I'm trying to implement a truth discovery algorithm from an academic paper. It is a streaming algorithm that infers the truth as well as source quality in real time. More details here if anyone is interested in reading the paper: http://dl.acm.org/citation.cfm?id=2661892
My problem is that I don't understand a formula in the algorithm, or to be precise the notation of one of the formulas and I'm having difficulties in implementing it in R or Python. It seems to be an exponential formula of some kind, but I haven't found anything about it in math books. To make things more complex there's a proportional to sign? instead of value assignment (=). Any pointers would be greatly appreciated.
The formula:
The expression consists of two exponential functions multiplied together, $$e^{a}e^{b},$$
where both $a$ and $b$ is a function of another function, $\psi$, which should be specified in the paper. We have $$a=\psi(a_1)-\psi(a_2),$$
where $a_1$ is some variable $\gamma_{i,j}^t$ and $a_2$ is a sum. $b$ consists of two terms: A double summation over all different $s\in S$ (which is found in the superscripts of the $\lambda$s) and $j$, and a term where we again see the function $\psi$ taking a sum as its variable.
Note that all sums over $m$ and $j$ only consists of two terms.
As for the proportionality (instead of the equality), you can make it an equality by introducing some constant (say $k$), so that $\eta=k e^ae^b$, but since the authors didn't include it, it probably won't be used; one could for instance imagine that the formula was only used when describing ratios of different $\eta$, where the $k$s would cancel (for instance in $\frac{\eta_1}{\eta_2}$, where no $k$ is needed).
I hope that clears things up a bit.