Uniform random generation of large acyclic digraphs

Directed acyclic graphs are the basic representation of the structure underlying Bayesian networks, which represent multivariate probability distributions. In many practical applications, such as the reverse engineering of gene regulatory networks, not only the estimation of model parameters but the reconstruction of the structure itself is of great interest. As well as for the assessment of different structure learning algorithms in simulation studies, a uniform sample from the space of directed acyclic graphs is required to evaluate the prevalence of certain structural features. Here we analyse how to sample acyclic digraphs uniformly at random through recursive enumeration, an approach previously thought too computationally involved. Based on complexity considerations, we discuss in particular how the enumeration directly provides an exact method, which avoids the convergence issues of the alternative Markov chain methods and is actually computationally much faster. The limiting behaviour of the distribution of acyclic digraphs then allows us to sample arbitrarily large graphs. Building on the ideas of recursive enumeration based sampling we also introduce a novel hybrid Markov chain with much faster convergence than current alternatives while still being easy to adapt to various restrictions. Finally we discuss how to include such restrictions in the combinatorial enumeration and the new hybrid Markov chain method for efficient uniform sampling of the corresponding graphs.Comment: 15 pages, 2 figures. To appear in Statistics and Computin

SimMarket: Multiagent-Based Customer Simulation and Decision Support for Category Management

A key to an optimal assortment of goods and pricing of individual items in a store is the knowledge about potential customer's behaviour. In this paper we present the simulation of individual customers based on a multiagent system which models the important elements and external influences as single agents. An agent can be member of several agent groups which are represented as holons. We model each individual customer as an agent which behaves according the customer's individual preferences. These preferences are extracted from real world data, such as customer cards, sales data and interviews. The customer's shopping behaviour is represented in behaviour networks (Bayesian nets) which are stored in the customer agents' knowledge bases. The behaviour of a representative group of customers induces the overall sales figures, which support decisions what to sell at which price. The presented concepts are based on ideas of Joachim Hertel from DACOS and Jrg Siekmann from the DFKI

Visual recognition with humans in the loop

Abstract. We present an interactive, hybrid human-computer method for object classification. The method applies to classes of objects that are recognizable by people with appropriate expertise (e.g., animal species or airplane model), but not (in general) by people without such expertise. It can be seen as a visual version of the 20 questions game, where questions based on simple visual attributes are posed interactively. The goal is to identify the true class while minimizing the number of questions asked, using the visual content of the image. We introduce a general framework for incorporating almost any off-the-shelf multi-class object recognition algorithm into the visual 20 questions game, and provide methodologies to account for imperfect user responses and unreliable computer vision algorithms. We evaluate our methods on Birds-200, a difficult dataset of 200 tightly-related bird species, and on the Animals With Attributes dataset. Our results demonstrate that incorporating user input drives up recognition accuracy to levels that are good enough for practical applications, while at the same time, computer vision reduces the amount of human interaction required.