In this paper we introduce a novel approach for an important problem of break detection. Specifically, we are interested in detection of an abrupt change in the covariance structure of a high-dimensional random process -a problem, which has applications in many areas e.g., neuroimaging and finance. The developed approach is essentially a testing procedure involving a choice of a critical level. To that end a non-standard bootstrap scheme is proposed and theoretically justified under mild assumptions. Theoretical study features a result providing guaranties for break detection. All the theoretical results are established in a high-dimensional setting (dimensionality p ≫ n). Multiscale nature of the approach allows for a trade-off between sensitivity of break detection and localization. The approach can be naturally employed in an on-line setting. Simulation study demonstrates that the approach matches the nominal level of false alarm probability and exhibits high power, outperforming a recent approach.MSC 2010 subject classifications: Primary 62M10, 62H15; secondary 91B84, 62P10.

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Unsupervised retrieval of image features is vital for many computer vision tasks where the annotation is missing or scarce. In this work, we propose a new unsupervised approach to detect the landmarks in images, and we validate it on the popular task of human face key-points extraction. The method is based on the idea of auto-encoding the wanted landmarks in the latent space while discarding the non-essential information in the image and effectively preserving the interpretability. The interpretable latent space representation is achieved with the aid of a novel two-step regularization paradigm. The first regularization step evaluates transport distance from a given set of landmarks to the average value (the barycenter by Wasserstein distance). The second regularization step controls deviations from the barycenter by applying random geometric deformations synchronously to the initial image and to the encoded landmarks. During decoding, we add style features generated from the noise and reconstruct the initial image by the generative adversarial network (GAN) with transposed convolutions modulated by this style. We demonstrate the effectiveness of the approach both in unsupervised and in semi-supervised training scenarios using the 300-W and the CelebA datasets. The proposed regularization paradigm is shown to prevent overfitting, and the detection quality is shown to improve beyond the supervised outcome.Preprint. Under review.

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