Tag: regression
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An iterative reweighted least squares miracle
In Section 4.3.3 of his “Pattern Recognition and Machine Learning,” Bishop discusses the application of iterative reweighted least squares (IRLS) to maximum likelihood estimation of the parameters in logistic regression. The expression we get after computing the Newton-Raphson update of the parameters is $$ \ww^\text{(new)} = (\bPhi^T \RR \bPhi)^{-1} \bPhi^T \RR \zz,$$ where $$ \zz…
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Reaction rate inference
Consider the toy example set of reactions\begin{align*}S_0 &\xrightarrow{k_1} S_1 + S_2\\S_2 &\xrightarrow{k_2}S_3 + S_4\\S_1 + S_3 &\xrightarrow{k_3} S_5\end{align*}We have (noisy) data on the concentrations of the species as a function of time. We want to infer the rates $k_1$ to $k_3$. Let’s write the derivatives:\begin{align*}\dot S_0 &=- k_1 S_0\\\dot S_1 &= k_1 S_0 -k_3 S_1…