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模型辅助变量聚类：极小极大最优恢复与算法AI 解读

The problem of variable clustering is that of estimating groups of similar components of a $p$-dimensional vector $X=(X_{1},\ldots ,X_{p})$ from $n$ independent copies of $X$. There exists a large number of algorithms that return data-dependent groups of variables, but their interpretation is limited to the algorithm that produced them. An alternative is model-based clustering, in which one begins by defining population level clusters relative to a model that embeds notions…

稀疏精度矩阵估计的约束 ℓ1 最小化方法AI 解读

This article proposes a constrained ℓ1 minimization method for estimating a sparse inverse covariance matrix based on a sample of n iid p-variate random variables. The resulting estimator is shown to have a number of desirable properties. In particular, the rate of convergence between the estimator and the true s-sparse precision matrix under the spectral norm is when the population distribution has either exponential-type tails or polynomial-type tails. We present…