RAS algorithm

The RAS algorithm proposed by Bacharach (1965) estimates a nonnegative matrix from its marginals, a task frequently arising in input-output analysis. RAS is similar to the Iterative Proportional Fitting Procedure (IPFP). Both algorithms iteratively apply interchanging row and column fitting steps to achieve entropy minimization and maximum-likelihood estimation under certain distributional assumptions.

RAS generates a matrix ${\hat {A}}$ similar to the intial matrix $A$, that is, small elements of $A$ are small in ${\hat {A}}$. This is the property of structure conservation. Assuming an underlying multinomial distribution, the estimated matrix ${\hat {A}}$ is the most probable one given the specified marginal constraints.