Human choice is complex in two ways. First, human choice often shows complex dependency on available alternatives. Second, human choice is often made after examining complex items such as images. The recently proposed choice model based on the restricted Boltzmann machine (RBM choice model) has been proved to represent three typical phenomena of human choice, which addresses the first complexity. We extend the RBM choice model to a deep choice model (DCM) to deal with the features of items, which are ignored in the RBM choice model. We then use deep learning to extract latent features from images and plug those latent features as input to the DCM. Our experiments show that the DCM adequately learns the choice that involves both of the two complexities in human choice.
The way that people make choices or exhibit preferences can be strongly affected by the set of available alternatives, often called the choice set. Furthermore, there are usually heterogeneous preferences, either at an individual level within small groups or within sub-populations of large groups. Given the availability of choice data, there are now many models that capture this behavior in order to make effective predictions. However, there is little work in understanding how directly changing the choice set can be used to influence a group's preferences or decisions. Here, we use discrete choice modeling to develop an optimization framework of such interventions for several problems of group influence, including maximizing agreement or disagreement and promoting a particular choice. We show that these problems are NP-hard in general but imposing restrictions reveals a fundamental boundary: promoting an item is easier than maximizing agreement or disagreement. After, we design approximation algorithms for the hard problems and show that they work extremely well for real-world choice data.
Many applications in preference learning assume that decisions come from the maximization of a stable utility function. Yet a large experimental literature shows that individual choices and judgements can be affected by "irrelevant" aspects of the context in which they are made. An important class of such contexts is the composition of the choice set. In this work, our goal is to discover such choice set effects from raw choice data. We introduce an extension of the Multinomial Logit (MNL) model, called the context dependent random utility model (CDM), which allows for a particular class of choice set effects. We show that the CDM can be thought of as a second-order approximation to a general choice system, can be inferred optimally using maximum likelihood and, importantly, is easily interpretable. We apply the CDM to both real and simulated choice data to perform principled exploratory analyses for the presence of choice set effects.
We study the problem of learning choice functions, which play an important role in various domains of application, most notably in the field of economics. Formally, a choice function is a mapping from sets to sets: Given a set of choice alternatives as input, a choice function identifies a subset of most preferred elements. Learning choice functions from suitable training data comes with a number of challenges. For example, the sets provided as input and the subsets produced as output can be of any size. Moreover, since the order in which alternatives are presented is irrelevant, a choice function should be symmetric. Perhaps most importantly, choice functions are naturally context-dependent, in the sense that the preference in favor of an alternative may depend on what other options are available. We formalize the problem of learning choice functions and present two general approaches based on two representations of context-dependent utility functions. Both approaches are instantiated by means of appropriate neural network architectures, and their performance is demonstrated on suitable benchmark tasks.