Model and learning algorithm

The functional form and learning algorithm for the nonlinear dynamic
factor analysis (NDFA) model proposed in this report are very close to
the ones introduced for NLFA in [4]: the mappings
**f** and
**g** are modelled by MLP networks and a gradient
based learning algorithm is used for iteratively updating the
approximation of the posterior probability of the unknown variables.
There are some modifications, however, which take into account the
fact that the mapping
**g** models the dynamics of the factors.

First of all, it can be expected that the values of the factors
**s**(*t*) are close to the values at the previous time step
**s**(*t*-1). This prior knowledge can be taken into account by
using the MLP network to model only the change in factors instead of
trying to learn the whole mapping from
**s**(*t*-1) to
**s**(*t*). The functional form of the dynamic mapping
**g**is thus

(3) |

while the observation mapping is

(4) |

It should be noted that the MLP network modelling the dynamics can learn to overrule the term

- Improved approximation of the posterior probability
- Feedforward and backward computations
- Correction of the step size
- Initialisation of the factors