Protein Fold Recognition Using Markov Logic Networks - Mathematical Approaches to Polymer Sequence Analysis and Related Problems - page 80

a cluster of solutions. A cluster of solutions is usually a set of connected solutions,
so that any two solutions within the cluster can be connected through a series of flips
without leaving the cluster. In many domains of interest, solutions exist in clusters
and it is highly useful to explore such clusters without leaving them. SA has good
properties in exploring a connected space; therefore, it samples near-uniformly and
often explores all the neighboring solutions.
Through MC-IRoTS, we can perform conditional inference given evidence to
compute probabilities for query predicates. These probabilities can be used to make
predictions from the model.

4.6.2 Discriminative Learning by Sampling with MC-IRoTS

Discriminative approaches to weight learning try to optimize the CLL. Precon-
ditioned scaled conjugate gradient (PSCG) is the state-of-the-art discriminative
training algorithm for MLN and it was shown in [ 15 ] to outperform the voted per-
ceptron. PSCG is a conjugate gradient method that uses samples from MC-SAT
to approximate the Hessian for MLNs instead of the line search to choose a step
size. This approach is also known as scaled conjugate gradient and was originally
proposed in [ 20 ] for training neural networks. PSCG, in each iteration, takes a step
in the diagonalized Newton direction (for details, see [ 15 ]). Here, we propose to
use MC-IRoTS to sample for approximating the Hessian for SMLNs. The goal is
to use samples from MC-IRoTS that can serve as good estimates for computing the
Hessian.

4.7 Modeling Protein Sequences in SMLNs

In this section, we describe how sequences of protein secondary structure can be
modeled in SMLNs, how to learn model parameters from the data, and how to make
predictions from the model.

4.7.1 Model Construction and Weight Learning

The approach we follow is quite simple: we write a few formulas that represent the
structure of the domain and then from the training sequences we learn the weights
of these formulas.
The dataset we refer to is that used in [ 10 ]. The data consist of logical sequences
of the secondary structure of protein domains:

beginSequence :
strand . 0 SB 0 ; null ; medium /: