Abstract:
We consider the distributional connection between the lossy compressed representation of a high-dimensional signal X using a random spherical code and the observation of ...Show MoreMetadata
Abstract:
We consider the distributional connection between the lossy compressed representation of a high-dimensional signal X using a random spherical code and the observation of X under an additive white Gaussian noise (AWGN). We show that the Wasserstein distance between a bitrate- R compressed version of X and its observation under an AWGN-channel of signal-to-noise ratio 22R-1 is bounded in the problem dimension. We utilize this fact to connect the risk of an estimator based on the compressed version of X to the risk attained by the same estimator when fed the AWGN-corrupted version of X. We demonstrate the usefulness of this connection by deriving various novel results for inference problems under compression constraints, including minimax estimation, sparse regression, compressed sensing, and universality of linear estimation in remote source coding.
Published in: IEEE Transactions on Information Theory ( Volume: 67, Issue: 8, August 2021)
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- IEEE Keywords
- Index Terms
- Source Code ,
- Quantization Error ,
- Gaussian Noise ,
- Additive Noise ,
- Linear Approximation ,
- Additive Gaussian Noise ,
- Dimensional Problems ,
- Random Code ,
- Compressed Representation ,
- Lossy Compression ,
- Dimensional Vector ,
- Estimation Problem ,
- Joint Distribution ,
- Random Vector ,
- Second Moment ,
- Lipschitz Continuous ,
- Sphere Of Radius ,
- Unit Sphere ,
- Rate-distortion ,
- Sequential Estimation ,
- Independent Gaussian Noise ,
- Codeword ,
- Squared Error Loss ,
- Almost Surely ,
- Complementary Cumulative Distribution Function ,
- Standard Gaussian ,
- Proof Of The Main Result ,
- Sparse Estimation
- Author Keywords
Keywords assist with retrieval of results and provide a means to discovering other relevant content. Learn more.
- IEEE Keywords
- Index Terms
- Source Code ,
- Quantization Error ,
- Gaussian Noise ,
- Additive Noise ,
- Linear Approximation ,
- Additive Gaussian Noise ,
- Dimensional Problems ,
- Random Code ,
- Compressed Representation ,
- Lossy Compression ,
- Dimensional Vector ,
- Estimation Problem ,
- Joint Distribution ,
- Random Vector ,
- Second Moment ,
- Lipschitz Continuous ,
- Sphere Of Radius ,
- Unit Sphere ,
- Rate-distortion ,
- Sequential Estimation ,
- Independent Gaussian Noise ,
- Codeword ,
- Squared Error Loss ,
- Almost Surely ,
- Complementary Cumulative Distribution Function ,
- Standard Gaussian ,
- Proof Of The Main Result ,
- Sparse Estimation
- Author Keywords