Recent advances in large-margin classification of data residing in general metric spaces (rather than Hilbert spaces) enable classification under various natural metrics, such as string edit and earthmover distance. A general framework developed for this purpose by von Luxburg and Bousquet [JMLR, 2004] left open the questions of computational efficiency and of providing direct bounds on generalization error.
We design a new algorithm for classification in general metric spaces, whose runtime and accuracy depend on the doubling dimension of the data points, and can thus achieve superior classification performance in many common scenarios. The algorithmic core of our approach is an approximate (rather than exact) solution to the classical problems of Lipschitz extension and of Nearest Neighbor Search. The algorithm's generalization performance is guaranteed via the fat-shattering dimension of Lipschitz classifiers, and we present experimental evidence of its superiority to some common kernel methods. As a by-product, we offer a new perspective on the nearest neighbor classifier, which yields significantly sharper risk asymptotics than the classic analysis of Cover and Hart [IEEE Trans. Info. Theory, 1967].
RTL Nederland B.V.（RTL荷兰公司）；University of Amsterdam（阿姆斯特丹大学）
Multiclass multilabel classification is the task of attributing multiple labels to examples via predictions. Current models formulate a reduction of the multilabel setting into either multiple binary classifications or multiclass classification, allowing for the use of existing loss functions (sigmoid, cross-entropy, logistic, etc.). Multilabel classification reductions do not accommodate for the prediction of varying numbers of labels per example and the underlying losses are distant estimates of the performance metrics. We propose a loss function, sigmoidF1, which is an approximation of the …
Metric learning for classification has been intensively studied over the last decade. The idea is to learn a metric space induced from a normed vector space on which data from different classes are well separated. Different measures of the separation thus lead to various designs of the objective function in the metric learning model. One classical metric is the Mahalanobis distance, where a linear transformation matrix is designed and applied on the original dataset to obtain a new subspace equipped with the Euclidean norm. The kernelized version has also been developed, followed by Multiple-K…
The University of Sydney（悉尼大学）；The University of New South Wales（新南威尔士大学）
Existing research into online multi-label classification, such as online sequential multi-label extreme learning machine (OSML-ELM) and stochastic gradient descent (SGD), has achieved promising performance. However, these works do not take label dependencies into consideration and lack a theoretical analysis of loss functions. Accordingly, we propose a novel online metric learning paradigm for multi-label classification to fill the current research gap. Generally, we first propose a new metric for multi-label classification which is based on $k$-Nearest Neighbour ($k$NN) and combined with larg…
We consider optimization of generalized performance metrics for binary classification by means of surrogate losses. We focus on a class of metrics, which are linear-fractional functions of the false positive and false negative rates (examples of which include $F_β$-measure, Jaccard similarity coefficient, AM measure, and many others). Our analysis concerns the following two-step procedure. First, a real-valued function $f$ is learned by minimizing a surrogate loss for binary classification on the training sample. It is assumed that the surrogate loss is a strongly proper composite loss functio…
With the increasing abundance of pretrained models in recent years, the problem of selecting the best pretrained checkpoint for a particular downstream classification task has been gaining increased attention. Although several methods have recently been proposed to tackle the selection problem (e.g. LEEP, H-score), these methods resort to applying heuristics that are not well motivated by learning theory. In this paper we present PACTran, a theoretically grounded family of metrics for pretrained model selection and transferability measurement. We first show how to derive PACTran metrics from t…
CRIF S.p.A.（CRIF股份公司）；Università degli Studi di Bologna（博洛尼亚大学）；University of Bologna（博洛尼亚大学）
Classification tasks in machine learning involving more than two classes are known by the name of "multi-class classification". Performance indicators are very useful when the aim is to evaluate and compare different classification models or machine learning techniques. Many metrics come in handy to test the ability of a multi-class classifier. Those metrics turn out to be useful at different stage of the development process, e.g. comparing the performance of two different models or analysing the behaviour of the same model by tuning different parameters. In this white paper we review a list o…
Clustering and classification critically rely on distance metrics that provide meaningful comparisons between data points. We present mixed-integer optimization approaches to find optimal distance metrics that generalize the Mahalanobis metric extensively studied in the literature. Additionally, we generalize and improve upon leading methods by removing reliance on pre-designated "target neighbors," "triplets," and "similarity pairs." Another salient feature of our method is its ability to enable active learning by recommending precise regions to sample after an optimal metric is computed to i…
Department of Computer Science, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校计算机科学系）；Google Inc.（谷歌公司）；Independent Researcher（独立研究者）
We propose a framework for constructing and analyzing multiclass and multioutput classification metrics, i.e., involving multiple, possibly correlated multiclass labels. Our analysis reveals novel insights on the geometry of feasible confusion tensors -- including necessary and sufficient conditions for the equivalence between optimizing an arbitrary non-decomposable metric and learning a weighted classifier. Further, we analyze averaging methodologies commonly used to compute multioutput metrics and characterize the corresponding Bayes optimal classifiers. We show that the plug-in estimator b…
Know-Center GmbH（Know-Center 有限公司）；Graz University of Technology（格拉茨技术大学）
Distance-based classification is among the most competitive classification methods for time series data. The most critical component of distance-based classification is the selected distance function. Past research has proposed various different distance metrics or measures dedicated to particular aspects of real-world time series data, yet there is an important aspect that has not been considered so far: Robustness against arbitrary data contamination. In this work, we propose a novel distance metric that is robust against arbitrarily "bad" contamination and has a worst-case computational com…
University of Central Florida（中佛罗里达大学）；Florida Institute of Technology（佛罗里达理工学院）
We propose a new method for local distance metric learning based on sample similarity as side information. These local metrics, which utilize conical combinations of metric weight matrices, are learned from the pooled spatial characteristics of the data, as well as the similarity profiles between the pairs of samples, whose distances are measured. The main objective of our framework is to yield metrics, such that the resulting distances between similar samples are small and distances between dissimilar samples are above a certain threshold. For learning and inference purposes, we describe a tr…
Given a learning problem with real-world tradeoffs, which cost function should the model be trained to optimize? This is the metric selection problem in machine learning. Despite its practical interest, there is limited formal guidance on how to select metrics for machine learning applications. This thesis outlines metric elicitation as a principled framework for selecting the performance metric that best reflects implicit user preferences. Once specified, the evaluation metric can be used to compare and train models. In this manuscript, we formalize the problem of Metric Elicitation and devis…
Bauman Moscow State Technical University（莫斯科鲍曼国立技术大学）
The article deals with the issue of modification of metric classification algorithms. In particular, it studies the algorithm k-Nearest Neighbours for its application to sequential data. A method of generalization of metric classification algorithms is proposed. As a part of it, there has been developed an algorithm for solving the problem of classification and labelling of sequential data. The advantages of the developed algorithm of classification in comparison with the existing one are also discussed in the article. There is a comparison of the effectiveness of the proposed algorithm with t…
National Security Institute（国家安全研究所）；Virginia Tech（弗吉尼亚理工大学）
Machine learning models are increasingly used in practice. However, many machine learning methods are sensitive to test or operational data that is dissimilar to training data. Out-of-distribution (OOD) data is known to increase the probability of error and research into metrics that identify what dissimilarities in data affect model performance is on-going. Recently, combinatorial coverage metrics have been explored in the literature as an alternative to distribution-based metrics. Results show that coverage metrics can correlate with classification error. However, other results show that the…
A Metric Topology of Deep Learning for Data Classification
Institute of Communications Engineering（通信工程研究所）；College of Electrical Engineering, National Yang Ming Chiao Tung University（国立阳明交通大学电机工程学院）；Department of Electrical and Computer Engineering, Mississippi State University（密西西比州立大学电机与计算机工程系）
Traditional text classifiers are limited to predicting over a fixed set of labels. However, in many real-world applications the label set is frequently changing. For example, in intent classification, new intents may be added over time while others are removed. We propose to address the problem of dynamic text classification by replacing the traditional, fixed-size output layer with a learned, semantically meaningful metric space. Here the distances between textual inputs are optimized to perform nearest-neighbor classification across overlapping label sets. Changing the label set does not inv…
The University of Tokyo（东京大学）；RIKEN AIP（理化学研究所先进智能项目中心）
Complex classification performance metrics such as the F${}_β$-measure and Jaccard index are often used, in order to handle class-imbalanced cases such as information retrieval and image segmentation. These performance metrics are not decomposable, that is, they cannot be expressed in a per-example manner, which hinders a straightforward application of M-estimation widely used in supervised learning. In this paper, we consider linear-fractional metrics, which are a family of classification performance metrics that encompasses many standard ones such as the F${}_β$-measure and Jaccard index, an…
University College London（伦敦大学学院）；Imperial College London（帝国理工学院）
The performance of distance-based classifiers heavily depends on the underlying distance metric, so it is valuable to learn a suitable metric from the data. To address the problem of multimodality, it is desirable to learn local metrics. In this short paper, we define a new intuitive distance with local metrics and influential regions, and subsequently propose a novel local metric learning method for distance-based classification. Our key intuition is to partition the metric space into influential regions and a background region, and then regulate the effectiveness of each local metric to be w…
We develop Distributionally Robust Optimization (DRO) formulations for Multivariate Linear Regression (MLR) and Multiclass Logistic Regression (MLG) when both the covariates and responses/labels may be contaminated by outliers. The DRO framework uses a probabilistic ambiguity set defined as a ball of distributions that are close to the empirical distribution of the training set in the sense of the Wasserstein metric. We relax the DRO formulation into a regularized learning problem whose regularizer is a norm of the coefficient matrix. We establish out-of-sample performance guarantees for the s…
We initiate the rigorous study of classification in quasi-metric spaces. These are point sets endowed with a distance function that is non-negative and also satisfies the triangle inequality, but is asymmetric. We develop and refine a learning algorithm for quasi-metrics based on sample compression and nearest neighbor, and prove that it has favorable statistical properties.
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…
To improve the classification performance in the context of hyperspectral image processing, many works have been developed based on two common strategies, namely the spatial-spectral information integration and the utilization of neural networks. However, both strategies typically require more training data than the classical algorithms, aggregating the shortage of labeled samples. In this letter, we propose a novel framework that organically combines the spectrum-based deep metric learning model and the conditional random field algorithm. The deep metric learning model is supervised by the ce…
University of Coimbra（科英布拉大学）；Central University of Las Villas（拉斯维利亚斯中央大学）
With the massive data challenges nowadays and the rapid growing of technology, stream mining has recently received considerable attention. To address the large number of scenarios in which this phenomenon manifests itself suitable tools are required in various research fields. Instance-based data stream algorithms generally employ the Euclidean distance for the classification task underlying this problem. A novel way to look into this issue is to take advantage of a more flexible metric due to the increased requirements imposed by the data stream scenario. In this paper we present a new algori…
Metric learning is one of the techniques in manifold learning with the goal of finding a projection subspace for increasing and decreasing the inter- and intra-class variances, respectively. Some of the metric learning methods are based on triplet learning with anchor-positive-negative triplets. Large margin metric learning for nearest neighbor classification is one of the fundamental methods to do this. Recently, Siamese networks have been introduced with the triplet loss. Many triplet mining methods have been developed for Siamese networks; however, these techniques have not been applied on …
Unintended bias in Machine Learning can manifest as systemic differences in performance for different demographic groups, potentially compounding existing challenges to fairness in society at large. In this paper, we introduce a suite of threshold-agnostic metrics that provide a nuanced view of this unintended bias, by considering the various ways that a classifier's score distribution can vary across designated groups. We also introduce a large new test set of online comments with crowd-sourced annotations for identity references. We use this to show how our metrics can be used to find new an…
In Ordinal Classification tasks, items have to be assigned to classes that have a relative ordering, such as positive, neutral, negative in sentiment analysis. Remarkably, the most popular evaluation metrics for ordinal classification tasks either ignore relevant information (for instance, precision/recall on each of the classes ignores their relative ordering) or assume additional information (for instance, Mean Average Error assumes absolute distances between classes). In this paper we propose a new metric for Ordinal Classification, Closeness Evaluation Measure, that is rooted on Measuremen…
Wroclaw University of Science and Technology（弗罗茨瓦夫理工大学）
In the classification of a class imbalance dataset, the performance measure used for the model selection and comparison to competing methods is a major issue. In order to overcome this problem several performance measures are defined and analyzed in several perspectives regarding in particular the imbalance ratio. There is still no clear indication which metric is universal and can be used for any skewed data problem. In this paper we introduced a new performance measure based on the harmonic mean of Recall and Selectivity normalized in class labels. This paper shows that the proposed performa…
Technische Universität Dortmund（多特蒙德工业大学）；Bergische Universität Wuppertal（伍珀塔尔大学）
We study the quantification of uncertainty of Convolutional Neural Networks (CNNs) based on gradient metrics. Unlike the classical softmax entropy, such metrics gather information from all layers of the CNN. We show for the EMNIST digits data set that for several such metrics we achieve the same meta classification accuracy -- i.e. the task of classifying predictions as correct or incorrect without knowing the actual label -- as for entropy thresholding. We apply meta classification to unknown concepts (out-of-distribution samples) -- EMNIST/Omniglot letters, CIFAR10 and noise -- and demonstra…
Exact Reformulation and Optimization for Direct Metric Optimization in Binary Imbalanced Classification
Department of Computer Science and Engineering, University of Minnesota, USA（明尼苏达大学计算机科学与工程系）；School of Statistics, University of Minnesota, USA（明尼苏达大学统计学系）；Department of Industrial Engineering and Operations Research, University of California, Berkeley, USA（加州大学伯克利分校工业工程与运筹学系）
Lanzhou University of Technology（兰州理工大学）；Beijing University of Posts and Telecommunications（北京邮电大学）；University of Glasgow（格拉斯哥大学）；University College London（伦敦大学学院）
Few-shot image classification is a challenging problem that aims to achieve the human level of recognition based only on a small number of training images. One main solution to few-shot image classification is deep metric learning. These methods, by classifying unseen samples according to their distances to few seen samples in an embedding space learned by powerful deep neural networks, can avoid overfitting to few training images in few-shot image classification and have achieved the state-of-the-art performance. In this paper, we provide an up-to-date review of deep metric learning methods f…
Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）
Recently, generated images could reach very high quality, even human eyes could not tell them apart from real images. Although there are already some methods for detecting generated images in current forensic community, most of these methods are used to detect a single type of generated images. The new types of generated images are emerging one after another, and the existing detection methods cannot cope well. These problems prompted us to propose a scalable framework for multi-class classification based on deep metric learning, which aims to classify the generated images finer. In addition, …
Cisco Systems（思科系统公司）；Czech Technical University in Prague（布拉格捷克理工大学）
The nearest prototype classification is a less computationally intensive replacement for the $k$-NN method, especially when large datasets are considered. In metric spaces, centroids are often used as prototypes to represent whole clusters. The selection of cluster prototypes in non-metric spaces is more challenging as the idea of computing centroids is not directly applicable. In this paper, we present CRS, a novel method for selecting a small yet representative subset of objects as a cluster prototype. Memory and computationally efficient selection of representatives is enabled by leveraging…
Algorithmic Accountability in Small Data: Sample-Size-Induced Bias Within Classification Metrics
School of Electrical Engineering & Computer Science, Washington State University（电气工程与计算机科学学院，华盛顿州立大学）；Department of Mathematics and Statistics, Washington State University（数学与统计学系，华盛顿州立大学）
Institute of Marine Research（海洋研究所）；University of Bergen（卑尔根大学）
Most classification models treat all misclassifications equally. However, different classes may be related, and these hierarchical relationships must be considered in some classification problems. These problems can be addressed by using hierarchical information during training. Unfortunately, this information is not available for all datasets. Many classification-based metric learning methods use class representatives in embedding space to represent different classes. The relationships among the learned class representatives can then be used to estimate class hierarchical structures. If we ha…
Institute of Mathematics；Computer Science (ICMC) University of São Paulo (USP) São Carlos, SP, Brazil
Complex Networks are a good approach to find internal relationships and represent the structure of classes in a dataset then they are used for High Level Classification. Previous works use K-Nearest Neighbors to build each Complex Network considering all the available samples. This paper introduces a different creation of Complex Networks, considering only sample which belongs to each class. And metric is used to analyze the structure of Complex Networks, besides an optimization approach to improve the performance is presented. Experiments are executed considering a cross validation process, t…
Recent works have shown that deep metric learning algorithms can benefit from weak supervision from another input modality. This additional modality can be incorporated directly into the popular triplet-based loss function as distances. Also recently, classification loss and proxy-based metric learning have been observed to lead to faster convergence as well as better retrieval results, all the while without requiring complex and costly sampling strategies. In this paper we propose an extension to the existing adaptive margin for classification-based deep metric learning. Our extension introdu…
John A. Paulson School of Engineering and Applied Sciences, Harvard University（哈佛大学约翰·A·保尔森工程与应用科学学院）
Predictive multiplicity occurs when classification models with statistically indistinguishable performances assign conflicting predictions to individual samples. When used for decision-making in applications of consequence (e.g., lending, education, criminal justice), models developed without regard for predictive multiplicity may result in unjustified and arbitrary decisions for specific individuals. We introduce a new metric, called Rashomon Capacity, to measure predictive multiplicity in probabilistic classification. Prior metrics for predictive multiplicity focus on classifiers that output…
Robust performance metrics for imbalanced classification problems
Philipps-Universität Marburg（马尔堡菲利普斯大学）；Karlsruher Institut für Technologie (KIT)（卡尔斯鲁厄理工学院）；Fachbereich Mathematik und Informatik（数学与信息学系）；Institut für Stochastik（统计研究所）
CISPA Helmholtz Center for Information Security（CISPA亥姆霍兹信息安全中心）；IBM T. J. Watson Research Center（IBM T. J. 沃森研究中心）
Adversarial examples are a type of attack on machine learning (ML) systems which cause misclassification of inputs. Achieving robustness against adversarial examples is crucial to apply ML in the real world. While most prior work on adversarial examples is empirical, a recent line of work establishes fundamental limitations of robust classification based on cryptographic hardness. Most positive and negative results in this field however assume that there is a fixed target metric which constrains the adversary, and we argue that this is often an unrealistic assumption. In this work we study the…
We propose a new embedding method for a single vector and for a pair of vectors. This embedding method enables: a) efficient classification and regression of functions of single vectors; b) efficient approximation of distance functions; and c) non-Euclidean, semimetric learning. To the best of our knowledge, this is the first work that enables learning any general, non-Euclidean, semimetrics. That is, our method is a universal semimetric learning and approximation method that can approximate any distance function with as high accuracy as needed with or without semimetric constraints. The proje…
The National Basketball Association(NBA) has expanded their data gathering and have heavily invested in new technologies to gather advanced performance metrics on players. This expanded data set allows analysts to use unique performance metrics in models to estimate and classify player performance. Instead of grouping players together based on physical attributes and positions played, analysts can group together players that play similar to each other based on these tracked metrics. Existing methods for player classification have typically used offensive metrics for clustering [1]. There have …
University of Chinese Academy of Sciences（中国科学院大学）；Beijing Unisound Information Technology Co., Ltd（北京云知声信息技术有限公司）
The training of deep-learning-based text classification models relies heavily on a huge amount of annotation data, which is difficult to obtain. When the labeled data is scarce, models tend to struggle to achieve satisfactory performance. However, human beings can distinguish new categories very efficiently with few examples. This is mainly due to the fact that human beings can leverage knowledge obtained from relevant tasks. Inspired by human intelligence, we propose to introduce external knowledge into few-shot learning to imitate human knowledge. A novel parameter generator network is inves…
Normandie Univ, UNICAEN, ENSICAEN, CNRS（诺曼底大学，卡昂大学，卡昂国立高等工程师学校，国家科学研究中心）；ONERA - The French Aerospace Lab（法国国家航空航天研究院）
Zero-Shot learning has been shown to be an efficient strategy for domain adaptation. In this context, this paper builds on the recent work of Bucher et al. [1], which proposed an approach to solve Zero-Shot classification problems (ZSC) by introducing a novel metric learning based objective function. This objective function allows to learn an optimal embedding of the attributes jointly with a measure of similarity between images and attributes. This paper extends their approach by proposing several schemes to control the generation of the negative pairs, resulting in a significant improvement …
AI Foundations – Learning, IBM Research（IBM研究院人工智能基础——学习部）；IBM T. J. Watson Research Center（IBM托马斯·J·沃森研究中心）
We study few-shot learning in natural language domains. Compared to many existing works that apply either metric-based or optimization-based meta-learning to image domain with low inter-task variance, we consider a more realistic setting, where tasks are diverse. However, it imposes tremendous difficulties to existing state-of-the-art metric-based algorithms since a single metric is insufficient to capture complex task variations in natural language domain. To alleviate the problem, we propose an adaptive metric learning approach that automatically determines the best weighted combination from…
Graduate School of Culture Technology, KAIST（韩国科学技术院文化技术研究生院）；Adobe Research（奥多比研究院）
Deep representation learning offers a powerful paradigm for mapping input data onto an organized embedding space and is useful for many music information retrieval tasks. Two central methods for representation learning include deep metric learning and classification, both having the same goal of learning a representation that can generalize well across tasks. Along with generalization, the emerging concept of disentangled representations is also of great interest, where multiple semantic concepts (e.g., genre, mood, instrumentation) are learned jointly but remain separable in the learned repre…
