On the optimality of classifier chain for multi-label classification

To capture the interdependencies between labels in multi-label classification problems, classifier chain (CC) tries to take the multiple labels of each instance into account under a deterministic high-order Markov Chain model. Since its performance is sensitive to the choice of label order, the key issue is how to determine the optimal label order for CC. In this work, we first generalize the CC model over a random label order. Then, we present a theoretical analysis of the generalization error for the proposed generalized model. Based on our results, we propose a dynamic programming based classifier chain (CC-DP) algorithm to search the globally optimal label order for CC and a greedy classifier chain (CC-Greedy) algorithm to find a locally optimal CC. Comprehensive experiments on a number of real-world multi-label data sets from various domains demonstrate that our proposed CC-DP algorithm outperforms state-of-the-art approaches and the CC-Greedy algorithm achieves comparable prediction performance with CC-DP

Learning to locate relative outliers

Outliers usually spread across regions of low density. However, due to the absence or scarcity of outliers, designing a robust detector to sift outliers from a given dataset is still very challenging. In this paper, we consider to identify relative outliers from the target dataset with respect to another reference dataset of normal data. Particularly, we employ Maximum Mean Discrepancy (MMD) for matching the distribution between these two datasets and present a novel learning framework to learn a relative outlier detector. The learning task is formulated as a Mixed Integer Programming (MIP) problem, which is computationally hard. To this end, we propose an effective procedure to find a largely violated labeling vector for identifying relative outliers from abundant normal patterns, and its convergence is also presented. Then, a set of largely violated labeling vectors are combined by multiple kernel learning methods to robustly locate relative outliers. Comprehensive empirical studies on real-world datasets verify that our proposed relative outlier detection outperforms existing methods. © 2011 S. Li & I.W. Tsang

Making decision trees feasible in ultrahigh feature and label dimensions

©2017 Weiwei Liu and Ivor W. Tsang. Due to the non-linear but highly interpretable representations, decision tree (DT) models have significantly attracted a lot of attention of researchers. However, it is difficult to understand and interpret DT models in ultrahigh dimensions and DT models usually suffer from the curse of dimensionality and achieve degenerated performance when there are many noisy features. To address these issues, this paper first presents a novel data-dependent generalization error bound for the perceptron decision tree (PDT), which provides the theoretical justification to learn a sparse linear hyperplane in each decision node and to prune the tree. Following our analysis, we introduce the notion of budget-aware classifier (BAC) with a budget constraint on the weight coefficients, and propose a supervised budgeted tree (SBT) algorithm to achieve non-linear prediction performance. To avoid generating an unstable and complicated decision tree and improve the generalization of the SBT, we present a pruning strategy by learning classifiers to minimize cross-validation errors on each BAC. To deal with ultrahigh label dimensions, based on three important phenomena of real-world data sets from a variety of application domains, we develop a sparse coding tree framework for multi-label annotation problems and provide the theoretical analysis. Extensive empirical studies verify that 1) SBT is easy to understand and interpret in ultrahigh dimensions and is more resilient to noisy features. 2) Compared with state-of-the-art algorithms, our proposed sparse coding tree framework is more efficient, yet accurate in ultrahigh label and feature dimensions

Large margin metric learning for multi-label prediction

Copyright © 2015, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. Canonical correlation analysis (CCA) and maximum margin output coding (MMOC) methods have shown promising results for multi-label prediction, where each instance is associated with multiple labels. However, these methods require an expensive decoding procedure to recover the multiple labels of each testing instance. The testing complexity becomes unacceptable when there are many labels. To avoid decoding completely, we present a novel large margin metric learning paradigm for multi-label prediction. In particular, the proposed method learns a distance metric to discover label dependency such that instances with very different multiple labels will be moved far away. To handle many labels, we present an accelerated proximal gradient procedure to speed up the learning process. Comprehensive experiments demonstrate that our proposed method is significantly faster than CCA and MMOC in terms of both training and testing complexities. Moreover, our method achieves superior prediction performance compared with state-of-the-art methods

Robust Plackett–Luce model for k-ary crowdsourced preferences

© 2017, The Author(s). The aggregation of k-ary preferences is an emerging ranking problem, which plays an important role in several aspects of our daily life, such as ordinal peer grading and online product recommendation. At the same time, crowdsourcing has become a trendy way to provide a plethora of k-ary preferences for this ranking problem, due to convenient platforms and low costs. However, k-ary preferences from crowdsourced workers are often noisy, which inevitably degenerates the performance of traditional aggregation models. To address this challenge, in this paper, we present a RObust PlAckett–Luce (ROPAL) model. Specifically, to ensure the robustness, ROPAL integrates the Plackett–Luce model with a denoising vector. Based on the Kendall-tau distance, this vector corrects k-ary crowdsourced preferences with a certain probability. In addition, we propose an online Bayesian inference to make ROPAL scalable to large-scale preferences. We conduct comprehensive experiments on simulated and real-world datasets. Empirical results on “massive synthetic” and “real-world” datasets show that ROPAL with online Bayesian inference achieves substantial improvements in robustness and noisy worker detection over current approaches

An easy-to-hard learning paradigm for multiple classes and multiple labels

© 2017 Weiwei Liu, Ivor W. Tsang and Klaus-Robert Müller. Many applications, such as human action recognition and object detection, can be formulated as a multiclass classification problem. One-vs-rest (OVR) is one of the most widely used approaches for multiclass classification due to its simplicity and excellent performance. However, many confusing classes in such applications will degrade its results. For example, hand clap and boxing are two confusing actions. Hand clap is easily misclassified as boxing, and vice versa. Therefore, precisely classifying confusing classes remains a challenging task. To obtain better performance for multiclass classifications that have confusing classes, we first develop a classifier chain model for multiclass classification (CCMC) to transfer class information between classifiers. Then, based on an analysis of our proposed model, we propose an easy-to-hard learning paradigm for multiclass classification to automatically identify easy and hard classes and then use the predictions from simpler classes to help solve harder classes. Similar to CCMC, the classifier chain (CC) model is also proposed by Read et al. (2009) to capture the label dependency for multi-label classification. However, CC does not consider the order of difficulty of the labels and achieves degenerated performance when there are many confusing labels. Therefore, it is non-trivial to learn the appropriate label order for CC. Motivated by our analysis for CCMC, we also propose the easy-to-hard learning paradigm for multi-label classi cation to automatically identify easy and hard labels, and then use the predictions from simpler labels to help solve harder labels. We also demonstrate that our proposed strategy can be successfully applied to a wide range of applications, such as ordinal classi cation and relationship prediction. Extensive empirical studies validate our analysis and the e-ectiveness of our proposed easy-to-hard learning strategies

Towards ultrahigh dimensional feature selection for big data

In this paper, we present a new adaptive feature scaling scheme for ultrahigh-dimensional feature selection on Big Data, and then reformulate it as a convex semi-infinite programming (SIP) problem. To address the SIP, we propose an eficient feature generating paradigm. Different from traditional gradient-based approaches that conduct optimization on all input features, the proposed paradigm iteratively activates a group of features, and solves a sequence of multiple kernel learning (MKL) subproblems. To further speed up the training, we propose to solve the MKL subproblems in their primal forms through a modified accelerated proximal gradient approach. Due to such optimization scheme, some eficient cache techniques are also developed. The feature generating paradigm is guaranteed to converge globally under mild conditions, and can achieve lower feature selection bias. Moreover, the proposed method can tackle two challenging tasks in feature selection: 1) group-based feature selection with complex structures, and 2) nonlinear feature selection with explicit feature mappings. Comprehensive experiments on a wide range of synthetic and real-world data sets of tens of million data points with O(1014) features demonstrate the competitive performance of the proposed method over state-of-the-art feature selection methods in terms of generalization performance and training eficiency. © 2014 Mingkui Tan, Ivor W. Tsang and Li Wang

Hybrid heterogeneous transfer learning through deep learning

Copyright © 2014, Association for the Advancement of Artificial Intelligence. Most previous heterogeneous transfer learning methods learn a cross-domain feature mapping between heterogeneous feature spaces based on a few cross-domain instance-correspondences, and these corresponding instances are assumed to be representative in the source and target domains respectively. However, in many realworld scenarios, this assumption may not hold. As a result, the constructed feature mapping may not be precise due to the bias issue of the correspondences in the target or (and) source domain(s). In this case, a classifier trained on the labeled transformed-sourcedomain data may not be useful for the target domain. In this paper, we present a new transfer learning framework called Hybrid Heterogeneous Transfer Learning (HHTL), which allows the corresponding instances across domains to be biased in either the source or target domain. Specifically, we propose a deep learning approach to learn a feature mapping between crossdomain heterogeneous features as well as a better feature representation for mapped data to reduce the bias issue caused by the cross-domain correspondences. Extensive experiments on several multilingual sentiment classification tasks verify the effectiveness of our proposed approach compared with some baseline methods