arXiv subjects

David M. Pennock

Publications and source records attributed to David M. Pennock.

22 records · Page 2Linked to original sources

arXiv2013

Compact Securities Markets for Pareto Optimal Reallocation of Risk

The emph{securities market} is the fundamental theoretical framework in economics and finance for resource allocation under uncertainty. Securities serve both to reallocate risk and to disseminate probabilistic information. emph{Complete} securities markets - which contain one security for every possible state of nature - support Pareto optimal allocations of risk. Complete markets suffer from the same exponential dependence on the number of underlying events as do joint probability distributions. We examine whether markets can be structured and "compacted" in the same manner as Bayesian network representations of joint distributions. We show that, if all agents' risk-neutral independencies agree with the independencies encoded in the market structure, then the market is emph{operationally complete}: risk is still Pareto optimally allocated, yet the number of securities can be exponentially smaller. For collections of agents of a certain type, agreement on Markov independencies is sufficient to admit compact and operationally complete markets.

cs.GT↗

arXiv2012

Price Updating in Combinatorial Prediction Markets with Bayesian Networks

To overcome the #P-hardness of computing/updating prices in logarithm market scoring rule-based (LMSR-based) combinatorial prediction markets, Chen et al. [5] recently used a simple Bayesian network to represent the prices of securities in combinatorial predictionmarkets for tournaments, and showed that two types of popular securities are structure preserving. In this paper, we significantly extend this idea by employing Bayesian networks in general combinatorial prediction markets. We reveal a very natural connection between LMSR-based combinatorial prediction markets and probabilistic belief aggregation,which leads to a complete characterization of all structure preserving securities for decomposable network structures. Notably, the main results by Chen et al. [5] are corollaries of our characterization. We then prove that in order for a very basic set of securities to be structure preserving, the graph of the Bayesian network must be decomposable. We also discuss some approximation techniques for securities that are not structure preserving.

cs.GT↗

arXiv2008

Complexity of Combinatorial Market Makers

We analyze the computational complexity of market maker pricing algorithms for combinatorial prediction markets. We focus on Hanson's popular logarithmic market scoring rule market maker (LMSR). Our goal is to implicitly maintain correct LMSR prices across an exponentially large outcome space. We examine both permutation combinatorics, where outcomes are permutations of objects, and Boolean combinatorics, where outcomes are combinations of binary events. We look at three restrictive languages that limit what traders can bet on. Even with severely limited languages, we find that LMSR pricing is $\SP$-hard, even when the same language admits polynomial-time matching without the market maker. We then propose an approximation technique for pricing permutation markets based on a recent algorithm for online permutation learning. The connections we draw between LMSR pricing and the vast literature on online learning with expert advice may be of independent interest.

cs.GT↗

arXiv2002

The structure of broad topics on the Web

The Web graph is a giant social network whose properties have been measured and modeled extensively in recent years. Most such studies concentrate on the graph structure alone, and do not consider textual properties of the nodes. Consequently, Web communities have been characterized purely in terms of graph structure and not on page content. We propose that a topic taxonomy such as Yahoo! or the Open Directory provides a useful framework for understanding the structure of content-based clusters and communities. In particular, using a topic taxonomy and an automatic classifier, we can measure the background distribution of broad topics on the Web, and analyze the capability of recent random walk algorithms to draw samples which follow such distributions. In addition, we can measure the probability that a page about one broad topic will link to another broad topic. Extending this experiment, we can measure how quickly topic context is lost while walking randomly on the Web graph. Estimates of this topic mixing distance may explain why a global PageRank is still meaningful in the context of broad queries. In general, our measurements may prove valuable in the design of community-specific crawlers and link-based ranking systems.

cs.IR↗