Crowdsourcing utilizes the wisdom of crowds for collective classification via information (e.g., labels of an item) provided by labelers. Current crowdsourcing algorithms are mainly unsupervised methods that are unaware of the quality of crowdsourced data. In this paper, we propose a supervised collective classification algorithm that aims to identify reliable labelers from the training data (e.g., items with known labels). The reliability (i.e., weighting factor) of each labeler is determined via a saddle point algorithm. The results on several crowdsourced data show that supervised methods can achieve better classification accuracy than unsupervised methods, and our proposed method outperforms other algorithms.

Next generation telecom services will execute on the telecom cloud, which combine the flexibility of today's computing clouds with the service quality of telecom systems. Real-time service assurance will become an integral part in transforming the general and flexible cloud into a robust and highly available cloud that can ensure low latency and agreed service quality to its customers. A service assurance system for telecom services must be able to detect and preferably also predict problems that may violate the agreed service quality. This is a complex task already in legacy systems and will become even more challenging when executing the services in the cloud. Further, the service assurance system must be able to remedy, in real time, these problems once detected. One promising approach to service assurance is based on machine learning, where the service quality and behavior is learned from observations of the system. The ambition is to do automated real-time predictions of the service quality in order to execute mitigation actions in a proactive manner. Machine learning has been used in the past to build prediction models for service quality assurance.

The speed with which a learning algorithm converges as it is presented with more data is a central problem in machine learning --- a fast rate of convergence means less data is needed for the same level of performance. The pursuit of fast rates in online and statistical learning has led to the discovery of many conditions in learning theory under which fast learning is possible. We show that most of these conditions are special cases of a single, unifying condition, that comes in two forms: the central condition for 'proper' learning algorithms that always output a hypothesis in the given model, and stochastic mixability for online algorithms that may make predictions outside of the model. We show that under surprisingly weak assumptions both conditions are, in a certain sense, equivalent. The central condition has a re-interpretation in terms of convexity of a set of pseudoprobabilities, linking it to density estimation under misspecification. For bounded losses, we show how the central condition enables a direct proof of fast rates and we prove its equivalence to the Bernstein condition, itself a generalization of the Tsybakov margin condition, both of which have played a central role in obtaining fast rates in statistical learning. Yet, while the Bernstein condition is two-sided, the central condition is one-sided, making it more suitable to deal with unbounded losses. In its stochastic mixability form, our condition generalizes both a stochastic exp-concavity condition identified by Juditsky, Rigollet and Tsybakov and Vovk's notion of mixability. Our unifying conditions thus provide a substantial step towards a characterization of fast rates in statistical learning, similar to how classical mixability characterizes constant regret in the sequential prediction with expert advice setting.

Online learning algorithms are designed to perform in non-stationary environments, but generally there is no notion of a dynamic state to model constraints on current and future actions as a function of past actions. State-based models are common in stochastic control settings, but commonly used frameworks such as Markov Decision Processes (MDPs) assume a known stationary environment. In recent years, there has been a growing interest in combining the above two frameworks and considering an MDP setting in which the cost function is allowed to change arbitrarily after each time step. However, most of the work in this area has been algorithmic: given a problem, one would develop an algorithm almost from scratch. Moreover, the presence of the state and the assumption of an arbitrarily varying environment complicate both the theoretical analysis and the development of computationally efficient methods. This paper describes a broad extension of the ideas proposed by Rakhlin et al. to give a general framework for deriving algorithms in an MDP setting with arbitrarily changing costs. This framework leads to a unifying view of existing methods and provides a general procedure for constructing new ones. Several new methods are presented, and one of them is shown to have important advantages over a similar method developed from scratch via an online version of approximate dynamic programming.

We study consistency properties of surrogate loss functions for general multiclass learning problems, defined by a general multiclass loss matrix. We extend the notion of classification calibration, which has been studied for binary and multiclass 0-1 classification problems (and for certain other specific learning problems), to the general multiclass setting, and derive necessary and sufficient conditions for a surrogate loss to be calibrated with respect to a loss matrix in this setting. We then introduce the notion of convex calibration dimension of a multiclass loss matrix, which measures the smallest'size' of a prediction space in which it is possible to design a convex surrogate that is calibrated with respect to the loss matrix. We derive both upper and lower bounds on this quantity, and use these results to analyze various loss matrices. In particular, we apply our framework to study various subset ranking losses, and use the convex calibration dimension as a tool to show both the existence and nonexistence of various types of convex calibrated surrogates for these losses. Our results strengthen recent results of Duchi et al. (2010) and Calauzènes et al. (2012) on the nonexistence of certain types of convex calibrated surrogates in subset ranking. We anticipate the convex calibration dimension may prove to be a useful tool in the study and design of surrogate losses for general multiclass learning problems. Keywords: Statistical consistency, multiclass loss, loss matrix, surrogate loss, convex surrogates, calibrated surrogates, classification calibration, subset ranking.

A popular approach within the signal processing and machine learning communities consists in modelling signals as sparse linear combinations of atoms selected from a learned dictionary. While this paradigm has led to numerous empirical successes in various fields ranging from image to audio processing, there have only been a few theoretical arguments supporting these evidences. In particular, sparse coding, or sparse dictionary learning, relies on a non-convex procedure whose local minima have not been fully analyzed yet. In this paper, we consider a probabilistic model of sparse signals, and show that, with high probability, sparse coding admits a local minimum around the reference dictionary generating the signals. Our study takes into account the case of over-complete dictionaries, noisy signals, and possible outliers, thus extending previous work limited to noiseless settings and/or under-complete dictionaries. The analysis we conduct is non-asymptotic and makes it possible to understand how the key quantities of the problem, such as the coherence or the level of noise, can scale with respect to the dimension of the signals, the number of atoms, the sparsity and the number of observations.

We propose a general framework for studying adaptive regret bounds in the online learning framework, including model selection bounds and data-dependent bounds. Given a data- or model-dependent bound we ask, "Does there exist some algorithm achieving this bound?" We show that modifications to recently introduced sequential complexity measures can be used to answer this question by providing sufficient conditions under which adaptive rates can be achieved. In particular each adaptive rate induces a set of so-called offset complexity measures, and obtaining small upper bounds on these quantities is sufficient to demonstrate achievability. A cornerstone of our analysis technique is the use of one-sided tail inequalities to bound suprema of offset random processes. Our framework recovers and improves a wide variety of adaptive bounds including quantile bounds, second-order data-dependent bounds, and small loss bounds. In addition we derive a new type of adaptive bound for online linear optimization based on the spectral norm, as well as a new online PAC-Bayes theorem that holds for countably infinite sets.

We consider the problem of identifying patterns in a data set that exhibit anomalous behavior, often referred to as anomaly detection. Similarity-based anomaly detection algorithms detect abnormally large amounts of similarity or dissimilarity, e.g.~as measured by nearest neighbor Euclidean distances between a test sample and the training samples. In many application domains there may not exist a single dissimilarity measure that captures all possible anomalous patterns. In such cases, multiple dissimilarity measures can be defined, including non-metric measures, and one can test for anomalies by scalarizing using a non-negative linear combination of them. If the relative importance of the different dissimilarity measures are not known in advance, as in many anomaly detection applications, the anomaly detection algorithm may need to be executed multiple times with different choices of weights in the linear combination. In this paper, we propose a method for similarity-based anomaly detection using a novel multi-criteria dissimilarity measure, the Pareto depth. The proposed Pareto depth analysis (PDA) anomaly detection algorithm uses the concept of Pareto optimality to detect anomalies under multiple criteria without having to run an algorithm multiple times with different choices of weights. The proposed PDA approach is provably better than using linear combinations of the criteria and shows superior performance on experiments with synthetic and real data sets.

Robust Principal Component Analysis (RPCA) via rank minimization is a powerful tool for recovering underlying low-rank structure of clean data corrupted with sparse noise/outliers. In many low-level vision problems, not only it is known that the underlying structure of clean data is low-rank, but the exact rank of clean data is also known. Yet, when applying conventional rank minimization for those problems, the objective function is formulated in a way that does not fully utilize a priori target rank information about the problems. This observation motivates us to investigate whether there is a better alternative solution when using rank minimization. In this paper, instead of minimizing the nuclear norm, we propose to minimize the partial sum of singular values, which implicitly encourages the target rank constraint. Our experimental analyses show that, when the number of samples is deficient, our approach leads to a higher success rate than conventional rank minimization, while the solutions obtained by the two approaches are almost identical when the number of samples is more than sufficient. We apply our approach to various low-level vision problems, e.g. high dynamic range imaging, motion edge detection, photometric stereo, image alignment and recovery, and show that our results outperform those obtained by the conventional nuclear norm rank minimization method.

Multi-task learning is a paradigm of machine learning for solving multiple related learning tasks simultaneously with the expectation that information brought by other related tasks can be mutually exploited to improve the accuracy [Caruana, 1997]. Multi-task learning is particularly useful when one has many related learning tasks to solve but only few training samples are available for each task, which is often the case in many real-world problems such as therapy screening [Bickel et al., 2008] and face verification [Wang et al., 2009]. Multi-task learning has been gathering a great deal of attention, and extensive studies have been conducted both theoretically and experimentally [Thrun, 1996, Evgeniou and Pontil, 2004, Ando and Zhang, 2005, Zhang, 2013, Baxter, 2000]. Thrun [1996] proposed the lifelong learning framework, which transfers the knowledge obtained from the tasks experienced in the past to a newly given task, and it was demonstrated to improve the performance of image recognition. Baxter Baxter [2000] defined a multi-task learning framework called inductive bias learning, and derived a generalization error bound. The semi-supervised multi-task learning method proposed by Ando and Zhang [2005] generates many auxiliary learning 2 tasks from unlabeled data and seeks a good feature mapping for the target learning task.