The problem of estimating subjective visual properties (SVP) of images (e.g., Shoes A is more comfortable than B) is gaining rising attention. Due to its highly subjective nature, different annotators often exhibit different interpretations of scales when adopting absolute value tests. Therefore, recent investigations turn to collect pairwise comparisons via crowdsourcing platforms. However, crowdsourcing data usually contains outliers. For this purpose, it is desired to develop a robust model for learning SVP from crowdsourced noisy annotations. In this paper, we construct a deep SVP prediction model which not only leads to better detection of annotation outliers but also enables learning with extremely sparse annotations. Specifically, we construct a comparison multi-graph based on the collected annotations, where different labeling results correspond to edges with different directions between two vertexes. Then, we propose a generalized deep probabilistic framework which consists of an SVP prediction module and an outlier modeling module that work collaboratively and are optimized jointly. Extensive experiments on various benchmark datasets demonstrate that our new approach guarantees promising results.
Existing ordinal embedding methods usually follow a two-stage routine: outlier detection is first employed to pick out the inconsistent comparisons; then an embedding is learned from the clean data. However, learning in a multi-stage manner is well-known to suffer from sub-optimal solutions. In this paper, we propose a unified framework to jointly identify the contaminated comparisons and derive reliable embeddings. The merits of our method are three-fold: (1) By virtue of the proposed unified framework, the sub-optimality of traditional methods is largely alleviated; (2) The proposed method is aware of global inconsistency by minimizing a corresponding cost, while traditional methods only involve local inconsistency; (3) Instead of considering the nuclear norm heuristics, we adopt an exact solution for rank equality constraint. Our studies are supported by experiments with both simulated examples and real-world data. The proposed framework provides us a promising tool for robust ordinal embedding from the contaminated comparisons.
In the absence of prior knowledge, ordinal embedding methods obtain new representation for items in a low-dimensional Euclidean space via a set of quadruple-wise comparisons. These ordinal comparisons often come from human annotators, and sufficient comparisons induce the success of classical approaches. However, collecting a large number of labeled data is known as a hard task, and most of the existing work pay little attention to the generalization ability with insufficient samples. Meanwhile, recent progress in large margin theory discloses that rather than just maximizing the minimum margin, both the margin mean and variance, which characterize the margin distribution, are more crucial to the overall generalization performance. To address the issue of insufficient training samples, we propose a margin distribution learning paradigm for ordinal embedding, entitled Distributional Margin based Ordinal Embedding (\textit{DMOE}). Precisely, we first define the margin for ordinal embedding problem. Secondly, we formulate a concise objective function which avoids maximizing margin mean and minimizing margin variance directly but exhibits the similar effect. Moreover, an Augmented Lagrange Multiplier based algorithm is customized to seek the optimal solution of \textit{DMOE} effectively. Experimental studies on both simulated and real-world datasets are provided to show the effectiveness of the proposed algorithm.
Visual attributes, which refer to human-labeled semantic annotations, have gained increasing popularity in a wide range of real world applications. Generally, the existing attribute learning methods fall into two categories: one focuses on learning user-specific labels separately for different attributes, while the other one focuses on learning crowd-sourced global labels jointly for multiple attributes. However, both categories ignore the joint effect of the two mentioned factors: the personal diversity with respect to the global consensus; and the intrinsic correlation among multiple attributes. To overcome this challenge, we propose a novel model to learn user-specific predictors across multiple attributes. In our proposed model, the diversity of personalized opinions and the intrinsic relationship among multiple attributes are unified in a common-to-special manner. To this end, we adopt a three-component decomposition. Specifically, our model integrates a common cognition factor, an attribute-specific bias factor and a user-specific bias factor. Meanwhile Lasso and group Lasso penalties are adopted to leverage efficient feature selection. Furthermore, theoretical analysis is conducted to show that our proposed method could reach reasonable performance. Eventually, the empirical study carried out in this paper demonstrates the effectiveness of our proposed method.
A preference order or ranking aggregated from pairwise comparison data is commonly understood as a strict total order. However, in real-world scenarios, some items are intrinsically ambiguous in comparisons, which may very well be an inherent uncertainty of the data. In this case, the conventional total order ranking can not capture such uncertainty with mere global ranking or utility scores. In this paper, we are specifically interested in the recent surge in crowdsourcing applications to predict partial but more accurate (i.e., making less incorrect statements) orders rather than complete ones. To do so, we propose a novel framework to learn some probabilistic models of partial orders as a \emph{margin-based Maximum Likelihood Estimate} (MLE) method. We prove that the induced MLE is a joint convex optimization problem with respect to all the parameters, including the global ranking scores and margin parameter. Moreover, three kinds of generalized linear models are studied, including the basic uniform model, Bradley-Terry model, and Thurstone-Mosteller model, equipped with some theoretical analysis on FDR and Power control for the proposed methods. The validity of these models are supported by experiments with both simulated and real-world datasets, which shows that the proposed models exhibit improvements compared with traditional state-of-the-art algorithms.
In crowdsourced preference aggregation, it is often assumed that all the annotators are subject to a common preference or social utility function which generates their comparison behaviors in experiments. However, in reality annotators are subject to variations due to multi-criteria, abnormal, or a mixture of such behaviors. In this paper, we propose a parsimonious mixed-effects model, which takes into account both the fixed effect that the majority of annotators follows a common linear utility model, and the random effect that some annotators might deviate from the common significantly and exhibit strongly personalized preferences. The key algorithm in this paper establishes a dynamic path from the social utility to individual variations, with different levels of sparsity on personalization. The algorithm is based on the Linearized Bregman Iterations, which leads to easy parallel implementations to meet the need of large-scale data analysis. In this unified framework, three kinds of random utility models are presented, including the basic linear model with L2 loss, Bradley-Terry model, and Thurstone-Mosteller model. The validity of these multi-level models are supported by experiments with both simulated and real-world datasets, which shows that the parsimonious multi-level models exhibit improvements in both interpretability and predictive precision compared with traditional HodgeRank.
Learning representation from relative similarity comparisons, often called ordinal embedding, gains rising attention in recent years. Most of the existing methods are batch methods designed mainly based on the convex optimization, say, the projected gradient descent method. However, they are generally time-consuming due to that the singular value decomposition (SVD) is commonly adopted during the update, especially when the data size is very large. To overcome this challenge, we propose a stochastic algorithm called SVRG-SBB, which has the following features: (a) SVD-free via dropping convexity, with good scalability by the use of stochastic algorithm, i.e., stochastic variance reduced gradient (SVRG), and (b) adaptive step size choice via introducing a new stabilized Barzilai-Borwein (SBB) method as the original version for convex problems might fail for the considered stochastic \textit{non-convex} optimization problem. Moreover, we show that the proposed algorithm converges to a stationary point at a rate $\mathcal{O}(\frac{1}{T})$ in our setting, where $T$ is the number of total iterations. Numerous simulations and real-world data experiments are conducted to show the effectiveness of the proposed algorithm via comparing with the state-of-the-art methods, particularly, much lower computational cost with good prediction performance.
Recently, crowdsourcing has emerged as an effective paradigm for human-powered large scale problem solving in various domains. However, task requester usually has a limited amount of budget, thus it is desirable to have a policy to wisely allocate the budget to achieve better quality. In this paper, we study the principle of information maximization for active sampling strategies in the framework of HodgeRank, an approach based on Hodge Decomposition of pairwise ranking data with multiple workers. The principle exhibits two scenarios of active sampling: Fisher information maximization that leads to unsupervised sampling based on a sequential maximization of graph algebraic connectivity without considering labels; and Bayesian information maximization that selects samples with the largest information gain from prior to posterior, which gives a supervised sampling involving the labels collected. Experiments show that the proposed methods boost the sampling efficiency as compared to traditional sampling schemes and are thus valuable to practical crowdsourcing experiments.
Outlier detection is a crucial part of robust evaluation for crowdsourceable assessment of Quality of Experience (QoE) and has attracted much attention in recent years. In this paper, we propose some simple and fast algorithms for outlier detection and robust QoE evaluation based on the nonconvex optimization principle. Several iterative procedures are designed with or without knowing the number of outliers in samples. Theoretical analysis is given to show that such procedures can reach statistically good estimates under mild conditions. Finally, experimental results with simulated and real-world crowdsourcing datasets show that the proposed algorithms could produce similar performance to Huber-LASSO approach in robust ranking, yet with nearly 8 or 90 times speed-up, without or with a prior knowledge on the sparsity size of outliers, respectively. Therefore the proposed methodology provides us a set of helpful tools for robust QoE evaluation with crowdsourcing data.
In crowdsourced preference aggregation, it is often assumed that all the annotators are subject to a common preference or utility function which generates their comparison behaviors in experiments. However, in reality annotators are subject to variations due to multi-criteria, abnormal, or a mixture of such behaviors. In this paper, we propose a parsimonious mixed-effects model based on HodgeRank, which takes into account both the fixed effect that the majority of annotators follows a common linear utility model, and the random effect that a small subset of annotators might deviate from the common significantly and exhibits strongly personalized preferences. HodgeRank has been successfully applied to subjective quality evaluation of multimedia and resolves pairwise crowdsourced ranking data into a global consensus ranking and cyclic conflicts of interests. As an extension, our proposed methodology further explores the conflicts of interests through the random effect in annotator specific variations. The key algorithm in this paper establishes a dynamic path from the common utility to individual variations, with different levels of parsimony or sparsity on personalization, based on newly developed Linearized Bregman Algorithms with Inverse Scale Space method. Finally the validity of the methodology are supported by experiments with both simulated examples and three real-world crowdsourcing datasets, which shows that our proposed method exhibits better performance (i.e. smaller test error) compared with HodgeRank due to its parsimonious property.