When observing multiple realizations of a stochasic
process such as an experimental system, large systematic sources of
variability are often present. For example, from one replicate to the
next, the time axis can be variously shifted, compressed and expanded,
in complex, non-linear ways. Additionally, in some circumstances,
the scale of the measured data varies systematically from replicate to
replicate, and even within a given replicate.
We propose a conditional Hidden Markov Model architecture for analyzing such data in which each realization is generated as a noisy transformation of a single latent trace. Hidden variables determine the transformation by controlling the time warping and amplitude scaling applied to the latent trace at each time. Learning in this model can be performed using the EM algorithm, as for input-output HMMs, except that the input is unknown and shared across all observation sequences. We apply this model to aligning data records from Liquid Chromatography - Mass Spectroscopy (LC-MS) experiments. In doing so we are able to leverage information contained in noisy, replicated experimental data, obtaining a single, superior resolution 'fusion' of the data. We also extend our model to allow similar, non-replicate data to be aligned and scaled, thereby enabling comparison of such data, as well as further downstream analysis.
This is work in progress, jointly with Sam Roweis and Radford Neal.