Exploiting monotonicity via logistic regression in Bayesian network learning

An important challenge in machine learning is to find ways of learning quickly from very small amounts of training data. The only way to learn from small data samples is to constrain the learning process by exploiting background knowledge. In this report, we present a theoretical analysis on the use of constrained logistic regression for estimating conditional probability distribution in Bayesian Networks (BN) by using background knowledge in the form of qualitative monotonicity statements. Such background knowledge is treated as a set of constraints on the parameters of a logistic function during training. Our goal of finding the appropriate BN model is two-fold: (a) we want to exploit any monotonic relationship between random variables that may generally exist as domain knowledge and (b) we want to be able to address the problem of estimating the conditional distribution of a random variable with a large number of parents. We discuss variants of the logistic regression model and present an analysis on the corresponding constraints required to implement monotonicity. More importantly, we outline the problem in some of these variants in terms of the number of parameters and constraints which, in some cases, can grow exponentially with the number of parent variables. To address this problem, we present two variants of the constrained logistic regression model, M[superscipt 2b][subscript CLR] and M³[subscript CLR], in which the number of constraints required to implement monotonicity does not grow exponentially with the number of parents hence providing a practicable method for estimating conditional probabilities with very sparse data.Keywords: logistic regression, Bayesian network learning, monotonicit

An Update Procedure for A Probabilistic Deductive Database

A sound and complete view update procedure for a probabilistic deductive database is formulated using SLDp derivation trees introduced by Ng and Subrahmanian in [8]. In order to reduce the number of valid translations that can satisfy an update request a preference criteria is proposed. Moreover, we introduce a method called Δ-factor to minimize the change effected by updates in the database

ARGUER: Using Argument Schemas for Argument Detection and Rebuttal in Dialogs

This paper presents a computational method for argumentation on the basis of a declarative characterizatio

Welfare implications of Pigovian taxation of a durable goods monopolist

This paper examines the effectiveness of Pigovian taxation in checking the behaviour of a durable goods monopolist who generates some externality in the production process. The durable good lasts two periods. It is found that while the effect of an increase in the tax is to lower the first period output, the second period output decreases only under certain conditions. The overall welfare effect of a Pigovian tax can either be positive or negative depending on the relative magnitudes of the price-cost margins, the extent of the negative externality, the extent of longevity (durability) of the first period output and the underproduction relative to social optima. Public policy implications are discussed.