On the Rate of Gaussian Approximation for Linear Regression Problems
This work provides theoretical bounds for statistical inference in online linear regression, which is incremental as it refines existing approximation results.
The paper tackles the problem of Gaussian approximation for online linear regression, deriving convergence rates that depend on dimension and design matrix properties, achieving a normal approximation rate of order sqrt(log n / n) for large sample sizes.
In this paper, we consider the problem of Gaussian approximation for the online linear regression task. We derive the corresponding rates for the setting of a constant learning rate and study the explicit dependence of the convergence rate upon the problem dimension $d$ and quantities related to the design matrix. When the number of iterations $n$ is known in advance, our results yield the rate of normal approximation of order $\sqrt{\log{n}/n}$, provided that the sample size $n$ is large enough.