Most classification approaches aim at achieving high prediction accuracy on a given dataset. However, in most practical cases, some action such as mailing an offer or treating a patient is to be taken on the classified objects, and we should model not the class probabilities themselves, but instead, the change in class probabilities caused by the action. The action should then be performed on those objects for which it will be most profitable. This problem is known as uplift modeling, differential response analysis, or true lift modeling, but has received very little attention in machine learning literature. An important modification of the problem involves several possible actions, when for each object, the model must also decide which action should be used in order to maximize profit. In this paper, we present tree-based classifiers designed for uplift modeling in both single and multiple treatment cases. To this end, we design new splitting criteria and pruning methods. The experiments confirm the usefulness of the proposed approaches and show significant improvement over previous uplift modeling techniques.

background or methods

/pdf/decision-trees-for-uplift-modeling-with-single-and-multiple-52az26jynb.pdf

Mathematics of information and coding

Decision trees for uplift modeling with single and multiple treatments

A sequence of binary random variables has found significant applications in modem digital communication systems. For such sequences, several kinds of linear feedback shift register sequences have been proposed. It is, however, well known in probability theory that the Bernoulli shift is a fundamental theoretic model of a sequence of independent identically distributed (i.i.d.) binary random variables. In this paper after reviewing fundamental subjects of chaotic dynamics, in particular a close relationship between information sources and Markov chains, we give the generation method of sequences of i.i.d. binary random variables using chaotic dynamics. Such a generation method is given as a sufficient condition composed of simple symmetric properties for some class of ergodic maps. Furthermore, we give the applications of such sequences: (1) to running-key sequences for stream cipher systems and (2) to a color image communication system through code-division multiple access channels and its extended version, a digital watermarking system. In addition, the performance of spread spectrum codes generated by a Markov chain is theoretically evaluated in asynchronous direct-sequence/code-division multiple access systems.

Information Sources Using Chaotic Dynamics

Information sources using chaotic dynamics

Starting with a new formulation for the mutual information (MI) between a pair of events, this paper derives alternative upper bounds and extends those to the case of two discrete random variables. Normalized mutual information (NMI) measures are then obtained from those bounds, emphasizing the use of least upper bounds. Conditional NMI measures are also derived for three different events and three different random variables. Since the MI formulation for a pair of events is always nonnegative, it can properly be extended to include weighted MI and NMI measures for pairs of events or for random variables that are analogous to the well-known weighted entropy. This weighted MI is generalized to the case of continuous random variables. Such weighted measures have the advantage over previously proposed measures of always being nonnegative. A simple transformation is derived for the NMI, such that the transformed measures have the value-validity property necessary for making various appropriate comparisons between values of those measures. A numerical example is provided.

background

On Normalized Mutual Information: Measure Derivations and Properties

Most classification approaches aim at achieving high prediction accuracy on a given dataset. However, in most practical cases, some action, such as mailing an offer or treating a patient, is to be taken on the classified objects and we should model not the class probabilities themselves, but instead, the change in class probabilities caused by the action. The action should then be performed on those objects for which it will be most profitable. This problem is known as uplift modeling, differential response analysis or true lift modeling, but has received very little attention in Machine Learning literature. In the paper we present a tree based classifier tailored specifically to this task. To this end, we design new splitting criteria and pruning methods. The experiments confirm the usefulness of the proposed approach and show significant improvement over previous uplift modeling techniques.

Decision Trees for Uplift Modeling

/pdf/mathematics-of-information-and-coding-5cegxs0q5g.pdf

Mathematics of information and coding

Citations

Decision trees for uplift modeling with single and multiple treatments

Information Sources Using Chaotic Dynamics

Information sources using chaotic dynamics

On Normalized Mutual Information: Measure Derivations and Properties

Decision Trees for Uplift Modeling

Related Papers (5)

Elements of information theory

An introduction to statistical communication theory

Elementary information theory

Image Analysis and Mathematical Morphology

Number theory in digital signal processing