In this paper, we propose a new machine learning method, called
adjustive linear regression, which can be regarded as
an ANN on an architecture with an input layer and an output layer
of a single node, wherein an error function is minimized
by choosing not only weights of the arcs but also
an activation function at each node in the two layers simultaneously.
Under some conditions,
such a minimization can be formulated as a linear program (LP)
and a prediction function with adjustive linear regression
is obtained as an optimal solution to the LP.
We apply the new machine learning method to
a framework of inferring a chemical compound with a desired property
(i.e., inverse QSAR).
From the results of our computational experiments,
we observe that a prediction function constructed by adjustive linear regression
for some chemical properties
drastically outperforms that by Lasso linear regression.