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利用尖峰总体特征值估计脑磁图信号源数量AI 解读

Magnetoencephalography (MEG) is an advanced imaging technique used to measure the magnetic fields outside the human head produced by the electrical activity inside the brain. Various source localization methods in MEG require the knowledge of the underlying active sources, which are identified by a priori. Common methods used to estimate the number of sources include principal component analysis or information criterion methods, both of which make use of the eigenvalue…

用于大型精度矩阵估计的偏相关筛选及其分类应用AI 解读

Given $n$ samples $X_{1},X_{2},\ldots,X_{n}$ from $N(0,\Sigma)$, we are interested in estimating the $p\times p$ precision matrix $\Omega=\Sigma^{-1}$; we assume $\Omega$ is sparse in that each row has relatively few nonzeros. We propose Partial Correlation Screening (PCS) as a new row-by-row approach. To estimate the $i$th row of $\Omega$, $1\leq i\leq p$, PCS uses a Screen step and a Clean step. In the Screen step, PCS recruits a (small) subset of indices using a…

稀疏高斯图模型中的最优分类AI 解读

Consider a two-class classification problem where the number of features is much larger than the sample size. The features are masked by Gaussian noise with mean zero and covariance matrix $\Sigma$, where the precision matrix $\Omega=\Sigma^{-1}$ is unknown but is presumably sparse. The useful features, also unknown, are sparse and each contributes weakly (i.e., rare and weak) to the classification decision. By obtaining a reasonably good estimate of $\Omega$, we formulate…