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An information-theoretic approach to distributed learning. distributed source coding under logarithmic loss

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  1. Tez No: 630832
  2. Yazar: YİĞİT UĞUR
  3. Danışmanlar: YRD. DOÇ. DANIŞMAN YOK
  4. Tez Türü: Doktora
  5. Konular: Matematik, Mathematics
  6. Anahtar Kelimeler: Belirtilmemiş.
  7. Yıl: 2020
  8. Dil: İngilizce
  9. Üniversite: Université Paris-Est
  10. Enstitü: Yurtdışı Enstitü
  11. Ana Bilim Dalı: Belirtilmemiş.
  12. Bilim Dalı: Belirtilmemiş.
  13. Sayfa Sayısı: 189

Özet

One substantial question, that is often argumentative in learning theory, is how to choose a `good' loss function that measures the delity of the reconstruction to the original. Logarithmic loss is a natural distortion measure in the settings in which the reconstructions are allowed to be `soft', rather than `hard' or deterministic. In other words, rather than just assigning a deterministic value to each sample of the source, the decoder also gives an assessment of the degree of con dence or reliability on each estimate, in the form of weights or probabilities. This measure has appreciable mathematical properties which establish some important connections with lossy universal compression. Logarithmic loss is widely used as a penalty criterion in various contexts, including clustering and classi cation, pattern recognition, learning and prediction, and image processing. Considering the high amount of research which is done recently in these elds, the logarithmic loss becomes a very important metric and will be the main focus as a distortion metric in this thesis. In this thesis, we investigate a distributed setup, so-called the Chief Executive Ocer (CEO) problem under logarithmic loss distortion measure. Speci cally, K  2 agents observe independently corrupted noisy versions of a remote source, and communicate independently with a decoder or CEO over rate-constrained noise-free links. The CEO also has its own noisy observation of the source and wants to reconstruct the remote source to within some prescribed distortion level where the incurred distortion is measured under the logarithmic loss penalty criterion. One of the main contributions of the thesis is the explicit characterization of the ratedistortion region of the vector Gaussian CEO problem, in which the source, observations and side information are jointly Gaussian. For the proof of this result, we rst extend Courtade- Weissman's result on the rate-distortion region of the discrete memoryless (DM) K-encoder CEO problem to the case in which the CEO has access to a correlated side information

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