Binary data matrices can represent many types of data such as social networks, votes, or gene expression. In some cases, the analysis of binary matrices can be tackled with nonnegative matrix factorization (NMF), where the observed data matrix is approximated by the product of two smaller nonnegative matrices. In this context, probabilistic NMF assumes a generative model where the data is usually Bernoulli-distributed. Often, a link function is used to map the factorization to the [0, 1] range, ensuring a valid Bernoulli mean parameter. However, link functions have the potential disadvantage to lead to uninterpretable models. Mean-parameterized NMF, on the contrary, overcomes this problem. We propose a unified framework for Bayesian mean-parameterized nonnegative binary matrix factorization models (NBMF). We analyze three models which correspond to three possible constraints that respect the mean-parameterization without the need for link functions. Furthermore, we derive a novel collapsed Gibbs sampler and a collapsed variational algorithm to infer the posterior distribution of the factors. Next, we extend the proposed models to a nonparametric setting where the number of used latent dimensions is automatically driven by the observed data. We analyze the performance of our NBMF methods in multiple datasets for different tasks such as dictionary learning and prediction of missing data. Experiments show that our methods provide similar or superior results than the state of the art, while automatically detecting the number of relevant components.

This paper tackles the problem of JPEG steganography and steganalysis for color images, a problem that has rarely been studied so far and which deserves more attention. After focusing on the 4:4:4 sampling strategy, we propose to modify for each channel the embedding rate of J-UNIWARD and UERD steganographic schemes in order to arbitrary spread the payload between the luminance and the chrominance components while keeping a constant message size for the different strategies. We also compare our spreading payload strategy w.r.t. two strategies: (i) the concatenation of the cost map (CONC) or (ii) equal embedding rates (EER) among channels. We then select good candidates within the feature sets designed either for JPEG or color steganography. Our conclusions are threefold: (i) the GFR or DCTR features sets, concatenated on the three channels offer better performance than ColorSRMQ1 for JPEG Quality Factor (QF) of 75 and 95 but ColorSRMQ1 is more sensitive for QF=100, (ii) the CONC or EER strategies are suboptimal, and (iii) depending of the quality factors and the embedding schemes, the empirical security is maximized when between 33% (QF=100, UERD) and 95% (QF=75, J-UNIWARD) of the payload is allocated to the luminance channel.

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Active learning is usually applied to acquire labels of informative data points in supervised learning, to maximize accuracy in a sample-efficient way. However, maximizing the accuracy is not the end goal when the results are used for decision-making, for example in personalized medicine or economics. We argue that when acquiring samples sequentially, separating learning and decision-making is sub-optimal, and we introduce a novel active learning strategy which takes the down-the-line decision problem into account. Specifically, we introduce a novel active learning criterion which maximizes the expected information gain on the posterior distribution of the optimal decision. We compare our decision-making-aware active learning strategy to existing alternatives on both simulated and real data, and show improved performance in decision-making accuracy.

Non-negative matrix factorization (NMF) has become a well-established class of methods for the analysis of non-negative data. In particular, a lot of effort has been devoted to probabilistic NMF, namely estimation or inference tasks in probabilistic models describing the data, based for example on Poisson or exponential likelihoods. When dealing with time series data, several works have proposed to model the evolution of the activation coefficients as a non-negative Markov chain, most of the time in relation with the Gamma distribution, giving rise to so-called temporal NMF models. In this paper, we review four Gamma Markov chains of the NMF literature, and show that they all share the same drawback: the absence of a well-defined stationary distribution. We then introduce a fifth process, an overlooked model of the time series literature named BGAR(1), which overcomes this limitation. These temporal NMF models are then compared in a MAP framework on a prediction task, in the context of the Poisson likelihood.