User:Nuri Purswani/NetworkReconstruction/Algorithms/Rangel

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Rangel et al 2008

General Description

Rangel's algorithm is a bayesian network inference approach that recovers network structure from gene expression data. The main steps of the algorithm can be summarised as follows:

1. Input time series data- From an in-silico model or from a microarray experiment.
   1. To achieve optimal performance, it is better to include many repeats and time points.
2. Based on the assumption that the probability distributions of the hidden states and observations are Gaussian distributed (see below), the algorithm applies the Expectation Maximization algorithm to estimate the log likelihood of any parameter, given the data observation.
3. The algorithm also contains a Kalman Smoothing step, that solves for the expectation values in the Linear Gaussian State Space Model.
4. To increase the accuracy of parameter estimation it generates NB independent bootstrap estimates, and computes the parameters and their distribution based on the results.

For a detailed derivation of these steps, see Rangel et. al 2005.

What are the inputs and outputs?

This Algorithm requires the data to be input in the following form:

[math]\displaystyle{ \bar x_{t+1} = A \bar x_t + \bar w_t }[/math]
[math]\displaystyle{ y_{t} = H \bar x_t }[/math]

where [math]\displaystyle{ \bar x_t = \begin{pmatrix} x_t \\ y_t \end{pmatrix} }[/math] and [math]\displaystyle{ x_t }[/math] and [math]\displaystyle{ y_t }[/math] are vectors of of length [math]\displaystyle{ T }[/math] with dimensions corresponding to the number of hidden states [math]\displaystyle{ k }[/math] and the number of observed states [math]\displaystyle{ p }[/math] respectively.

What are the Mathematical Assumptions?

Flow Diagram