论文标题
有效维度的规模依赖性概念
A scale-dependent notion of effective dimension
论文作者
论文摘要
我们介绍了一个统计模型的“有效维度”的概念，该概念基于尺寸$ 1/\ sqrt {n} $的立方体数量，以覆盖模型空间，而将Fisher Information Matrix作为度量标准，$ n $是观测值的数量。观察次数固定了自然量表或分辨率。然后，通过使用此天然量表正规化的Fisher Information矩阵来测量有效维度。
We introduce a notion of "effective dimension" of a statistical model based on the number of cubes of size $1/\sqrt{n}$ needed to cover the model space when endowed with the Fisher Information Matrix as metric, $n$ being the number of observations. The number of observations fixes a natural scale or resolution. The effective dimension is then measured via the spectrum of the Fisher Information Matrix regularized using this natural scale.
