Ordinal regression with anchored reference samples (ORARS) has been proposed for predicting the subjective Mean Opinion Score (MOS) of input stimuli automatically. The ORARS addresses the MOS prediction problem by pairing a test sample with each of the pre-scored anchored reference samples. A trained binary classifier is then used to predict which sample, test or anchor, is better statistically. Posteriors of the binary preference decision are then used to predict the MOS of the test sample. In this paper, rigorous framework, analysis, and experiments to demonstrate that ORARS are advantageous over simple regressions are presented. The contributions of this work are: 1) Show that traditional regression can be reformulated into multiple preference tests to yield a better performance, which is confirmed with simulations experimentally; 2) Generalize ORARS to other regression problems and verify its effectiveness; 3) Provide some prerequisite conditions which can insure proper application of ORARS.
In this work, we present a regression-based ordinal regression algorithm for supervised classification of instances into ordinal categories. In contrast to previous methods, in this work the decision boundaries between categories are predefined, and the algorithm learns to project the input examples onto their appropriate scores according to these predefined boundaries. This is achieved by adding a novel threshold-based pairwise loss function that aims at minimizing the regression error, which in turn minimizes the Mean Absolute Error (MAE) measure. We implemented our proposed architecture-agn…
Booz Allen Hamilton（博思艾伦汉密尔顿）；Univ. of Maryland, Baltimore County（马里兰大学巴尔的摩县分校）
Ordinal regression is a classification task where classes have an order and prediction error increases the further the predicted class is from the true class. The standard approach for modeling ordinal data involves fitting parallel separating hyperplanes that optimize a certain loss function. This assumption offers sample efficient learning via inductive bias, but is often too restrictive in real-world datasets where features may have varying effects across different categories. Allowing class-specific hyperplane slopes creates generalized logistic ordinal regression, increasing the flexibili…
Indiana University-Purdue University Indianapolis（印第安纳大学与普渡大学印第安纳波利斯联合分校）；eBay Inc.（易贝公司）
Query similarity prediction task is generally solved by regression based models with square loss. Such a model is agnostic of absolute similarity values and it penalizes the regression error at all ranges of similarity values at the same scale. However, to boost e-commerce platform's monetization, it is important to predict high-level similarity more accurately than low-level similarity, as highly similar queries retrieves items according to user-intents, whereas moderately similar item retrieves related items, which may not lead to a purchase. Regression models fail to customize its loss func…
The real-world data is often susceptible to label noise, which might constrict the effectiveness of the existing state of the art algorithms for ordinal regression. Existing works on ordinal regression do not take label noise into account. We propose a theoretically grounded approach for class conditional label noise in ordinal regression problems. We present a deep learning implementation of two commonly used loss functions for ordinal regression that is both - 1) robust to label noise, and 2) rank consistent for a good ranking rule. We verify these properties of the algorithm empirically and…
INRIA（法国国家信息与自动化研究所）；École normale supérieure（巴黎高等师范学院）；CNRS（法国国家科学研究中心）；PSL Research University（巴黎文理研究大学）；Télécom ParisTech（巴黎高等电信学院）；Université Paris-Saclay（巴黎萨克雷大学）
Many of the ordinal regression models that have been proposed in the literature can be seen as methods that minimize a convex surrogate of the zero-one, absolute, or squared loss functions. A key property that allows to study the statistical implications of such approximations is that of Fisher consistency. Fisher consistency is a desirable property for surrogate loss functions and implies that in the population setting, i.e., if the probability distribution that generates the data were available, then optimization of the surrogate would yield the best possible model. In this paper we will cha…
Despite the pervasiveness of ordinal labels in supervised learning, it remains common practice in deep learning to treat such problems as categorical classification using the categorical cross entropy loss. Recent methods attempting to address this issue while respecting the ordinal structure of the labels have resorted to converting ordinal regression into a series of extended binary classification subtasks. However, the adoption of such methods remains inconsistent due to theoretical and practical limitations. Here we address these limitations by demonstrating that the subtask probabilities …
StepMania is a popular open-source clone of a rhythm-based video game. As is common in popular games, there is a large number of community-designed levels. It is often difficult for players and level authors to determine the difficulty level of such community contributions. In this work, we formalize and analyze the difficulty prediction task on StepMania levels as an ordinal regression (OR) task. We standardize a more extensive and diverse selection of this data resulting in five data sets, two of which are extensions of previous work. We evaluate many competitive OR and non-OR models, demons…
Contrastive Learning for Semi-Supervised Deep Regression with Generalized Ordinal Rankings from Spectral Seriation
Department of Electronic and Computer Engineering, The Hong Kong University of Science and Technology（香港科学与技术大学电子与计算机工程系）；School of Science, Sun Yat-sen University（中山大学科学学院）；Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University（复旦大学脑启发式智能科学与技术研究院）
Many real-world datasets are labeled with natural orders, i.e., ordinal labels. Ordinal regression is a method to predict ordinal labels that finds a wide range of applications in data-rich domains, such as natural, health and social sciences. Most existing ordinal regression approaches work well for independent and identically distributed (IID) instances via formulating a single ordinal regression task. However, for heterogeneous non-IID instances with well-defined local geometric structures, e.g., subpopulation groups, multi-task learning (MTL) provides a promising framework to encode task (…
University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；Michigan State University（密歇根州立大学）
In many real-world prediction tasks, class labels include information about the relative ordering between labels, which is not captured by commonly-used loss functions such as multi-category cross-entropy. Recently, the deep learning community adopted ordinal regression frameworks to take such ordering information into account. Neural networks were equipped with ordinal regression capabilities by transforming ordinal targets into binary classification subtasks. However, this method suffers from inconsistencies among the different binary classifiers. To resolve these inconsistencies, we propose…
Tsinghua University（清华大学）；Beijing National Research Center for Information Science and Technology（北京信息科学与技术国家研究中心）；Beijing Normal University（北京师范大学）
Uncertainty is the only certainty there is. Modeling data uncertainty is essential for regression, especially in unconstrained settings. Traditionally the direct regression formulation is considered and the uncertainty is modeled by modifying the output space to a certain family of probabilistic distributions. On the other hand, classification based regression and ranking based solutions are more popular in practice while the direct regression methods suffer from the limited performance. How to model the uncertainty within the present-day technologies for regression remains an open issue. In t…
This study presents an Ordinal version of Residual Logit (Ordinal-ResLogit) model to investigate the ordinal responses. We integrate the standard ResLogit model into COnsistent RAnk Logits (CORAL) framework, classified as a binary classification algorithm, to develop a fully interpretable deep learning-based ordinal regression model. As the formulation of the Ordinal-ResLogit model enjoys the Residual Neural Networks concept, our proposed model addresses the main constraint of machine learning algorithms, known as black-box. Moreover, the Ordinal-ResLogit model, as a binary classification fram…
The University of Tokyo（东京大学）；RIKEN AIP（理化学研究所先进智能项目中心）；Kyoto University（京都大学）
Ordinal regression is aimed at predicting an ordinal class label. In this paper, we consider its semi-supervised formulation, in which we have unlabeled data along with ordinal-labeled data to train an ordinal regressor. There are several metrics to evaluate the performance of ordinal regression, such as the mean absolute error, mean zero-one error, and mean squared error. However, the existing studies do not take the evaluation metric into account, have a restriction on the model choice, and have no theoretical guarantee. To overcome these problems, we propose a novel generic framework for se…
Deep neural networks are a family of computational models that are naturally suited to the analysis of hierarchical data such as, for instance, sequential data with the use of recurrent neural networks. In the other hand, ordinal regression is a well-known predictive modelling problem used in fields as diverse as psychometry to deep neural network based voice modelling. Their specificity lies in the properties of their outcome variable, typically considered as a categorical variable with natural ordering properties, typically allowing comparisons between different states ("a little" is less th…
This paper extends the class of ordinal regression models with a structured interpretation of the problem by applying a novel treatment of encoded labels. The net effect of this is to transform the underlying problem from an ordinal regression task to a (structured) classification task which we solve with conditional random fields, thereby achieving a coherent and probabilistic model in which all model parameters are jointly learnt. Importantly, we show that although we have cast ordinal regression to classification, our method still fall within the class of decomposition methods in the ordina…
It is often desired that ordinal regression models yield unimodal predictions. However, in many recent works this characteristic is either absent, or implemented using soft targets, which do not guarantee unimodal outputs at inference. In addition, we argue that the standard maximum likelihood objective is not suitable for ordinal regression problems, and that optimal transport is better suited for this task, as it naturally captures the order of the classes. In this work, we propose a framework for deep ordinal regression, based on unimodal output distribution and optimal transport loss. Insp…
National University of Singapore（新加坡国立大学）；Huawei International Pte Ltd（华为国际私人有限公司）
In computer vision, it is often observed that formulating regression problems as a classification task often yields better performance. We investigate this curious phenomenon and provide a derivation to show that classification, with the cross-entropy loss, outperforms regression with a mean squared error loss in its ability to learn high-entropy feature representations. Based on the analysis, we propose an ordinal entropy loss to encourage higher-entropy feature spaces while maintaining ordinal relationships to improve the performance of regression tasks. Experiments on synthetic and real-wor…
Bielefeld University（比勒费尔德大学）；University of Groningen（格罗宁根大学）；University of Birmingham（伯明翰大学）
The increasing occurrence of ordinal data, mainly sociodemographic, led to a renewed research interest in ordinal regression, i.e. the prediction of ordered classes. Besides model accuracy, the interpretation of these models itself is of high relevance, and existing approaches therefore enforce e.g. model sparsity. For high dimensional or highly correlated data, however, this might be misleading due to strong variable dependencies. In this contribution, we aim for an identification of feature relevance bounds which - besides identifying all relevant features - explicitly differentiates between…
University of Zurich（苏黎世大学）；Zurich University of Applied Sciences（苏黎世应用科学大学）；Konstanz University of Applied Sciences（康斯坦茨应用科学大学）
Outcomes with a natural order commonly occur in prediction tasks and often the available input data are a mixture of complex data like images and tabular predictors. Deep Learning (DL) models are state-of-the-art for image classification tasks but frequently treat ordinal outcomes as unordered and lack interpretability. In contrast, classical ordinal regression models consider the outcome's order and yield interpretable predictor effects but are limited to tabular data. We present ordinal neural network transformation models (ONTRAMs), which unite DL with classical ordinal regression approache…
We initiate the study of fairness for ordinal regression. We adapt two fairness notions previously considered in fair ranking and propose a strategy for training a predictor that is approximately fair according to either notion. Our predictor has the form of a threshold model, composed of a scoring function and a set of thresholds, and our strategy is based on a reduction to fair binary classification for learning the scoring function and local search for choosing the thresholds. We provide generalization guarantees on the error and fairness violation of our predictor, and we illustrate the ef…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；University of Pennsylvania（宾夕法尼亚大学）
In applications such as recommendation systems and revenue management, it is important to predict preferences on items that have not been seen by a user or predict outcomes of comparisons among those that have never been compared. A popular discrete choice model of multinomial logit model captures the structure of the hidden preferences with a low-rank matrix. In order to predict the preferences, we want to learn the underlying model from noisy observations of the low-rank matrix, collected as revealed preferences in various forms of ordinal data. A natural approach to learn such a model is to…
Ordinal Regression (OR) aims to model the ordering information between different data categories, which is a crucial topic in multi-label learning. An important class of approaches to OR models the problem as a linear combination of basis functions that map features to a high dimensional non-linear space. However, most of the basis function-based algorithms are time consuming. We propose an incremental sparse Bayesian approach to OR tasks and introduce an algorithm to sequentially learn the relevant basis functions in the ordinal scenario. Our method, called Incremental Sparse Bayesian Ordinal…
Ordinal regression falls between discrete-valued classification and continuous-valued regression. Ordinal target variables can be associated with ranked random variables. These random variables are known as order statistics and they are closely related to ordinal regression. However, the challenge of using order statistics for ordinal regression prediction is finding a suitable parent distribution. In this work, we provide a case study of a real-world orienteering relay race by viewing it as a random process. For this process, we show that accurate order statistical ordinal regression predicti…
Nanjing University of Information Science & Technology（南京信息工程大学）；JD Finance America Corporation（京东金融美国公司）；University of Western Ontario（西安大略大学）；University of Pittsburgh（匹兹堡大学）
Semi-supervised ordinal regression (S$^2$OR) problems are ubiquitous in real-world applications, where only a few ordered instances are labeled and massive instances remain unlabeled. Recent researches have shown that directly optimizing concordance index or AUC can impose a better ranking on the data than optimizing the traditional error rate in ordinal regression (OR) problems. In this paper, we propose an unbiased objective function for S$^2$OR AUC optimization based on ordinal binary decomposition approach. Besides, to handle the large-scale kernelized learning problems, we propose a scala…
We develop a novel probabilistic generative model based on the variational autoencoder approach. Notable aspects of our architecture are: a novel way of specifying the latent variables prior, and the introduction of an ordinality enforcing unit. We describe how to do supervised, unsupervised and semi-supervised learning, and nominal and ordinal classification, with the model. We analyze generative properties of the approach, and the classification effectiveness under nominal and ordinal classification, using two benchmark datasets. Our results show that our model can achieve comparable results…
Classifying Phonotrauma Severity from Vocal Fold Images with Soft Ordinal Regression
Massachusetts Institute of Technology（麻省理工学院）；School of Communication Sciences and Disorders University of Central Florida（中央佛罗里达大学通信科学与障碍学系）；Harvard Medical School（哈佛医学院）；Massachusetts General Hospital（麻省总医院）；Center for Laryngeal Surgery and Voice Rehabilitation（嗓音外科与嗓音康复中心）；Department of Surgery（外科部门）；Institute of Health Professions（健康专业研究所）；Athinoula Martinos Center（阿提尼奥拉马丁诺斯中心）
Institute of Digital Games, University of Malta（马耳他大学数字游戏研究所）
Preference learning (PL) is a core area of machine learning that handles datasets with ordinal relations. As the number of generated data of ordinal nature is increasing, the importance and role of the PL field becomes central within machine learning research and practice. This paper introduces an open source, scalable, efficient and accessible preference learning toolbox that supports the key phases of the data training process incorporating various popular data preprocessing, feature selection and preference learning methods.
North Carolina State University（北卡罗来纳州立大学）；Alexa AI, Amazon（亚马逊Alexa人工智能部门）；Global Emancipation Network（全球解放网络）
Sex trafficking is a global epidemic. Escort websites are a primary vehicle for selling the services of such trafficking victims and thus a major driver of trafficker revenue. Many law enforcement agencies do not have the resources to manually identify leads from the millions of escort ads posted across dozens of public websites. We propose an ordinal regression neural network to identify escort ads that are likely linked to sex trafficking. Our model uses a modified cost function to mitigate inconsistencies in predictions often associated with nonparametric ordinal regression and leverages re…
Xidian University（西安电子科技大学）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）
To build recommender systems that not only consider user-item interactions represented as ordinal variables, but also exploit the social network describing the relationships between the users, we develop a hierarchical Bayesian model termed ordinal graph factor analysis (OGFA), which jointly models user-item and user-user interactions. OGFA not only achieves good recommendation performance, but also extracts interpretable latent factors corresponding to representative user preferences. We further extend OGFA to ordinal graph gamma belief network, which is a multi-stochastic-layer deep probabil…
Machine Learning Department（机器学习系）；Department of Statistics and Data Science（统计与数据科学系）；Auton Lab, The Robotics Institute（奥顿实验室（机器人研究所））；Carnegie Mellon University（卡内基梅隆大学）
In supervised learning, we typically leverage a fully labeled dataset to design methods for function estimation or prediction. In many practical situations, we are able to obtain alternative feedback, possibly at a low cost. A broad goal is to understand the usefulness of, and to design algorithms to exploit, this alternative feedback. In this paper, we consider a semi-supervised regression setting, where we obtain additional ordinal (or comparison) information for the unlabeled samples. We consider ordinal feedback of varying qualities where we have either a perfect ordering of the samples, a…
University of Chinese Academy of Sciences（中国科学院大学）；The Chinese University of Hong Kong（香港中文大学）
Ordinal regression (OR) is a special multiclass classification problem where an order relation exists among the labels. Recent years, people share their opinions and sentimental judgments conveniently with social networks and E-Commerce so that plentiful large-scale OR problems arise. However, few studies have focused on this kind of problems. Nonparallel Support Vector Ordinal Regression (NPSVOR) is a SVM-based OR model, which learns a hyperplane for each rank by solving a series of independent sub-optimization problems and then ensembles those learned hyperplanes to predict. The previous stu…
University of Oxford（牛津大学）；Mind Foundry Ltd.（思维铸造有限公司）
Recurrent neural networks (RNNs) are state-of-the-art in several sequential learning tasks, but they often require considerable amounts of data to generalise well. For many time series forecasting (TSF) tasks, only a few dozens of observations may be available at training time, which restricts use of this class of models. We propose a novel RNN-based model that directly addresses this problem by learning a shared feature embedding over the space of many quantised time series. We show how this enables our RNN framework to accurately and reliably forecast unseen time series, even when there is l…
Arm Research（安谋研究）；Center for Mathematical Sciences, Lund University（隆德大学数学科学中心）
Regression via classification (RvC) is a common method used for regression problems in deep learning, where the target variable belongs to a set of continuous values. By discretizing the target into a set of non-overlapping classes, it has been shown that training a classifier can improve neural network accuracy compared to using a standard regression approach. However, it is not clear how the set of discrete classes should be chosen and how it affects the overall solution. In this work, we propose that using several discrete data representations simultaneously can improve neural network learn…
Xi’an Jiaotong University（西安交通大学）；City University of Hong Kong（香港城市大学）
Ordinal regression predicts the objects' labels that exhibit a natural ordering, which is important to many managerial problems such as credit scoring and clinical diagnosis. In these problems, the ability to explain how the attributes affect the prediction is critical to users. However, most, if not all, existing ordinal regression models simplify such explanation in the form of constant coefficients for the main and interaction effects of individual attributes. Such explanation cannot characterize the contributions of attributes at different value scales. To address this challenge, we propos…
Sentence level pronunciation assessment is important for Computer Assisted Language Learning (CALL). Traditional speech pronunciation assessment, based on the Goodness of Pronunciation (GOP) algorithm, has some weakness in assessing a speech utterance: 1) Phoneme GOP scores cannot be easily translated into a sentence score with a simple average for effective assessment; 2) The rank ordering information has not been well exploited in GOP scoring for delivering a robust assessment and correlate well with a human rater's evaluations. In this paper, we propose two new statistical features, average…
MIT Computer Science and Artificial Intelligence Laboratory（麻省理工学院计算机科学与人工智能实验室）；SiteGround Hosting EOOD（SiteGround托管有限责任公司）；Harvard University（哈佛大学）；Qatar Computing Research Institute, HBKU（哈马德·本·哈利法大学卡塔尔计算研究所）
In the context of fake news, bias, and propaganda, we study two important but relatively under-explored problems: (i) trustworthiness estimation (on a 3-point scale) and (ii) political ideology detection (left/right bias on a 7-point scale) of entire news outlets, as opposed to evaluating individual articles. In particular, we propose a multi-task ordinal regression framework that models the two problems jointly. This is motivated by the observation that hyper-partisanship is often linked to low trustworthiness, e.g., appealing to emotions rather than sticking to the facts, while center media …
Prognostics or Remaining Useful Life (RUL) Estimation from multi-sensor time series data is useful to enable condition-based maintenance and ensure high operational availability of equipment. We propose a novel deep learning based approach for Prognostics with Uncertainty Quantification that is useful in scenarios where: (i) access to labeled failure data is scarce due to rarity of failures (ii) future operational conditions are unobserved and (iii) inherent noise is present in the sensor readings. All three scenarios mentioned are unavoidable sources of uncertainty in the RUL estimation proce…
