Learning bipartite Bayesian networks under monotonicity restrictions

ABSTRACT

Learning parameters of a probabilistic model is a necessary step in machine learning tasks. We present a method to improve learning from small datasets by using monotonicity conditions. Monotonicity simplifies the learning and it is often required by users. We present an algorithm for Bayesian Networks parameter learning. The algorithm and monotonicity conditions are described, and it is shown that with the monotonicity conditions we can better fit underlying data. Our algorithm is tested on artificial and empiric datasets. We use different methods satisfying monotonicity conditions: the proposed gradient descent, isotonic regression EM, and non-linear optimization. We also provide results of unrestricted EM and gradient descent methods. Learned models are compared with respect to their ability to fit data in terms of log-likelihood and their fit of parameters of the generating model. Our proposed method outperforms other methods for small sets, and provides better or comparable results for larger sets.