests to evaluate whether the relevance metrics satisfy the minimal requirements for similarity-based explanation. Our experiments revealed th…
Aalto University（阿尔托大学）；University of Manchester（曼彻斯特大学）
Similarity metrics such as representational similarity analysis (RSA) and centered kernel alignment (CKA) have been used to compare layer-wise representations between neural networks. However, these metrics are confounded by the population structure of data items in the input space, leading to spuriously high similarity for even completely random neural networks and inconsistent domain relations in transfer learning. We introduce a simple and generally applicable fix to adjust for the confounder with covariate adjustment regression, which retains the intuitive invariance properties of the orig…
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；Purdue University（普渡大学）
We introduce GSimCNN (Graph Similarity Computation via Convolutional Neural Networks) for predicting the similarity score between two graphs. As the core operation of graph similarity search, pairwise graph similarity computation is a challenging problem due to the NP-hard nature of computing many graph distance/similarity metrics. We demonstrate our model using the Graph Edit Distance (GED) as the example metric. Experiments on three real graph datasets demonstrate that our model achieves the state-of-the-art performance on graph similarity search.
Learning generalizeable policies from visual input in the presence of visual distractions is a challenging problem in reinforcement learning. Recently, there has been renewed interest in bisimulation metrics as a tool to address this issue; these metrics can be used to learn representations that are, in principle, invariant to irrelevant distractions by measuring behavioural similarity between states. An accurate, unbiased, and scalable estimation of these metrics has proved elusive in continuous state and action scenarios. We propose entangled bisimulation, a bisimulation metric that allows t…
Active learning is commonly used to train label-efficient models by adaptively selecting the most informative queries. However, most active learning strategies are designed to either learn a representation of the data (e.g., embedding or metric learning) or perform well on a task (e.g., classification) on the data. However, many machine learning tasks involve a combination of both representation learning and a task-specific goal. Motivated by this, we propose a novel unified query framework that can be applied to any problem in which a key component is learning a representation of the data tha…
McGill University（麦吉尔大学）；Quebec AI Institute（魁北克人工智能研究所）；UC Berkeley（加州大学伯克利分校）；Google Brain（谷歌大脑）
Reinforcement learning (RL) agents are widely used for solving complex sequential decision making tasks, but still exhibit difficulty in generalizing to scenarios not seen during training. While prior online approaches demonstrated that using additional signals beyond the reward function can lead to better generalization capabilities in RL agents, i.e. using self-supervised learning (SSL), they struggle in the offline RL setting, i.e. learning from a static dataset. We show that performance of online algorithms for generalization in RL can be hindered in the offline setting due to poor estimat…
Music similarity search is useful for a variety of creative tasks such as replacing one music recording with another recording with a similar "feel", a common task in video editing. For this task, it is typically necessary to define a similarity metric to compare one recording to another. Music similarity, however, is hard to define and depends on multiple simultaneous notions of similarity (i.e. genre, mood, instrument, tempo). While prior work ignore this issue, we embrace this idea and introduce the concept of multidimensional similarity and unify both global and specialized similarity metr…
Although the notion of task similarity is potentially interesting in a wide range of areas such as curriculum learning or automated planning, it has mostly been tied to transfer learning. Transfer is based on the idea of reusing the knowledge acquired in the learning of a set of source tasks to a new learning process in a target task, assuming that the target and source tasks are close enough. In recent years, transfer learning has succeeded in making Reinforcement Learning (RL) algorithms more efficient (e.g., by reducing the number of samples needed to achieve the (near-)optimal performance)…
The rapid development of such natural language processing tasks as style transfer, paraphrase, and machine translation often calls for the use of semantic similarity metrics. In recent years a lot of methods to measure the semantic similarity of two short texts were developed. This paper provides a comprehensive analysis for more than a dozen of such methods. Using a new dataset of fourteen thousand sentence pairs human-labeled according to their semantic similarity, we demonstrate that none of the metrics widely used in the literature is close enough to human judgment in these tasks. A number…
Similarity/Distance measures play a key role in many machine learning, pattern recognition, and data mining algorithms, which leads to the emergence of metric learning field. Many metric learning algorithms learn a global distance function from data that satisfy the constraints of the problem. However, in many real-world datasets that the discrimination power of features varies in the different regions of input space, a global metric is often unable to capture the complexity of the task. To address this challenge, local metric learning methods are proposed that learn multiple metrics across th…
University of Copenhagen（哥本哈根大学）；Technical University of Denmark（丹麦技术大学）
We propose a semantic similarity metric for image registration. Existing metrics like euclidean distance or normalized cross-correlation focus on aligning intensity values, giving difficulties with low intensity contrast or noise. Our semantic approach learns dataset-specific features that drive the optimization of a learning-based registration model. Comparing to existing unsupervised and supervised methods across multiple image modalities and applications, we achieve consistently high registration accuracy and faster convergence than state of the art, and the learned invariance to noise give…
Similarity search is a fundamental problem for many data analysis techniques. Many efficient search techniques rely on the triangle inequality of metrics, which allows pruning parts of the search space based on transitive bounds on distances. Recently, Cosine similarity has become a popular alternative choice to the standard Euclidean metric, in particular in the context of textual data and neural network embeddings. Unfortunately, Cosine similarity is not metric and does not satisfy the standard triangle inequality. Instead, many search techniques for Cosine rely on approximation techniques s…
A Universal Metric of Dataset Similarity for Cross-silo Federated Learning
Department of Biomedical Informatics, Columbia University, NY, USA（生物医学信息学系，哥伦比亚大学）；New York Genome Center, NY, USA（纽约基因中心）；Department of Computer Science, Columbia University, NY, USA（计算机科学系，哥伦比亚大学）
Royal Holloway, University of London（伦敦大学皇家霍洛威学院）；University of Edinburgh（爱丁堡大学）；FISCAL Technologies Ltd（FISCAL技术有限公司）
Businesses, governmental bodies and NGO's have an ever-increasing amount of data at their disposal from which they try to extract valuable information. Often, this needs to be done not only accurately but also within a short time frame. Clean and consistent data is therefore crucial. Data matching is the field that tries to identify instances in data that refer to the same real-world entity. In this study, machine learning techniques are combined with string similarity functions to the field of data matching. A dataset of invoices from a variety of businesses and organizations was preprocessed…
Xidian University（西安电子科技大学）；JD Finance American Corporation（京东金融美国公司）；University of Pittsburgh（匹兹堡大学）
Deep Metric Learning (DML) plays a critical role in various machine learning tasks. However, most existing deep metric learning methods with binary similarity are sensitive to noisy labels, which are widely present in real-world data. Since these noisy labels often cause severe performance degradation, it is crucial to enhance the robustness and generalization ability of DML. In this paper, we propose an Adaptive Hierarchical Similarity Metric Learning method. It considers two noise-insensitive information, \textit{i.e.}, class-wise divergence and sample-wise consistency. Specifically, class-w…
Cosine similarity is a widely used measure of the relatedness of pre-trained word embeddings, trained on a language modeling goal. Datasets such as WordSim-353 and SimLex-999 rate how similar words are according to human annotators, and as such are often used to evaluate the performance of language models. Thus, any improvement on the word similarity task requires an improved word representation. In this paper, we propose instead the use of an extended cosine similarity measure to improve performance on that task, with gains in interpretability. We explore the hypothesis that this approach is …
University of Copenhagen（哥本哈根大学）；Technical University of Denmark（丹麦技术大学）
We propose a semantic similarity metric for image registration. Existing metrics like Euclidean Distance or Normalized Cross-Correlation focus on aligning intensity values, giving difficulties with low intensity contrast or noise. Our approach learns dataset-specific features that drive the optimization of a learning-based registration model. We train both an unsupervised approach using an auto-encoder, and a semi-supervised approach using supplemental segmentation data to extract semantic features for image registration. Comparing to existing methods across multiple image modalities and appli…
The University of Sydney（悉尼大学）；King Fahd University of Petroleum and Minerals（法赫德国王石油与矿产大学）
SpectralNet is a graph clustering method that uses neural network to find an embedding that separates the data. So far it was only used with $k$-nn graphs, which are usually constructed using a distance metric (e.g., Euclidean distance). $k$-nn graphs restrict the points to have a fixed number of neighbors regardless of the local statistics around them. We proposed a new SpectralNet similarity metric based on random projection trees (rpTrees). Our experiments revealed that SpectralNet produces better clustering accuracy using rpTree similarity metric compared to $k$-nn graph with a distance me…
Graph Neural Networks (GNNs) achieve state-of-the-art performance on graph-structured data across numerous domains. Their underlying ability to represent nodes as summaries of their vicinities has proven effective for homophilous graphs in particular, in which same-type nodes tend to connect. On heterophilous graphs, in which different-type nodes are likely connected, GNNs perform less consistently, as neighborhood information might be less representative or even misleading. On the other hand, GNN performance is not inferior on all heterophilous graphs, and there is a lack of understanding of …
Measuring the Measures: Discriminative Capacity of Representational Similarity Metrics Across Model Families
Department of Computer Science and Engineering, UC San Diego（计算机科学与工程系，UC San Diego）；Department of Electrical and Computer Engineering, UC San Diego（电气与计算机工程系，UC San Diego）；Department of Cognitive Science, UC San Diego（认知科学系，UC San Diego）
There are several issues with the existing general machine translation or natural language generation evaluation metrics, and question-answering (QA) systems are indifferent in that context. To build robust QA systems, we need the ability to have equivalently robust evaluation systems to verify whether model predictions to questions are similar to ground-truth annotations. The ability to compare similarity based on semantics as opposed to pure string overlap is important to compare models fairly and to indicate more realistic acceptance criteria in real-life applications. We build upon the fir…
