论文标题
从压缩数据中估算的量化误差的高斯近似值
Gaussian Approximation of Quantization Error for Estimation from Compressed Data
论文作者
论文摘要
我们考虑使用随机球形代码的高维信号$ x $的有损压缩表示之间的分布连接与在加性白色高斯噪声（AWGN）下观察$ x $之间的分布连接。我们表明，$ x $的比特率 - $ r $压缩版之间的wasserstein距离及其在信噪比的AWGN频道下的观察值$ 2^{2r} -1 $在问题维度中是次线性。我们利用这一事实将基于$ x $的AWGN腐败版本的估计器的风险与供给其比特率$ r $量化版本时所达到的风险联系起来。我们通过在压缩约束下的推理问题得出各种新的结果来证明这种联系的有用性，包括最小值估计，稀疏回归，压缩感应以及远程源编码中线性估计的普遍性。
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 $2^{2R}-1$ is sub-linear in the problem dimension. We utilize this fact to connect the risk of an estimator based on an AWGN-corrupted version of $X$ to the risk attained by the same estimator when fed with its bitrate-$R$ quantized version. 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 the universality of linear estimation in remote source coding.
