Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: While several papers have investigated computationally and statistically efficient methods for learning Gaussian mixtures, precise minimax bounds for their statistical performance as ll as fundamental limits in high-dimensional settings are not ll-understood. ,  provide precise information theoretic bounds on the clustering accuracy and sample complexity of learning a mixture of two isotropic Gaussians in high dimensions under small mean separation. If there is a sparse subset of relevant dimensions that determine the mean separation, then the sample complexity only depends on the number of relevant dimensions and mean separation, and can be achieved by a simple computationally efficient procedure. Our results provide the first step of a theoretical basis for recent methods that combine feature selection and clustering.
['Martin Azizyan', 'Aarti Singh', 'Larry Wasserman']
I am writing a research paper on a idea Minimax Theory for High-dimensional Gaussian Mixtures with Sparse Mean Separation
[{"from": "human", "value": "I am writing a research paper on a idea Minimax Theory for High-dimensional Gaussian Mixtures with Sparse Mean Separation"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: While several papers have investigated computationally and statistically efficient methods for learning Gaussian mixtures, precise minimax bounds for their statistical performance as ll as fundamental limits in high-dimensional settings are not ll-understood. ,  provide precise information theoretic bounds on the clustering accuracy and sample complexity of learning a mixture of two isotropic Gaussians in high dimensions under small mean separation. If there is a sparse subset of relevant dimensions that determine the mean separation, then the sample complexity only depends on the number of relevant dimensions and mean separation, and can be achieved by a simple computationally efficient procedure. Our results provide the first step of a theoretical basis for recent methods that combine feature selection and clustering."}]