Abstract: In many applications, it is a priori known that the
target function should satisfy certain constraints imposed by, for
example, economic theory or a human-decision maker. Here we
consider partially monotone problems, where the target variable
depends monotonically on some of the predictor variables but not all.
We propose an approach to build partially monotone models based
on the convolution of monotone neural networks and kernel
functions. The results from simulations and a real case study on
house pricing show that our approach has significantly better
performance than partially monotone linear models. Furthermore, the
incorporation of partial monotonicity constraints not only leads to
models that are in accordance with the decision maker's expertise,
but also reduces considerably the model variance in comparison to
standard neural networks with weight decay.
Abstract: In many data mining applications, it is a priori known
that the target function should satisfy certain constraints imposed
by, for example, economic theory or a human-decision maker. In this
paper we consider partially monotone prediction problems, where the
target variable depends monotonically on some of the input variables
but not on all. We propose a novel method to construct prediction
models, where monotone dependences with respect to some of
the input variables are preserved by virtue of construction. Our
method belongs to the class of mixture models. The basic idea is to
convolute monotone neural networks with weight (kernel) functions
to make predictions. By using simulation and real case studies,
we demonstrate the application of our method. To obtain sound
assessment for the performance of our approach, we use standard
neural networks with weight decay and partially monotone linear
models as benchmark methods for comparison. The results show that
our approach outperforms partially monotone linear models in terms
of accuracy. Furthermore, the incorporation of partial monotonicity
constraints not only leads to models that are in accordance with the
decision maker's expertise, but also reduces considerably the model
variance in comparison to standard neural networks with weight
decay.