Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Suppose the random variable X ∈ ℝD has mean zero and finite second moments.  show that there is a precise sense in which almost all linear projections of X into ℝD (for d < D) look like a scale-mixture of spherical Gaussians—specifically, a mixture of distributions N(0, σ2Id) where the the σ values follow the same distribution as ‖X‖/√D. The extent of this effect depends upon the ratio of d to D, and upon a particular coefficient of eccentricity of X's distribution.#R##N##R##N# explore this result in a variety of experiments.
['Sanjoy Dasgupta', 'Daniel J. Hsu', 'Nakul Verma']
I am writing a research paper on a idea A concentration theorem for projections
[{"from": "human", "value": "I am writing a research paper on a idea A concentration theorem for projections"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Suppose the random variable X \u2208 \u211dD has mean zero and finite second moments.  show that there is a precise sense in which almost all linear projections of X into \u211dD (for d < D) look like a scale-mixture of spherical Gaussians\u2014specifically, a mixture of distributions N(0, \u03c32Id) where the the \u03c3 values follow the same distribution as \u2016X\u2016/\u221aD. The extent of this effect depends upon the ratio of d to D, and upon a particular coefficient of eccentricity of X's distribution.#R##N##R##N# explore this result in a variety of experiments."}]