We present a principled approach for detecting overlapping temporal community structure in dynamic networks. Our method is based on the following framework: find the overlapping temporal community structure that maximizes a quality function associated with each snapshot of the network subject to a temporal smoothness constraint. A novel quality function and a smoothness constraint are proposed to handle overlaps, and a new convex relaxation is used to solve the resulting combinatorial optimization problem. We provide theoretical guarantees as well as experimental results that reveal community structure in real and synthetic networks. Our main insight is that certain structures can be identified only when temporal correlation is considered and when communities are allowed to overlap. In general, discovering such overlapping temporal community structure can enhance our understanding of real-world complex networks by revealing the underlying stability behind their seemingly chaotic evolution.

(l) I have enough evidence to render the sentence S probable. (la) So, relative to what I know, it is rational of me to believe S. (2) Now that I have more evidence, S may no longer be probable. (2a) So now, relative to what I know, it is not rational of me to believe S. These seem a perfectly ordinary, common sense, pair of situations. Generally and vaguely, I take them to embody what I shall call probabilistic inference. This form of inference is clearly non-monotonic. Relatively few people have taken this form of inference, based on high probability, to serve as a foundation for non-monotonic logic or for a logical or defeasible inference. There are exceptions: Jane Nutter [16] thinks that sometimes probability has something to do with non-monotonic reasoning. Judea Pearl [ 17] has recently been exploring the possibility. There are any number of people whom one might call probability enthusiasts who feel that probability provides all the answers by itself, with no need of help from logic. Cheeseman [1], Henrion [5] and others think it useful to look at a distribution of probabilities over a whole algebra of statements, to update that distribution in the light of new evidence, and to use the latest updated distribution of probability over the algebra as a basis for planning and decision making. A slightly weaker form of this approach is captured by Nilsson [15], where one assumes certain probabilities for certain statements, and infers the probabilities, or constraints on the probabilities of other statement. None of this corresponds to what I call probabilistic inference. All of the inference that is taking place, either in Bayesian updating, or in probabilistic logic, is strictly deductive. Deductive inference, particularly that concerned with the distribution of classical probabilities or chances, is of great importance. But this is not to say that there is no important role for what earlier logicians have called "ampliative" or "inductive" or "scientific" inference, in which the conclusion goes beyond the premises, asserts more than do the premises. This depends on what David Israel [6] has called "real rules of inference". It is characteristic of any such logic or inference procedure that it can go wrong: that statements accepted at one point may be rejected at a later point. Research underlying the results reported here has been partially supported by the Signals Warfare Center of the United States Army.

This paper addresses fundamental issues on the nature of the concepts and structures of fuzzy logic, focusing, in particular, on the conceptual and functional differences that exist between probabilistic and possibilistic approaches. A semantic model provides the basic framework to define possibilistic structures and concepts by means of a function that quantifies proximity, closeness, or resemblance between pairs of possible worlds. The resulting model is a natural extension, based on multiple conceivability relations, of the modal logic concepts of necessity and possibility. By contrast, chance-oriented probabilistic concepts and structures rely on measures of set extension that quantify the proportion of possible worlds where a proposition is true. Resemblance between possible worlds is quantified by a generalized similarity relation: a function that assigns a number between O and 1 to every pair of possible worlds. Using this similarity relation, which is a form of numerical complement of a classic metric or distance, it is possible to define and interpret the major constructs and methods of fuzzy logic: conditional and unconditioned possibility and necessity distributions and the generalized modus ponens of Zadeh.

Unaided human decision making appears to systematically violate consistency constraints imposed by normative theories; these biases in turn appear to justify the application of formal decision-analytic models. It is argued that both claims are wrong. In particular, we will argue that the "confirmation bias" is premised on an overly narrow view of how conflicting evidence is and ought to be handled. Effective decision aiding should focus on supporting the contral processes by means of which knowledge is extended into novel situations and in which assumptions are adopted, utilized, and revised. The Non- Monotonic Probabilist represents initial work toward such an aid.

Bayesian inference systems should be able to explain their reasoning to users, translating from numerical to natural language. Previous empirical work has investigated the correspondence between absolute probabilities and linguistic phrases. This study extends that work to the correspondence between changes in probabilities (updates) and relative probability phrases, such as "much more likely" or "a little less likely." Subjects selected such phrases to best describe numerical probability updates. We examined three hypotheses about the correspondence, and found the most descriptively accurate of these three to be that each such phrase corresponds to a fixed difference in probability (rather than fixed ratio of probabilities or of odds). The empirically derived phrase selection function uses eight phrases and achieved a 72% accuracy in correspondence with the subjects' actual usage.

The investigations reported in this paper center on the process of dynamic uncertainty assessment during interpretation tasks in real domain. In particular, we are interested here in the nature of the control structure of computer programs that can support multiple interpretation and smooth transitions between them, in real time. Each step of the processing involves the interpretation of one input item and the appropriate re-establishment of the system's confidence of the correctness of its interpretation(s).

An automated explanation facility for Bayesian conditioning aimed at improving user acceptance of probability-based decision support systems has been developed. The domain-independent facility is based on an information processing perspective on reasoning about conditional evidence that accounts both for biased and normative inferences. Experimental results indicate that the facility is both acceptable to naive users and effective in improving understanding.

In this paper we provide an overview of a new framework for robot perception, real-world modelling, and navigation that uses a stochastic tesselated representation of spatial information called the Occupancy Grid. The Occupancy Grid is a multi-dimensional random field model that maintains probabilistic estimates of the occupancy state of each cell in a spatial lattice. Bayesian estimation mechanisms employing stochastic sensor models allow incremental updating of the Occupancy Grid using multi-view, multi-sensor data, composition of multiple maps, decision-making, and incorporation of robot and sensor position uncertainty. We present the underlying stochastic formulation of the Occupancy Grid framework, and discuss its application to a variety of robotic tusks. These include range-based mapping, multi-sensor integration, path-planning and obstacle avoidance, handling of robot position uncertainty, incorporation of pre-compiled maps, recovery of geometric representations, and other related problems. The experimental results show that the Occupancy Grid approach generates dense world models, is robust under sensor uncertainty and errors, and allows explicit handling of uncertainty. It supports the development of robust and agile sensor interpretation methods, incremental discovery procedures, and composition of information from multiple sources. Furthermore, the results illustrate that robotic tasks can be addressed through operations performed di- rectly on the Occupancy Grid, and that these operations have strong parallels to operations performed in the image processing domain.

The fundamental elements of evidential reasoning problems are described, followed by a discussion of the structure of various types of problems. Bayesian inference networks and state space formalism are used as the tool for problem representation. A human-oriented decision making cycle for solving evidential reasoning problems is described and illustrated for a military situation assessment problem. The implementation of this cycle may serve as the basis for an expert system shell for evidential reasoning; i.e. a situation assessment processor.

We show an approach to automated control of machine vision systems based on incremental creation and evaluation of a particular family of influence diagrams that represent hypotheses of imagery interpretation and possible subsequent processing decisions. In our approach, model-based machine vision techniques are integrated with hierarchical Bayesian inference to provide a framework for representing and matching instances of objects and relationships in imagery and for accruing probabilities to rank order conflicting scene interpretations. We extend a result of Tatman and Shachter to show that the sequence of processing decisions derived from evaluating the diagrams at each stage is the same as the sequence that would have been derived by evaluating the final influence diagram that contains all random variables created during the run of the vision system.