Most existing works on crowdsourcing assume that the workers follow the Dawid-Skene model, or the one-coin model as its special case, where every worker makes mistakes independently of other workers and with the same error probability for every task. We study a significant extension of this restricted model. We allow almost half of the workers to deviate from the one-coin model and for those workers, their probabilities of making an error to be task-dependent and to be arbitrarily correlated. In other words, we allow for arbitrary adversaries, for which not only error probabilities can be high, but which can also perfectly collude. In this adversarial scenario, we design an efficient algorithm to consistently estimate the workers’ error probabilities.

While crowdsourcing has become an important means to label data, there is great interest in estimating the ground truth from unreliable labels produced by crowdworkers. The Dawid and Skene (DS) model is one of the most well-known models in the study of crowdsourcing.Despite its practical popularity, theoretical error analysis for the DS model has been conducted only under restrictive assumptions on class priors, confusion matrices, or the number of labels each worker provides.In this paper, we derive a minimax error rate under more practical setting for a broader class of crowdsourcing models including the DS model as a special case.We further propose the worker clustering model, which is more practical than the DS model under real crowdsourcing settings.The wide applicability of our theoretical analysis allows us to immediately investigate the behavior of this proposed model, which can not be analyzed by existing studies.Experimental results showed that there is a strong similarity between the lower bound of the minimax error rate derived by our theoretical analysis and the empirical error of the estimated value.

Many parametric statistical models are not properly normalised and only specified up to an intractable partition function, which renders parameter estimation difficult. Examples of unnormalised models are Gibbs distributions, Markov random fields, and neural network models in unsupervised deep learning. In previous work, the estimation principle called noise-contrastive estimation (NCE) was introduced where unnormalised models are estimated by learning to distinguish between data and auxiliary noise. An open question is how to best choose the auxiliary noise distribution. We here propose a new method that addresses this issue. The proposed method shares with NCE the idea of formulating density estimation as a supervised learning problem but in contrast to NCE, the proposed method leverages the observed data when generating noise samples. The noise can thus be generated in a semi-automated manner. We first present the underlying theory of the new method, show that score matching emerges as a limiting case, validate the method on continuous and discrete valued synthetic data, and show that we can expect an improved performance compared to NCE when the data lie in a lower-dimensional manifold. Then we demonstrate its applicability in unsupervised deep learning by estimating a four-layer neural image model.

Despite the great advances made by deep learning in many machine learning problems, there is a relative dearth of deep learning approaches for anomaly detection. Those approaches which do exist involve networks trained to perform a task other than anomaly detection, namely generative models or compression, which are in turn adapted for use in anomaly detection; they are not trained on an anomaly detection based objective. In this paper we introduce a new anomaly detection method---Deep Support Vector Data Description---, which is trained on an anomaly detection based objective. The adaptation to the deep regime necessitates that our neural network and training procedure satisfy certain properties, which we demonstrate theoretically. We show the effectiveness of our method on MNIST and CIFAR-10 image benchmark datasets as well as on the detection of adversarial examples of GTSRB stop signs.

We propose a unified framework for deep density models by formally defining density destructors. A density destructor is an invertible function that transforms a given density to the uniform density---essentially destroying any structure in the original density. This destructive transformation generalizes Gaussianization via ICA and more recent autoregressive models such as MAF and Real NVP. Informally, this transformation can be seen as a generalized whitening procedure or a multivariate generalization of the univariate CDF function. Unlike Gaussianization, our destructive transformation has the elegant property that the density function is equal to the absolute value of the Jacobian determinant. Thus, each layer of a deep density can be seen as a shallow density---uncovering a fundamental connection between shallow and deep densities. In addition, our framework provides a common interface for all previous methods enabling them to be systematically combined, evaluated and improved. Leveraging the connection to shallow densities, we also propose a novel tree destructor based on tree densities and an image-specific destructor based on pixel locality. We illustrate our framework on a 2D dataset, MNIST, and CIFAR-10. Code is available on first author's website.