# tonyday567/online-random

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# online-random

Random stream experiments

## alpha

\begin{align} \alpha & = \frac{\sum y \sum x^2 - \sum x \sum xy}{n\sum x^2 - (\sum x)^2} \ & = \frac{n^2 \bar{y} \overline{x^2} - n^2 \bar{x} \overline{xy}}{n^2 \overline{x^2} - n^2 \bar{x}^2} \ & = \frac{\bar{y} \overline{x^2} - \bar{x} \overline{xy}}{\overline{x^2} - \bar{x}^2} \

\end{align}

## beta

\begin{align} \beta & = \frac{n\sum xy - \sum x \sum y}{n\sum x^2 - (\sum x)^2} \ & = \frac{n^2 \overline{xy} - n^2 \bar{x} \bar{y}}{n^2 \overline{x^2} - n^2 \bar{x}^2} \ & = \frac{\overline{xy} - \bar{x} \bar{y}}{\overline{x^2} - \bar{x}^2} \

\end{align}

## Dependencies across moments

\begin{align}

x_{t+1} & = (alpha_t^x + beta_t^{x->x} * ma_t^x + beta_t^{s->x} * std_t^x) + s_{t+1}\ s_{t+1} & = (alpha_t^s + beta_t^{x->s} * ma_t^x + beta_t^{s->s} * std_t^x) * N(0,1)

\end{align}

## online algorithm references

$$\Gamma _{i}=\Gamma {i-1}-{\frac {\Gamma {i-1}x{i}x{i}^{T}\Gamma {i-1}}{1+x{i}^{T}\Gamma {i-1}x{i}}}$$

$$w_{i}=w_{i-1}-\Gamma {i}x{i}(x_{i}^{T}w_{i-1}-y_{i})$$

# workflow

stack build --test --exec "$(stack path --local-install-root)/bin/orand" --exec "$(stack path --local-bin)/pandoc -f markdown -i other/header.md readme.md other/footer.md -t html -o index.html --filter pandoc-include --mathjax" --file-watch