  The Regression Tsetlin Machine (RTM) addresses the lack of interpretability
impeding state-of-the-art nonlinear regression models. It does this by using
conjunctive clauses in propositional logic to capture the underlying non-linear
frequent patterns in the data. These, in turn, are combined into a continuous
output through summation, akin to a linear regression function, however, with
non-linear components and unity weights. Although the RTM has solved non-linear
regression problems with competitive accuracy, the resolution of the output is
proportional to the number of clauses employed. This means that computation
cost increases with resolution. To reduce this problem, we here introduce
integer weighted RTM clauses. Our integer weighted clause is a compact
representation of multiple clauses that capture the same sub-pattern-N
repeating clauses are turned into one, with an integer weight N. This reduces
computation cost N times, and increases interpretability through a sparser
representation. We further introduce a novel learning scheme that allows us to
simultaneously learn both the clauses and their weights, taking advantage of
so-called stochastic searching on the line. We evaluate the potential of the
integer weighted RTM empirically using six artificial datasets. The results
show that the integer weighted RTM is able to acquire on par or better accuracy
using significantly less computational resources compared to regular RTMs. We
further show that integer weights yield improved accuracy over real-valued
ones.
