Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  propose a novel high-dimensional linear regression estimator: the  Discrete Dantzig Selector , which minimizes the number of nonzero regression coefficients subject to a budget on the maximal absolute correlation beten the features and residuals. Motivated by the significant advances in integer optimization over the past 10–15 years,  present a mixed integer linear optimization ( MILO ) approach to obtain  certifiably optimal  global solutions to this nonconvex optimization problem. The current state of algorithmics in integer optimization makes our proposal substantially more computationally attractive than the least squares subset selection framework based on integer  quadratic  optimization, recently proposed by Bertsimas  et al.  and the continuous nonconvex quadratic optimization framework of Liu  et al. .  propose new discrete first-order methods, which when paired with the state-of-the-art  MILO  solvers, lead to good solutions for the  Discrete Dantzig Selector  problem for a given computational budget.  illustrate that our integrated approach provides globally optimal solutions in significantly shorter computation times, when compared to off-the-shelf  MILO  solvers.  demonstrate both theoretically and empirically that in a wide range of regimes the statistical properties of the  Discrete Dantzig Selector  are superior to those of popular    $\ell _{1}$   -based approaches.  illustrate that our approach can handle problem instances with    $p =10,\!000$    features with certifiable optimality making it a highly scalable combinatorial variable selection approach in sparse linear modeling.
['Rahul Mazumder', 'Peter Radchenko']
I am writing a research paper on a idea The Discrete Dantzig Selector : Estimating Sparse Linear Models via Mixed Integer Linear Optimization
[{"from": "human", "value": "I am writing a research paper on a idea The Discrete Dantzig Selector : Estimating Sparse Linear Models via Mixed Integer Linear Optimization"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  propose a novel high-dimensional linear regression estimator: the  Discrete Dantzig Selector , which minimizes the number of nonzero regression coefficients subject to a budget on the maximal absolute correlation beten the features and residuals. Motivated by the significant advances in integer optimization over the past 10\u201315 years,  present a mixed integer linear optimization ( MILO ) approach to obtain  certifiably optimal  global solutions to this nonconvex optimization problem. The current state of algorithmics in integer optimization makes our proposal substantially more computationally attractive than the least squares subset selection framework based on integer  quadratic  optimization, recently proposed by Bertsimas  et al.  and the continuous nonconvex quadratic optimization framework of Liu  et al. .  propose new discrete first-order methods, which when paired with the state-of-the-art  MILO  solvers, lead to good solutions for the  Discrete Dantzig Selector  problem for a given computational budget.  illustrate that our integrated approach provides globally optimal solutions in significantly shorter computation times, when compared to off-the-shelf  MILO  solvers.  demonstrate both theoretically and empirically that in a wide range of regimes the statistical properties of the  Discrete Dantzig Selector  are superior to those of popular    $\\ell _{1}$   -based approaches.  illustrate that our approach can handle problem instances with    $p =10,\\!000$    features with certifiable optimality making it a highly scalable combinatorial variable selection approach in sparse linear modeling."}]