Abstract In contextual anomaly detection, an object is only considered anomalous within a specific context. Most existing methods use a single context based on a set of user-specified contextual features. However, identifying the right context can be very challenging in practice, especially in datasets with a large number of attributes. Furthermore, in real-world systems, there might be multiple anomalies that occur in different contexts and, therefore, require a combination of several “useful” contexts to unveil them. In this work, we propose a novel approach, called wisdom of the contexts (WisCon), to effectively detect complex contextual anomalies in situations where the true contextual and behavioral attributes are unknown. Our method constructs an ensemble of multiple contexts, with varying importance scores, based on the assumption that not all useful contexts are equally so. We estimate the importance of each context using an active learning approach with a novel query strategy. Experiments show that WisCon significantly outperforms existing baselines in different categories (i.e., active learning methods, unsupervised contextual and non-contextual anomaly detectors) on 18 datasets. Furthermore, the results support our initial hypothesis that there is no single perfect context that successfully uncovers all kinds of contextual anomalies, and leveraging the “wisdom” of multiple contexts is necessary.

Recent developments in differentially private (DP) machine learning and DP Bayesian learning have enabled learning under strong privacy guarantees for the training data subjects. In this paper, we further extend the applicability of DP Bayesian learning by presenting the first general DP Markov chain Monte Carlo (MCMC) algorithm whose privacy-guarantees are not subject to unrealistic assumptions on Markov chain convergence and that is applicable to posterior inference in arbitrary models. Our algorithm is based on a decomposition of the Barker acceptance test that allows evaluating the Rényi DP privacy cost of the accept-reject choice. We further show how to improve the DP guarantee through data subsampling and approximate acceptance tests.

Methods for detection of overlapping sound events in audio involve matrix factorization approaches, often assigning separated components to event classes. We present a method that bypasses the supervised construction of class models. The method learns the components as a non-negative dictionary in a coupled matrix factorization problem, where the spectral representation and the class activity annotation of the audio signal share the activation matrix. In testing, the dictionaries are used to estimate directly the class activations. For dealing with large amount of training data, two methods are proposed for reducing the size of the dictionary. The methods were tested on a database of real life recordings, and outperformed previous approaches by over 10%.

Information divergence that measures the difference between two nonnegative matrices or tensors has found its use in a variety of machine learning problems. Examples are Nonnegative Matrix/Tensor Factorization, Stochastic Neighbor Embedding, topic models, and Bayesian network optimization. The success of such a learning task depends heavily on a suitable divergence. A large variety of divergences have been suggested and analyzed, but very few results are available for an objective choice of the optimal divergence for a given task. Here we present a framework that facilitates automatic selection of the best divergence among a given family, based on standard maximum likelihood estimation. We first propose an approximated Tweedie distribution for the β-divergence family. Selecting the best β then becomes a machine learning problem solved by maximum likelihood. Next, we reformulate α-divergence in terms of β-divergence, which enables automatic selection of α by maximum likelihood with reuse of the learning principle for β-divergence. Furthermore, we show the connections between γ- and β-divergences as well as Renyi- and α-divergences, such that our automatic selection framework is extended to non-separable divergences. Experiments on both synthetic and real-world data demonstrate that our method can quite accurately select information divergence across different learning problems and various divergence families.

Nonnegative Matrix Factorization (NMF) is a promising relaxation technique for clustering analysis. However, conventional NMF methods that directly approximate the pairwise similarities using the least square error often yield mediocre performance for data in curved manifolds because they can capture only the immediate similarities between data samples. Here we propose a new NMF clustering method which replaces the approximated matrix with its smoothed version using random walk. Our method can thus accommodate farther relationships between data samples. Furthermore, we introduce a novel regularization in the proposed objective function in order to improve over spectral clustering. The new learning objective is optimized by a multiplicative Majorization-Minimization algorithm with a scalable implementation for learning the factorizing matrix. Extensive experimental results on real-world datasets show that our method has strong performance in terms of cluster purity.

We describe an alternative to standard nonnegative matrix factorisation (NMF) for nonnegative dictionary learning. NMF with the Kullback-Leibler divergence can be seen as maximisation of the joint likelihood of the dictionary and the expansion coefficients under Poisson observation noise. This approach lacks optimality be cause the number of parameters (which include the expansion coefficients) grows with the number of observations. As such, we describe a variational EM algorithm for optimisation of the marginal likelihood, i.e., the likelihood of the dictionary where the expansion coefficients have been integrated out (given a Gamma conjugate prior). We compare the output of both maximum joint likelihood estimation (i.e., standard NMF) and maximum marginal likelihood estimation (MMLE) on real and synthetical data. The MMLE approach is shown to embed automatic model order selection, similar to automatic relevance determination.

In this paper we describe a maximum likelihood likelihood approach for dictionary learning in the multiplicative exponential noise model. This model is prevalent in audio signal processing where it underlies a generative composite model of the power spectrogram. Maximum joint likelihood estimation of the dictionary and expansion coefficients leads to a nonnegative matrix factorization problem where the Itakura-Saito divergence is used. The optimality of this approach is in question because the number of parameters (which include the expansion coefficients) grows with the number of observations. In this paper we describe a variational procedure for optimization of the marginal likelihood, i.e., the likelihood of the dictionary where the activation coefficients have been integrated out (given a specific prior). We compare the output of both maximum joint likelihood estimation (i.e., standard Itakura-Saito NMF) and maximum marginal likelihood estimation (MMLE) on real and synthetical datasets. The MMLE approach is shown to embed automatic model order selection, akin to automatic relevance determination.

In many audio processing tasks, such as source separation, denoising or compression, it is crucial to construct realistic and flexible models to capture the physical properties of audio signals. This can be accomplished in the Bayesian framework through the use of appropriate prior distributions. In this paper, we describe a class of prior models called Gamma Markov random fields (GMRFs) to model the sparsity and the local dependency of the energies (i.e., variances) of time-frequency expansion coefficients. A GMRF model describes a non-normalised joint distribution over unobserved variance variables, where given the field the actual source coefficients are independent. Our construction ensures a positive coupling between the variance variables, so that signal energy changes smoothly over both axes to capture the temporal and spectral continuity. The coupling strength is controlled by a set of hyperparameters. Inference on the overall model is convenient because of the conditional conjugacy of all of the variables in the model, but automatic optimization of hyperparameters is crucial to obtain better fits. The marginal likelihood of the model is not available because of the intractable normalizing constant of GMRFs. In this paper, we optimize the hyperparameters of our GMRF-based audio model using contrastive divergence and compare this method to alternatives such as score matching and pseudolikelihood maximization where applicable. We present the performance of the GMRF models in denoising and single-channel source separation problems in completely blind scenarios, where all the hyperparameters are jointly estimated given only audio data.