Multivariate Gaussian Distribution
Consider the i.i.d. Gaussian variables \(z_i \sim N(\mu,\sigma)\), where \(\mu=0\)
and \(\sigma=1\). The random variables from a linear combination of \(z_i\), e.g.
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Mapping the real domain into a finite interval
How to construct \(f: \mathbb{R} \mapsto (a,b)\)?
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Newton's method
To numerically find a root of \(f(x)=0\), we may use the Newton’s method. Assuming
the root is at the proximity of \(x_k\), to find a better approximate \(x_{k+1}\),
we consider the tangent line at \((x_k, f(x_k))\), which is provided by the
equation
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Property of Matrix and Its Eigenvalues
For a matrix \(A\), and its eigenvalue \(\lambda_i\)
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Covariance & Correlation
Consider random variables \(X\) and \(Y\), to measure how much they change together, we use covariance:
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