Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Quantile regression is a method to estimate the quantiles of the conditional distribution of a response variable, and as such it permits a much more accurate portrayal of the relationship beten the response variable and observed covariates than methods such as Least-squares or Least Absolute Deviations regression. It can be expressed as a linear program, and interior-point methods can be used to find a solution for moderately large problems. Dealing with very large problems, e.g., involving data up to and beyond the terabyte regime, remains a challenge. Here,  present a randomized algorithm that runs in time that is nearly linear in the size of the input and that, with constant probability, computes a (1+e) approximate solution to an arbitrary quantile regression problem. Our algorithm computes a low-distortion subspace-preserving embedding with respect to the loss function of quantile regression. Our empirical evaluation illustrates that our algorithm is competitive with the best previous work on small to medium-sized problems, and that it can be implemented in MapReduce-like environments and applied to terabyte-sized problems.
['Jiyan Yang', 'Xiangrui Meng', 'Michael W. Mahoney']
I am writing a research paper on a idea Quantile Regression for Large-scale Applications
[{"from": "human", "value": "I am writing a research paper on a idea Quantile Regression for Large-scale Applications"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Quantile regression is a method to estimate the quantiles of the conditional distribution of a response variable, and as such it permits a much more accurate portrayal of the relationship beten the response variable and observed covariates than methods such as Least-squares or Least Absolute Deviations regression. It can be expressed as a linear program, and interior-point methods can be used to find a solution for moderately large problems. Dealing with very large problems, e.g., involving data up to and beyond the terabyte regime, remains a challenge. Here,  present a randomized algorithm that runs in time that is nearly linear in the size of the input and that, with constant probability, computes a (1+e) approximate solution to an arbitrary quantile regression problem. Our algorithm computes a low-distortion subspace-preserving embedding with respect to the loss function of quantile regression. Our empirical evaluation illustrates that our algorithm is competitive with the best previous work on small to medium-sized problems, and that it can be implemented in MapReduce-like environments and applied to terabyte-sized problems."}]