In supervised learning, we often face with ambiguous (A) samples that are difficult to label even by domain experts. In this paper, we consider a binary classification problem in the presence of such A samples. This problem is substantially different from semi-supervised learning since unlabeled samples are not necessarily difficult samples. Also, it is different from 3-class classification with the positive (P), negative (N), and A classes since we do not want to classify test samples into the A class. Our proposed method extends binary classification with reject option, which trains a classifier and a rejector simultaneously using P and N samples based on the 0-1-$c$ loss with rejection cost $c$. More specifically, we propose to train a classifier and a rejector under the 0-1-$c$-$d$ loss using P, N, and A samples, where $d$ is the misclassification penalty for ambiguous samples. In our practical implementation, we use a convex upper bound of the 0-1-$c$-$d$ loss for computational tractability. Numerical experiments demonstrate that our method can successfully utilize the additional information brought by such A training data.
Academy of Mathematics and Systems Science（数学与系统科学研究院）；Chinese Academy of Sciences（中国科学院）；School of Mathematical Sciences（数学科学学院）；University of Chinese Academy of Sciences（中国科学院大学）；University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
Outcome labeling ambiguity and subjectivity are ubiquitous in real-world datasets. While practitioners commonly combine ambiguous outcome labels for all data points (instances) in an ad hoc way to improve the accuracy of multi-class classification, there lacks a principled approach to guide the label combination for all data points by any optimality criterion. To address this problem, we propose the information-theoretic classification accuracy (ITCA), a criterion that balances the trade-off between prediction accuracy (how well do predicted labels agree with actual labels) and classification …
University of Washington（华盛顿大学）；Carnegie Mellon University（卡内基梅隆大学）
In most classification tasks there are observations that are ambiguous and therefore difficult to correctly label. Set-valued classifiers output sets of plausible labels rather than a single label, thereby giving a more appropriate and informative treatment to the labeling of ambiguous instances. We introduce a framework for multiclass set-valued classification, where the classifiers guarantee user-defined levels of coverage or confidence (the probability that the true label is contained in the set) while minimizing the ambiguity (the expected size of the output). We first derive oracle classi…
We introduce a simple and computationally trivial method for binary classification based on the evaluation of potential functions. We demonstrate that despite the conceptual and computational simplicity of the method its performance can match or exceed that of standard Support Vector Machine methods.
Language is ambiguous; many terms and expressions can convey the same idea. This is especially true in creative practice, where ideas and design intents are highly subjective. We present a dataset, Ambiguous Descriptions of Art Images (ADARI), of contemporary workpieces, which aims to provide a foundational resource for subjective image description and multimodal word disambiguation in the context of creative practice. The dataset contains a total of 240k images labeled with 260k descriptive sentences. It is additionally organized into sub-domains of architecture, art, design, fashion, furnitu…
In this work, we briefly revise the reduced dilation-erosion perceptron (r-DEP) models for binary classification tasks. Then, we present the so-called linear dilation-erosion perceptron (l-DEP), in which a linear transformation is applied before the application of the morphological operators. Furthermore, we propose to train the l-DEP classifier by minimizing a regularized hinge-loss function subject to concave-convex restrictions. A simple example is given for illustrative purposes.
Classification of datasets into two or more distinct classes is an important machine learning task. Many methods are able to classify binary classification tasks with a very high accuracy on test data, but cannot provide any easily interpretable explanation for users to have a deeper understanding of reasons for the split of data into two classes. In this paper, we highlight and evaluate a recently proposed nonlinear decision tree approach with a number of commonly used classification methods on a number of datasets involving a few to a large number of features. The study reveals key issues su…
The purpose of this research report is to present the our learning curve and the exposure to the Machine Learning life cycle, with the use of a Kaggle binary classification data set and taking to explore various techniques from pre-processing to the final optimization and model evaluation, also we highlight on the data imbalance issue and we discuss the different methods of handling that imbalance on the data level by over-sampling and under sampling not only to reach a balanced class representation but to improve the overall performance. This work also opens some gaps for future work.
Thakur Institute Of Management Studies, Career Development & Research（塔库尔管理研究、职业发展与研究学院）；University of Mumbai（孟买大学）
High dimensional data for classification does create many difficulties for machine learning algorithms. The generalization can be done using ensemble learning methods such as bagging based supervised non-parametric random forest algorithm. In this paper we solve the problem of binary classification for high dimensional data using random forest for polycystic ovary syndrome dataset. We have performed the implementation and provided a detailed visualization of the data for general inference. The training accuracy that we have achieved is 95.6% and validation accuracy over 91.74% respectively.
In many real-world pattern recognition scenarios, such as in medical applications, the corresponding classification tasks can be of an imbalanced nature. In the current study, we focus on binary, imbalanced classification tasks, i.e.~binary classification tasks in which one of the two classes is under-represented (minority class) in comparison to the other class (majority class). In the literature, many different approaches have been proposed, such as under- or oversampling, to counter class imbalance. In the current work, we introduce a novel method, which addresses the issues of class imbala…
Finding discriminant functions of minimum risk binary classification systems is a novel geometric locus problem -- which requires solving a system of fundamental locus equations of binary classification -- subject to deep-seated statistical laws. We show that a discriminant function of a minimum risk binary classification system is the solution of a locus equation that represents the geometric locus of the decision boundary of the system, wherein the discriminant function is connected to the decision boundary by an exclusive principal eigen-coordinate system -- at which point the discriminant …
Support Vector Machines (SVMs) were primarily designed for 2-class classification. But they have been extended for N-class classification also based on the requirement of multiclasses in the practical applications. Although N-class classification using SVM has considerable research attention, getting minimum number of classifiers at the time of training and testing is still a continuing research. We propose a new algorithm CBTS-SVM (Centroid based Binary Tree Structured SVM) which addresses this issue. In this we build a binary tree of SVM models based on the similarity of the class labels by …
Instituto Paulo Gontijo（保罗·贡蒂霍研究所）；FGV/EAESP（巴西应用经济研究所（FGV/EAESP））
In this work we cast the problem of binary classification in terms of estimating a partition on Bernoulli data. When the explanatory variables are all categorical, the problem can be modelled using the language of boolean functions. We offer a probabilistic analysis of the problem, and propose two algorithms for learning boolean functions from binary data.
We present generalization bounds for the TS-MKL framework for two stage multiple kernel learning. We also present bounds for sparse kernel learning formulations within the TS-MKL framework.
SequeL-INRIA/LIFL-CNRS（SequeL-法国国家信息与自动化研究所/法国国家科学研究中心LIFL实验室）；Université de Lille（里尔大学）
We show how binary classification methods developed to work on i.i.d. data can be used for solving statistical problems that are seemingly unrelated to classification and concern highly-dependent time series. Specifically, the problems of time-series clustering, homogeneity testing and the three-sample problem are addressed. The algorithms that we construct for solving these problems are based on a new metric between time-series distributions, which can be evaluated using binary classification methods. Universal consistency of the proposed algorithms is proven under most general assumptions. T…
To cope with high annotation costs, training a classifier only from weakly supervised data has attracted a great deal of attention these days. Among various approaches, strengthening supervision from completely unsupervised classification is a promising direction, which typically employs class priors as the only supervision and trains a binary classifier from unlabeled (U) datasets. While existing risk-consistent methods are theoretically grounded with high flexibility, they can learn only from two U sets. In this paper, we propose a new approach for binary classification from $m$ U-sets for $…
Nanjing University of Science and Technology（南京理工大学）
Recently the deep learning techniques have achieved success in multi-label classification due to its automatic representation learning ability and the end-to-end learning framework. Existing deep neural networks in multi-label classification can be divided into two kinds: binary relevance neural network (BRNN) and threshold dependent neural network (TDNN). However, the former needs to train a set of isolate binary networks which ignore dependencies between labels and have heavy computational load, while the latter needs an additional threshold function mechanism to transform the multi-class pr…
From a geometric perspective most nonlinear binary classification algorithms, including state of the art versions of Support Vector Machine (SVM) and Radial Basis Function Network (RBFN) classifiers, and are based on the idea of reconstructing indicator functions. We propose instead to use reconstruction of the signed distance function (SDF) as a basis for binary classification. We discuss properties of the signed distance function that can be exploited in classification algorithms. We develop simple versions of such classifiers and test them on several linear and nonlinear problems. On linear…
We present three evolutionary symbolic regression-based classification algorithms for binary and multinomial datasets: GPLearnClf, CartesianClf, and ClaSyCo. Tested over 162 datasets and compared to three state-of-the-art machine learning algorithms -- XGBoost, LightGBM, and a deep neural network -- we find our algorithms to be competitive. Further, we demonstrate how to find the best method for one's dataset automatically, through the use of a state-of-the-art hyperparameter optimizer.
In recent years, deep neural networks have had great success in machine learning and pattern recognition. Architecture size for a neural network contributes significantly to the success of any neural network. In this study, we optimize the selection process by investigating different search algorithms to find a neural network architecture size that yields the highest accuracy. We apply binary search on a very well-defined binary classification network search space and compare the results to those of linear search. We also propose how to relax some of the assumptions regarding the dataset so th…
Can we learn a binary classifier from only positive data, without any negative data or unlabeled data? We show that if one can equip positive data with confidence (positive-confidence), one can successfully learn a binary classifier, which we name positive-confidence (Pconf) classification. Our work is related to one-class classification which is aimed at "describing" the positive class by clustering-related methods, but one-class classification does not have the ability to tune hyper-parameters and their aim is not on "discriminating" positive and negative classes. For the Pconf classificatio…
Classification involves the learning of the mapping function that associates input samples to corresponding target label. There are two major categories of classification problems: Single-label classification and Multi-label classification. Traditional binary and multi-class classifications are sub-categories of single-label classification. Several classifiers are developed for binary, multi-class and multi-label classification problems, but there are no classifiers available in the literature capable of performing all three types of classification. In this paper, a novel online universal clas…
In classification problems, especially those that categorize data into a large number of classes, the classes often naturally follow a hierarchical structure. That is, some classes are likely to share similar structures and features. Those characteristics can be captured by considering a hierarchical relationship among the class labels. Here, we extend a recent simple classification approach on binary data in order to efficiently classify hierarchical data. In certain settings, specifically, when some classes are significantly easier to identify than others, we showcase computational and accur…
In this note, we point out a basic link between generative adversarial (GA) training and binary classification -- any powerful discriminator essentially computes an (f-)divergence between real and generated samples. The result, repeatedly re-derived in decision theory, has implications for GA Networks (GANs), providing an alternative perspective on training f-GANs by designing the discriminator loss function.
School of Computer Science and Engineering, The Hebrew University（计算机科学与工程学院，希伯来大学）；The Hebrew University（希伯来大学）
We present a new approach for mitigating unfairness in learned classifiers. In particular, we focus on binary classification tasks over individuals from two populations, where, as our criterion for fairness, we wish to achieve similar false positive rates in both populations, and similar false negative rates in both populations. As a proof of concept, we implement our approach and empirically evaluate its ability to achieve both fairness and accuracy, using datasets from the fields of criminal risk assessment, credit, lending, and college admissions.
AI Labs, Didi Chuxing（滴滴出行人工智能实验室）；AI Labs, Didi Research America（滴滴美国研究院人工智能实验室）
Multi-class text classification is one of the key problems in machine learning and natural language processing. Emerging neural networks deal with the problem using a multi-output softmax layer and achieve substantial progress, but they do not explicitly learn the correlation among classes. In this paper, we use a multi-task framework to address multi-class classification, where a multi-class classifier and multiple binary classifiers are trained together. Moreover, we employ adversarial training to distinguish the class-specific features and the class-agnostic features. The model benefits fro…
MTA SZTAKI: The Institute for Computer Science and Control, Hungarian Academy of Sciences（匈牙利科学院MTA SZTAKI计算机科学与控制研究所）
The paper studies binary classification and aims at estimating the underlying regression function which is the conditional expectation of the class labels given the inputs. The regression function is the key component of the Bayes optimal classifier, moreover, besides providing optimal predictions, it can also assess the risk of misclassification. We aim at building non-asymptotic confidence regions for the regression function and suggest three kernel-based semi-parametric resampling methods. We prove that all of them guarantee regions with exact coverage probabilities and they are strongly co…
Saint-Petersburg State University（圣彼得堡国立大学）；Research Institute of Influenza（流感研究所）
In this paper there is proposed a generalized version of the SVM for binary classification problems in the case of using an arbitrary transformation x -> y. An approach similar to the classic SVM method is used. The problem is widely explained. Various formulations of primal and dual problems are proposed. For one of the most important cases the formulae are derived in detail. A simple computational example is demonstrated. The algorithm and its implementation is presented in Octave language.
Aalto University（阿尔托大学）；Helsinki Institute for Information Technology HIIT（赫尔辛基信息技术研究所HIIT）
Our study revisits the problem of accuracy-fairness tradeoff in binary classification. We argue that comparison of non-discriminatory classifiers needs to account for different rates of positive predictions, otherwise conclusions about performance may be misleading, because accuracy and discrimination of naive baselines on the same dataset vary with different rates of positive predictions. We provide methodological recommendations for sound comparison of non-discriminatory classifiers, and present a brief theoretical and empirical analysis of tradeoffs between accuracy and non-discrimination.
Dimension reduction and data quantization are two important methods for reducing data complexity. In the paper, we study the methodology of first reducing data dimension by random projection and then quantizing the projections to ternary or binary codes, which has been widely applied in classification. Usually, the quantization will seriously degrade the accuracy of classification due to high quantization errors. Interestingly, however, we observe that the quantization could provide comparable and often superior accuracy, as the data to be quantized are sparse features generated with common fi…
Unified Binary and Multiclass Margin-Based Classification
University of Michigan（密歇根大学）；Department of Electrical Engineering and Computer Science（电气工程与计算机科学系）；Michigan Institute of Data Science（密歇根数据科学研究所）；Department of Statistics（统计学系）
University of Insubria（因苏布里亚大学）；University of Essex（埃塞克斯大学）
One-class classifiers are trained with target class only samples. Intuitively, their conservative modelling of the class description may benefit classical classification tasks where classes are difficult to separate due to overlapping and data imbalance. In this work, three methods are proposed which leverage on the combination of one-class classifiers based on non-parametric models, N-ary Trees and Minimum Spanning Trees class descriptors (MST-CD), to tackle binary classification problems. The methods deal with the inconsistencies arising from combining multiple classifiers and with spurious …
Technical University of Munich（慕尼黑工业大学）；Munich Center for Quantum Science and Technology（慕尼黑量子科学与技术中心）
In classical statistical learning theory, one of the most well studied problems is that of binary classification. The information-theoretic sample complexity of this task is tightly characterized by the Vapnik-Chervonenkis (VC) dimension. A quantum analog of this task, with training data given as a quantum state has also been intensely studied and is now known to have the same sample complexity as its classical counterpart. We propose a novel quantum version of the classical binary classification task by considering maps with classical input and quantum output and corresponding classical-quant…
We study universal consistency of non-i.i.d. processes in the context of online learning. A stochastic process is said to admit universal consistency if there exists a learner that achieves vanishing average loss for any measurable response function on this process. When the loss function is unbounded, Blanchard et al. showed that the only processes admitting strong universal consistency are those taking a finite number of values almost surely. However, when the loss function is bounded, the class of processes admitting strong universal consistency is much richer and its characterization could…
We propose a quantum representation of binary classification trees with binary features based on a probabilistic approach. By using the quantum computer as a processor for probability distributions, a probabilistic traversal of the decision tree can be realized via measurements of a quantum circuit. We describe how tree inductions and the prediction of class labels of query data can be integrated into this framework. An on-demand sampling method enables predictions with a constant number of classical memory slots, independent of the tree depth. We experimentally study our approach using both a…
A Generalised Exponentiated Gradient Approach to Enhance Fairness in Binary and Multi-class Classification Tasks
Laboratoire d’Intelligence Artificielle et Systèmes Industriels (LIASI), HESTIM Engineering and Business School（人工智能与工业系统实验室（LIASI），HESTIM工程与商业学院）；Laboratory LAMAI, Faculty of Sciences and Technologies, Cadi Ayyad University（LAMAI实验室，科学与技术学院，卡迪·阿亚德大学）；Department of Information Engineering, Computer Science and Mathematics, University of L'Aquila（信息工程、计算机科学与数学系，拉奎拉大学）
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
In today's data driven world, storing, processing, and gleaning insights from large-scale data are major challenges. Data compression is often required in order to store large amounts of high-dimensional data, and thus, efficient inference methods for analyzing compressed data are necessary. Building on a recently designed simple framework for classification using binary data, we demonstrate that one can improve classification accuracy of this approach through iterative applications whose output serves as input to the next application. As a side consequence, we show that the original framework…
Gordon Center for Medical Imaging（戈登医学影像中心）；Center for Advanced Medical Computing and Analysis（高级医学计算与分析中心）；Massachusetts General Hospital（麻省总医院）；Harvard Medical School（哈佛医学院）
Deterministic solutions are becoming more critical for interpretability. Weighted Least-Squares (WLS) has been widely used as a deterministic batch solution with a specific weight design. In the online settings of WLS, exact reweighting is necessary to converge to its batch settings. In order to comply with its necessity, the iteratively reweighted least-squares algorithm is mainly utilized with a linearly growing time complexity which is not attractive for online learning. Due to the high and growing computational costs, an efficient online formulation of reweighted least-squares is desired. …
Despite the enormous success of machine learning models in various applications, most of these models lack resilience to (even small) perturbations in their input data. Hence, new methods to robustify machine learning models seem very essential. To this end, in this paper we consider the problem of binary classification with adversarial perturbations. Investigating the solution to a min-max optimization (which considers the worst-case loss in the presence of adversarial perturbations) we introduce a generalization to the max-margin classifier which takes into account the power of the adversary…
University of Oxford（牛津大学）；UiT The Arctic University of Norway（挪威特罗姆瑟大学（北极大学））；Carnegie Mellon University（卡内基梅隆大学）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）
Entanglement is a physical phenomenon, which has fueled recent successes of quantum algorithms. Although quantum neural networks (QNNs) have shown promising results in solving simple machine learning tasks recently, for the time being, the effect of entanglement in QNNs and the behavior of QNNs in binary pattern classification are still underexplored. In this work, we provide some theoretical insight into the properties of QNNs by presenting and analyzing a new form of invariance embedded in QNNs for both quantum binary classification and quantum representation learning, which we term negation…
Loss functions drive the optimization of machine learning algorithms. The choice of a loss function can have a significant impact on the training of a model, and how the model learns the data. Binary classification is one of the major pillars of machine learning problems, used in medical imaging to failure detection applications. The most commonly used surrogate loss functions for binary classification include the binary cross-entropy and the hinge loss functions, which form the focus of our study. In this paper, we provide an overview of a novel loss function, the Xtreme Margin loss function.…
Compared to Multilayer Neural Networks with real weights, Binary Multilayer Neural Networks (BMNNs) can be implemented more efficiently on dedicated hardware. BMNNs have been demonstrated to be effective on binary classification tasks with Expectation BackPropagation (EBP) algorithm on high dimensional text datasets. In this paper, we investigate the capability of BMNNs using the EBP algorithm on multiclass image classification tasks. The performances of binary neural networks with multiple hidden layers and different numbers of hidden units are examined on MNIST. We also explore the effective…
We propose a new approach to address the text classification problems when learning with partial labels is beneficial. Instead of offering each training sample a set of candidate labels, we assign negative-oriented labels to the ambiguous training examples if they are unlikely fall into certain classes. We construct our new maximum likelihood estimators with self-correction property, and prove that under some conditions, our estimators converge faster. Also we discuss the advantages of applying one of our estimator to a fully supervised learning problem. The proposed method has potential appli…
Nagoya University（名古屋大学）；Human Dataware Lab. Co.（Human Dataware Lab. 公司）
An anomalous sound detection system to detect unknown anomalous sounds usually needs to be built using only normal sound data. Moreover, it is desirable to improve the system by effectively using a small amount of anomalous sound data, which will be accumulated through the system's operation. As one of the methods to meet these requirements, we focus on a binary classification model that is developed by using not only normal data but also outlier data in the other domains as pseudo-anomalous sound data, which can be easily updated by using anomalous data. In this paper, we implement a new loss…
Carnegie Mellon University（卡内基梅隆大学）；University of Cambridge（剑桥大学）；MPI for Intelligent Systems（马克斯·普朗克智能系统研究所）；Alan Turing Institute（艾伦·图灵研究所）
State-of-the-art deep face recognition methods are mostly trained with a softmax-based multi-class classification framework. Despite being popular and effective, these methods still have a few shortcomings that limit empirical performance. In this paper, we start by identifying the discrepancy between training and evaluation in the existing multi-class classification framework and then discuss the potential limitations caused by the "competitive" nature of softmax normalization. Motivated by these limitations, we propose a novel binary classification training framework, termed SphereFace2. In …
