Simulating Ability: Representing Skills in Games

Throughout the history of games, representing the abilities of the various agents acting on behalf of the players has been a central concern. With increasingly sophisticated games emerging, these simulations have become more realistic, but the underlying mechanisms are still, to a large extent, of an ad hoc nature. This paper proposes using a logistic model from psychometrics as a unified mechanism for task resolution in simulation-oriented games

A paradox concerning rate of information

A natural definition of the rate of transmission of information is given, arising out of the usual theory. We call it the “Riemannian” rate of transmission. It is shown that the definition leads to a paradox if taken in conjunction with the notion of (time-unlimited) band-limited white noise. A mathematical model can hardly contain both these notions at the same time. The Riemannian rate of transmission does however lead to sensible results if used in conjunction with periodic band-limited white noise. In particular it leads to the Hartley-Wiener-Tuller-Sullivan-Shannon formula without the necessity of introducing Shannon's notion of “dimension rate.” The discussion refers to matrix signal-to-noise ratios and to the entropy of singular multivariate normal distributions

Adaptive Regret Minimization in Bounded-Memory Games

Online learning algorithms that minimize regret provide strong guarantees in situations that involve repeatedly making decisions in an uncertain environment, e.g. a driver deciding what route to drive to work every day. While regret minimization has been extensively studied in repeated games, we study regret minimization for a richer class of games called bounded memory games. In each round of a two-player bounded memory-m game, both players simultaneously play an action, observe an outcome and receive a reward. The reward may depend on the last m outcomes as well as the actions of the players in the current round. The standard notion of regret for repeated games is no longer suitable because actions and rewards can depend on the history of play. To account for this generality, we introduce the notion of k-adaptive regret, which compares the reward obtained by playing actions prescribed by the algorithm against a hypothetical k-adaptive adversary with the reward obtained by the best expert in hindsight against the same adversary. Roughly, a hypothetical k-adaptive adversary adapts her strategy to the defender's actions exactly as the real adversary would within each window of k rounds. Our definition is parametrized by a set of experts, which can include both fixed and adaptive defender strategies. We investigate the inherent complexity of and design algorithms for adaptive regret minimization in bounded memory games of perfect and imperfect information. We prove a hardness result showing that, with imperfect information, any k-adaptive regret minimizing algorithm (with fixed strategies as experts) must be inefficient unless NP=RP even when playing against an oblivious adversary. In contrast, for bounded memory games of perfect and imperfect information we present approximate 0-adaptive regret minimization algorithms against an oblivious adversary running in time n^{O(1)}.Comment: Full Version. GameSec 2013 (Invited Paper

Offline to Online Conversion

We consider the problem of converting offline estimators into an online predictor or estimator with small extra regret. Formally this is the problem of merging a collection of probability measures over strings of length 1,2,3,... into a single probability measure over infinite sequences. We describe various approaches and their pros and cons on various examples. As a side-result we give an elementary non-heuristic purely combinatoric derivation of Turing's famous estimator. Our main technical contribution is to determine the computational complexity of online estimators with good guarantees in general.Comment: 20 LaTeX page

Multispecies virial expansions

We study the virial expansion of mixtures of countably many different types of particles. The main tool is the Lagrange–Good inversion formula, which has other applications such as counting coloured trees or studying probability generating functions in multi-type branching processes. We prove that the virial expansion converges absolutely in a domain of small densities. In addition, we establish that the virial coefficients can be expressed in terms of two-connected graphs

Linear Statistics of Point Processes via Orthogonal Polynomials

For arbitrary $\beta > 0$, we use the orthogonal polynomials techniques developed by R. Killip and I. Nenciu to study certain linear statistics associated with the circular and Jacobi $\beta$ ensembles. We identify the distribution of these statistics then prove a joint central limit theorem. In the circular case, similar statements have been proved using different methods by a number of authors. In the Jacobi case these results are new.Comment: Added references, corrected typos. To appear, J. Stat. Phy

Interval Estimation Naïve Bayes

Abstract. Recent work in supervised learning has shown that a surprisingly simple Bayesian classifier with assumptions of conditional independence among features given the class, called naïve Bayes, is competitive with state of the art classifiers. On this paper a new naive Bayes classifier called Interval Estimation naïve Bayes is proposed. Interval Estimation naïve Bayes performs on two phases. On the first phase an interval estimation of each probability necessary to specify the naïve Bayes is estimated. On the second phase the best combination of values inside these intervals is calculated with a heuristic search that is guided by the accuracy of the classifiers. The founded values in the search are the new parameters for the naïve Bayes classifier. Our new approach has shown to be quite competitive related to simple naïve Bayes. Experimental tests have been done with 21 data sets from the UCI repository.

A Three-Way Decision Approach to Email Spam Filtering

Abstract. Many classification techniques used for identifying spam emails, treat spam filtering as a binary classification problem. That is, the in-coming email is either spam or non-spam. This treatment is more for mathematical simplicity other than reflecting the true state of nature. In this paper, we introduce a three-way decision approach to spam filtering based on Bayesian decision theory, which provides a more sensible feed-back to users for precautionary handling their incoming emails, thereby reduces the chances of misclassification. The main advantage of our ap-proach is that it allows the possibility of rejection, i.e., of refusing to make a decision. The undecided cases must be re-examined by collect-ing additional information. A loss function is defined to state how costly each action is, a pair of threshold values on the posterior odds ratio is systematically calculated based on the loss function, and the final deci-sion is to select the action for which the overall cost is minimum. Our experimental results show that the new approach reduces the error rate of classifying a legitimate email to spam, and provides better spam pre-cision and weighted accuracy. Key words: spam filter, three-way decision, naive Bayesian classifica-tion, Bayesian decision theory, cost