1. In a method for linear prediction of information determinable from at least one input signal comprising a plurality of data points, a method for training a linear prediction filter comprising: providing at least one reference signal comprising reference data having known values; collecting observed data corresponding to the at least one reference signal; identifying a reduced order data space comprising a reduced order Krylov subspace between the observed data and the reference data; and maximizing mutual data between the observed data and the reference data in the reduced order data space to define an autoregressive weight for use in the linear prediction filter.