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.