Data-driven analytics — in areas ranging from consumer marketing to public policy — often allow behavior prediction at the level of individuals rather than population segments , offering the opportunity to improve decisions that impact large populations. Modeling such (generalized) assignment problems as linear programs, we propose a general value-directed compression technique for solving such problems at scale. We dynamically segment the population into cells using a form of column generation, constructing groups of individuals who can provably be treated identically in the optimal solution. This compression allows problems, unsolvable using standard LP techniques, to be solved effectively. Indeed, once a compressed LP is constructed, problems can solved in milliseconds. We provide a theoretical analysis of themethods, outline the distributed implementation of the requisite data processing, and show how a single compressed LP can be used to solve multiple variants of the original LP near-optimally in real-time (e.g., tosupport scenario analysis). We also show how the method can be leveraged in integer programming models.  Experimental results on marketing contact optimization and political legislature problems validate the performance of our technique.

This is the Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence, which was held in San Francisco, CA, June 30 - July 3, 2000

We consider voting situations in which some candidates may turn out to be unavailable. When determining availability is costly (e.g., in terms of money, time, or computation), voting prior to determining candidate availability and testing the winner's availability after the vote may be beneficial. However, since few voting rules are robust to candidate deletion, winner determination requires a number of such availability tests. We outline a model for analyzing such problems, defining robust winners relative to potential candidate unavailability. We assess the complexity of computing robust winners for several voting rules. Assuming a distribution over availability, and costs for availability tests/queries, we describe algorithms for computing optimal query policies, which minimize the expected cost of determining true winners.

Stackelberg security games (SSGs) have been deployed in a number of real-world domains. One key challenge in these applications is the assessment of attacker payoffs, which may not be perfectly known. Previous work has studied SSGs with uncertain payoffs modeled by interval uncertainty and provided maximin-based robust solutions. In contrast, in this work we propose the use of the less conservative minimax regret decision criterion for such payoff-uncertain SSGs and present the first algorithms for computing minimax regret for SSGs. We also address the challenge of preference elicitation, using minimax regret to develop the first elicitation strategies for SSGs. Experimental results validate the effectiveness of our approaches.

Vendors of all types face the problem of selecting a slate of product offerings—their assortment or catalog—that will maximize their profits. The profitability of a catalog is determined by both customer preferences and the offerings of their competitors. We develop a game-theoretic model for analyzing the vendor catalog optimization problem in the face of competing vendors. We show that computing a best response is intractable in general, but can be solved by dynamic programming given certain informational or structural assumptions about consumer preferences. We also analyze conditions under which pure Nash equilibria exist and provide several price of anarchy/stability results

While stable matching problems are widely studied, little work has investigated schemes for effectively eliciting agent preferences using either preference (e.g., comparison) queries for interviews (to form such comparisons); and no work has addressed how to combine both. We develop a new model for representing and assessing agent preferences that accommodates both forms of information and (heuristically) minimizes the number of queries and interviews required to determine a stable matching. Our Refine-then-Interview (RtI) scheme uses coarse preference queries to refine knowledge of agent preferences and relies on interviews only to assess comparisons of relatively “close” options. Empirical results show that RtI compares favorably to a recent pure interview minimization algorithm, and that the number of interviews it requires is generally independent of the size of the market.

The increasing use of group discounts has provided opportunities for buying groups with diverse preferences to coordinate their behavior in order to exploit the best offers from multiple vendors. We analyze this problem from the viewpoint of the vendors, asking under what conditions a vendor should adopt a volume-based price schedule rather than posting a fixed price, either as a monopolist or when competing with other vendors. When vendors have uncertainty about buyers' valuations specified by a known distribution, we show that a vendor is always better off posting a fixed price, provided that buyers' types are i.i.d. and that other vendors also use fixed prices. We also show that these assumptions cannot be relaxed: if buyers are not i.i.d., or other vendors post discount schedules, then posting a schedule may yield higher profit for the vendor. We provide similar results under a distribution-free uncertainty model, where vendors minimize their maximum regret over all type realizations.

Possibilistic logic has been proposed as a numerical formalism for reasoning with uncertainty. There has been interest in developing qualitative accounts of possibility, as well as an explanation of the relationship between possibility and modal logics. We present two modal logics that can be used to represent and reason with qualitative statements of possibility and necessity. Within this modal framework, we are able to identify interesting relationships between possibilistic logic, beliefs and conditionals. In particular, the most natural conditional definable via possibilistic means for default reasoning is identical to Pearl's conditional for e-semantics.

We present a semantics for adding uncertainty to conditional logics for default reasoning and belief revision. We are able to treat conditional sentences as statements of conditional probability, and express rules for revision such as "If A were believed, then B would be believed to degree p." This method of revision extends conditionalization by allowing meaningful revision by sentences whose probability is zero. This is achieved through the use of counterfactual probabilities. Thus, our system accounts for the best properties of qualitative methods of update (in particular, the AGM theory of revision) and probabilistic methods. We also show how our system can be viewed as a unification of probability theory and possibility theory, highlighting their orthogonality and providing a means for expressing the probability of a possibility. We also demonstrate the connection to Lewis's method of imaging.

Bayesian networks provide a language for qualitatively representing the conditional independence properties of a distribution. This allows a natural and compact representation of the distribution, eases knowledge acquisition, and supports effective inference algorithms. It is well-known, however, that there are certain independencies that we cannot capture qualitatively within the Bayesian network structure: independencies that hold only in certain contexts, i.e., given a specific assignment of values to certain variables. In this paper, we propose a formal notion of context-specific independence (CSI), based on regularities in the conditional probability tables (CPTs) at a node. We present a technique, analogous to (and based on) d-separation, for determining when such independence holds in a given network. We then focus on a particular qualitative representation scheme - tree-structured CPTs - for capturing CSI. We suggest ways in which this representation can be used to support effective inference algorithms. In particular, we present a structural decomposition of the resulting network which can improve the performance of clustering algorithms, and an alternative algorithm based on cutset conditioning.