有限混合物的局部几何
The local geometry of finite mixtures
摘要：
证明了当q>=1时，q平移光滑概率密度的凸组合类具有与q成比例的局部加倍维数.证明中的关键难点是控制混合类的局部几何结构。我们的局部几何定理产生的（括号）度量熵的一类正规化密度，从一个一般的切片程序推导出的局部熵界。
英文摘要：
We establish that for q>=1, the class of convex combinations of q translates of a smooth probability density has local doubling dimension proportional to q. The key difficulty in the proof is to control the local geometric structure of mixture classes. Our local geometry theorem yields a bound on the (bracketing) metric entropy of a class of normalized densities, from which a local entropy bound is deduced by a general slicing procedure.
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