We study the problem of distributed and rate-adaptive feature compression for
linear regression. A set of distributed sensors collect disjoint features of
regressor data. A fusion center is assumed to contain a pretrained linear
regression model, trained on a dataset of the entire uncompressed data. At
inference time, the sensors compress their observations and send them to the
fusion center through communication-constrained channels, whose rates can
change with time. Our goal is to design a feature compression {scheme} that can
adapt to the varying communication constraints, while maximizing the inference
performance at the fusion center. We first obtain the form of optimal
quantizers assuming knowledge of underlying regressor data distribution. Under
a practically reasonable approximation, we then propose a distributed
compression scheme which works by quantizing a one-dimensional projection of
the sensor data. We also propose a simple adaptive scheme for handling changes
in communication constraints. We demonstrate the effectiveness of the
distributed adaptive compression scheme through simulated experiments.

我们研究了分布式和自适应速率的特征压缩问题，通过传感器收集线性回归模型的不同特征，设计了一种特征压缩方案以适应不断变化的通信约束，并通过模拟实验证明了该方案的有效性。