Spectral dimensionality reduction for HMMs

Hidden Markov Models (HMMs) can be accurately approximated using co-occurrence frequencies of pairs and triples of observations by using a fast spectral method in contrast to the usual slow methods like EM or Gibbs sampling. We provide a new spectral method which significantly reduces the number of model parameters that need to be estimated, and generates a sample complexity that does not depend on the size of the observation vocabulary. We present an elementary proof giving bounds on the relative accuracy of probability estimates from our model. (Correlaries show our bounds can be weakened to provide either L1 bounds or KL bounds which provide easier direct comparisons to previous work.) Our theorem uses conditions that are checkable from the data, instead of putting conditions on the unobservable Markov transition matrix

Structural Logistic Regression for Link Analysis

We present Structural Logistic Regression, an extension of logistic regression to modeling relational data. It is an integrated approach to building regression models from data stored in relational databases in which potential predictors, both boolean and real-valued, are generated by structured search in the space of queries to the database, and then tested with statistical information criteria for inclusion in a logistic regression. Using statistics and relational representation allows modeling in noisy domains with complex structure. Link prediction is a task of high interest with exactly such characteristics. Be it in the domain of scientific citations, social networks or hypertext, the underlying data are extremely noisy and the features useful for prediction are not readily available in a flat file format. We propose the application of Structural Logistic Regression to building link prediction models, and present experimental results for the task of predicting citations made in scientific literature using relational data taken from the CiteSeer search engine. This data includes the citation graph, authorship and publication venues of papers, as well as their word content

An Auction-Based Method for Decentralized Train Scheduling

We present a computational study of an auction-based method for decentralized train scheduling. The method is well suited to the natural information and control structure of mod- ern railroads. We assume separate network territories, with an autonomous dispatch agent responsible for the ow of trains over each territory. Each train is represented by a self-interested agent that bids for the right to travel across the network from its source to destination, submitting bids to multiple dispatch agents along its route as necessary. The bidding language allows trains to bid for the right to enter and exit territories at particular times, and also to represent indifference over a range of times. Computational results on a simple network with straight-forward best-response bid- ding strategies demonstrate that the auction computes near- optimal system-wide schedules. In addition, the method appears to have useful scaling properties, both with the number of trains and with the number of dispatchers, and generates less extremal solutions than those obtained using traditional centralized optimization techniques.Engineering and Applied Science

An Ascending-Price Generalized Vickrey Auction

A simple characterization of the equilibrium conditions required to compute Vickrey payments in the Combinatorial Allocation Problem leads to an ascending price Generalized Vickrey Auction. The ascending auc- tion, iBundle Extend & Adjust (iBEA), maintains non-linear and perhaps non-anonymous prices on bundles of items, and terminates with the ef- cient allocation and the Vickrey payments in ex post Nash equilibrium. Crucially, iBEA is able to implement the Vickrey outcome even when the Vickrey payments are not supported in a single competitive equilibrium. The auction closes with Universal competitive equilibrium prices, which provide enough information to compute individualized discounts to adjust the nal prices and implement Vickrey payments.Engineering and Applied Science

Preventing Strategic Manipulation in Iterative Auctions: Proxy Agents and Price-Adjustment

Iterative auctions have many computational advantages over sealed-bid auctions, but can present new possibilities for strategic manipulation. We propose a two-stage technique to make iterative auctions that compute optimal allocations with myopic best-response bidding strategies more robust to manipulation. First, introduce proxy bidding agents to constrain bidding strategies to (possibly untruthful) myopic bestresponse. Second, after the auction terminates adjust the prices towards those given in the Vickrey auction, a sealedbid auction in which truth-revelation is optimal. We present an application of this methodology to iBundle, an iterative combinatorial auction which gives optimal allocations for myopic best-response agents.Engineering and Applied Science

Iterative Combinatorial Auctions: Theory and Practice

Combinatorial auctions, which allow agents to bid directly for bundles of resources, are necessary for optimal auction-based solutions to resource allocation problems with agents that have non-additive values for resources, such as distributed scheduling and task assignment problems. We introduce iBundle, the first iterative combinatorial auction that is optimal for a reasonable agent bidding strategy, in this case myopic best-response bidding. Its optimality is proved with a novel connection to primal-dual optimization theory. We demonstrate orders of magnitude performance improvements over the only other known optimal combinatorial auction, the Generalized Vickrey Auction.Engineering and Applied Science

Learning and Adaption in Multiagent Systems

The goal of a self-interested agent within a multiagent system is to maximize its utility over time. In a situation of strategic interdependence, where the actions of one agent may a ect the utilities of other agents, the optimal behavior of an agent must be conditioned on the expected behaviors of the other agents in the system. Standard game theory assumes that the rationality and preferences of all the agents is common knowledge: each agent is then able to compute the set of possible equilibria, and if there is a unique equilibrium, choose a best-response to the actions that the other agents will all play. Real agents acting within a multiagent system face multiple problems: the agents may have incomplete information about the preferences and rationality of the other agents in the game, computing the equilibria can be computationally complex, and there might be many equilibria from which to choose. An alternative explanation of the emergence of a stable equilibrium is that it arises as the long-run outcome of a repeated game, in which bounded-rational agents adapt their strategies as they learn about the other agents in the system. We review some possible models of learning for games, and then show the pros and cons of using learning in a particular game, the Compensation Mechanism, a mechanism for the efficient coordination of actions within a multiagent system.Engineering and Applied Science