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Foveal autoregressive neural time-series modeling

Abstract : This dissertation studies unsupervised time-series modelling. We first focus on the problem of linearly predicting future values of a time-series under the assumption of long-range dependencies, which requires to take into account a large past. We introduce a family of causal and foveal wavelets which project past values on a subspace which is adapted to the problem, thereby reducing the variance of the associated estimators. We then investigate under which conditions non-linear predictors exhibit better performances than linear ones. Time-series which admit a sparse time-frequency representation, such as audio ones, satisfy those requirements, and we propose a prediction algorithm using such a representation. The last problem we tackle is audio time-series synthesis. We propose a new generation method relying on a deep convolutional neural network, with an encoder-decoder architecture, which allows to synthesize new realistic signals. Contrary to state-of-the-art methods, we explicitly use time-frequency properties of sounds to define an encoder with the scattering transform, while the decoder is trained to solve an inverse problem in an adapted metric.
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https://tel.archives-ouvertes.fr/tel-03338394
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Mathieu Andreux. Foveal autoregressive neural time-series modeling. Neural and Evolutionary Computing [cs.NE]. Université Paris sciences et lettres, 2018. English. ⟨NNT : 2018PSLEE073⟩. ⟨tel-03338394⟩

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