the multivariate Gaussian is parameterized by: mean vector μ and covariance matrix Σ

Principal component analysis

Eigenvectors point along maximum variance

the determinant tells you about volume scaling under a linear transformation

The determinant of a matrix representing a linear transformation indicates the factor by which volumes are scaled

the Gram-Schmidt process does: orthogonalizes a set of vectors

Orthogonalizes a set of vectors using Gram-Schmidt

to standardize: when you need zero mean and unit variance for gradient-based optimization

Standardize when zero mean and unit variance are required for gradient-based optimization

PCA vs t-SNE: PCA preserves global variance linearly, t-SNE preserves local structure nonlinearly

PCA: Linear variance preservation, t-SNE: Nonlinear local structure preservation

2024 in hip-hop

LoRA rank r controls model capacity and parameters