Stable Mixing of Complete and Incomplete Information

An increasing number of parameter estimation tasks involve the use of at least two information sources, one complete but limited, the other abundant but incomplete. Standard algorithms such as EM (or em) used in this context are unfortunately not stable in the sense that they can lead to a dramatic loss of accuracy with the inclusion of incomplete observations. We provide a more controlled solution to this problem through differential equations that govern the evolution of locally optimal solutions (fixed points) as a function of the source weighting. This approach permits us to explicitly identify any critical (bifurcation) points leading to choices unsupported by the available complete data. The approach readily applies to any graphical model in O(n^3) time where n is the number of parameters. We use the naive Bayes model to illustrate these ideas and demonstrate the effectiveness of our approach in the context of text classification problems

Planning with Incomplete Information

Planning is a natural domain of application for frameworks of reasoning about actions and change. In this paper we study how one such framework, the Language E, can form the basis for planning under (possibly) incomplete information. We define two types of plans: weak and safe plans, and propose a planner, called the E-Planner, which is often able to extend an initial weak plan into a safe plan even though the (explicit) information available is incomplete, e.g. for cases where the initial state is not completely known. The E-Planner is based upon a reformulation of the Language E in argumentation terms and a natural proof theory resulting from the reformulation. It uses an extension of this proof theory by means of abduction for the generation of plans and adopts argumentation-based techniques for extending weak plans into safe plans. We provide representative examples illustrating the behaviour of the E-Planner, in particular for cases where the status of fluents is incompletely known.Comment: Proceedings of the 8th International Workshop on Non-Monotonic Reasoning, April 9-11, 2000, Breckenridge, Colorad

Bargaining with Incomplete Information

A central question in economics is understanding the difficulties that parties have in reaching mutually beneficial agreements. Informational differences provide an appealing explanation for bargaining inefficiencies. This chapter provides an overview of the theoretical and empirical literature on bargaining with incomplete information. The chapter begins with an analysis of bargaining within a mechanism design framework. A modern development is provided of the classic result that, given two parties with independent private valuations, ex post efficiency is attainable if and only if it is common knowledge that gains from trade exist. The classic problems of efficient trade with one-sided incomplete information but interdependent valuations, and of efficiently dissolving a partnership with two-sided incomplete information, are also reviewed using mechanism design. The chapter then proceeds to study bargaining where the parties sequentially exchange offers. Under one-sided incomplete information, it considers sequential bargaining between a seller with a known valuation and a buyer with a private valuation. When there is a "gap" between the seller's valuation and the support of buyer valuations, the seller-offer game has essentially a unique sequential equilibrium. This equilibrium exhibits the following properties: it is stationary, trade occurs in finite time, and the price is favorable to the informed party (the Coase Conjecture). The alternating-offer game exhibits similar properties, when a refinement of sequential equilibrium is applied. However, in the case of "no gap" between the seller's valuation and the support of buyer valuations, the bargaining does not conclude with probability one after any finite number of periods, and it does not follow that sequential equilibria need be stationary. If stationarity is nevertheless assumed, then the results parallel those for the "gap" case. However, if stationarity is not assumed, then instead a folk theorem obtains, so substantial delay is possible and the uninformed party may receive substantial surplus. The chapter also briefly sketches results for sequential bargaining with two-sided incomplete information. Finally, it reviews the empirical evidence on strategic bargaining with private information by focusing on one of the most prominent examples of bargaining: union contract negotiations.Bargaining; Delay; Incomplete Information

Games with Incomplete Information

Prize Lecture to the memory of Alfred Nobel, December 9, 1994.Game Theory; Incomplete Information

Nonextensive statistics and incomplete information

We comment on some open questions and theoretical peculiarities in Tsallis nonextensive statistical mechanics. It is shown that the theoretical basis of the successful Tsallis' generalized exponential distribution shows some worrying properties with the conventional normalization and the escort probability. These theoretical difficulties may be avoided by introducing an so called incomplete normalization allowing to deduce Tsallis' generalized distribution in a more convincing and consistent way.Comment: 21 pages, RevTeX, no figures, published version to appear in Euro. J. Phys. B (2002

Robust Localization from Incomplete Local Information

We consider the problem of localizing wireless devices in an ad-hoc network embedded in a d-dimensional Euclidean space. Obtaining a good estimation of where wireless devices are located is crucial in wireless network applications including environment monitoring, geographic routing and topology control. When the positions of the devices are unknown and only local distance information is given, we need to infer the positions from these local distance measurements. This problem is particularly challenging when we only have access to measurements that have limited accuracy and are incomplete. We consider the extreme case of this limitation on the available information, namely only the connectivity information is available, i.e., we only know whether a pair of nodes is within a fixed detection range of each other or not, and no information is known about how far apart they are. Further, to account for detection failures, we assume that even if a pair of devices is within the detection range, it fails to detect the presence of one another with some probability and this probability of failure depends on how far apart those devices are. Given this limited information, we investigate the performance of a centralized positioning algorithm MDS-MAP introduced by Shang et al., and a distributed positioning algorithm, introduced by Savarese et al., called HOP-TERRAIN. In particular, for a network consisting of n devices positioned randomly, we provide a bound on the resulting error for both algorithms. We show that the error is bounded, decreasing at a rate that is proportional to R/Rc, where Rc is the critical detection range when the resulting random network starts to be connected, and R is the detection range of each device.Comment: 40 pages, 13 figure

Incomplete information and fractal phase space

The incomplete statistics for complex systems is characterized by a so called incompleteness parameter $\omega$ which equals unity when information is completely accessible to our treatment. This paper is devoted to the discussion of the incompleteness of accessible information and of the physical signification of $\omega$ on the basis of fractal phase space. $\omega$ is shown to be proportional to the fractal dimension of the phase space and can be linked to the phase volume expansion and information growth during the scale refining process.Comment: 12 pages, 2 ps figure, Te