Below are the abstract, introduction, and conclusion of a computer science research paper. Please summarize the main contribution of the work in a single sentence. Your response should include the summary and no additional text.

Paper text:

We study the following three fundamental problems about ridge regression: (1) what is the structure of the estimator?
(2) how to correctly use cross-validation to choose the regularization parameter?
and (3) how to accelerate computation without losing too much accuracy?
We consider the three problems in a unified large-data linear model.
We give a precise representation of ridge regression as a covariance matrix-dependent linear combination of the true parameter and the noise. 

We study the bias of $K$-fold cross-validation for choosing the regularization parameter, and propose a simple bias-correction.
We analyze the accuracy of primal and dual sketching for ridge regression, showing they are surprisingly accurate.
Our results are illustrated by simulations and by analyzing empirical data.
Ridge or 2 -regularized regression is a widely used method for prediction and estimation when the data dimension p is large compared to the number of datapoints n.
This is especially so in problems with many good features, where sparsity assumptions may not be justified.
A great deal is known about ridge regression.
It is Bayes optimal for any quadratic loss in a Bayesian linear model where the parameters and noise are Gaussian.
The asymptotic properties of ridge have been widely studied (e.g., Tulino & Verdú, 2004; Serdobolskii, 2007; Couillet & Debbah, 2011; Dicker, 2016; Dobriban & Wager, 2018, etc) .
For choosing the regularization parameter in practice, cross-validation (CV) is widely used.
In addition, there is an exact shortcut (e.g., Hastie et al., 2009, p. 243) , which has good consistency properties (Hastie et al., 2019) .
There is also a lot of work on fast approximate algorithms for ridge, e.g., using sketching methods (e.g., el Alaoui & Mahoney, 2015; Chen et al., 2015; Wang et al., 2018; Chowdhury et al., 2018, among
We study the structure of ridge regression in a high-dimensional asymptotic framework, and get insights about cross-validation and sketching.