Bounds and dynamics for empirical game theoretic analysis

This paper provides several theoretical results for empirical game theory. Specifically, we introduce bounds for empirical game theoretical analysis of complex multi-agent interactions. In doing so we provide insights in the empirical meta game showing that a Nash equilibrium of the estimated meta-game is an approximate Nash equilibrium of the true underlying meta-game. We investigate and show how many data samples are required to obtain a close enough approximation of the underlying game. Additionally, we extend the evolutionary dynamics analysis of meta-games using heuristic payoff tables (HPTs) to asymmetric games. The state-of-the-art has only considered evolutionary dynamics of symmetric HPTs in which agents have access to the same strategy sets and the payoff structure is symmetric, implying that agents are interchangeable. Finally, we carry out an empirical illustration of the generalised method in several domains, illustrating the theory and evolutionary dynamics of several versions of the AlphaGo algorithm (symmetric), the dynamics of the Colonel Blotto game played by human players on Facebook (symmetric), the dynamics of several teams of players in the capture the flag game (symmetric), and an example of a meta-game in Leduc Poker (asymmetric), generated by the policy-space response oracle multi-agent learning algorithm

Web-Scale Bayesian click-through rate prediction for sponsored search advertising in Microsoft's Bing search engine

We describe a new Bayesian click-through rate (CTR) prediction algorithm used for Sponsored Search in Microsoft's Bing search engine. The algorithm is based on a probit regression model that maps discrete or real-valued input features to probabilities. It maintains Gaussian beliefs over weights of the model and performs Gaussian online updates derived from approximate message passing. Scalability of the algorithm is ensured through a principled weight pruning procedure and an approximate parallel implementation. We discuss the challenges arising from evaluating and tuning the predictor as part of the complex system of sponsored search where the predictions made by the algorithm decide about future training sample composition. Finally, we show experimental results from the production system and compare to a calibrated Naïve Bayes algorithm

Depth optimized efficient homomorphic sorting

We introduce a sorting scheme which is capable of efficiently sorting encrypted data without the secret key. The technique is obtained by focusing on the multiplicative depth of the sorting circuit alongside the more traditional metrics such as number of comparisons and number of iterations. The reduced depth allows much reduced noise growth and thereby makes it possible to select smaller parameter sizes in somewhat homomorphic encryption instantiations resulting in greater efficiency savings. We first consider a number of well known comparison based sorting algorithms as well as some sorting networks, and analyze their circuit implementations with respect to multiplicative depth. In what follows, we introduce a new ranking based sorting scheme and rigorously analyze the multiplicative depth complexity as O(log(N) + log(l)), where N is the size of the array to be sorted and l is the bit size of the array elements. Finally, we simulate our sorting scheme using a leveled/batched instantiation of a SWHE library. Our sorting scheme performs favorably over the analyzed classical sorting algorithms

Game Plan: What AI can do for Football, and What Football can do for AI

The rapid progress in artificial intelligence (AI) and machine learning has opened unprecedented analytics possibilities in various team and individual sports, including baseball, basketball, and tennis. More recently, AI techniques have been applied to football, due to a huge increase in data collection by professional teams, increased computational power, and advances in machine learning, with the goal of better addressing new scientific challenges involved in the analysis of both individual players’ and coordinated teams’ behaviors. The research challenges associated with predictive and prescriptive football analytics require new developments and progress at the intersection of statistical learning, game theory, and computer vision. In this paper, we provide an overarching perspective highlighting how the combination of these fields, in particular, forms a unique microcosm for AI research, while offering mutual benefits for professional teams, spectators, and broadcasters in the years to come. We illustrate that this duality makes football analytics a game changer of tremendous value, in terms of not only changing the game of football itself, but also in terms of what this domain can mean for the field of AI. We review the state-of-theart and exemplify the types of analysis enabled by combining the aforementioned fields, including illustrative examples of counterfactual analysis using predictive models, and the combination of game-theoretic analysis of penalty kicks with statistical learning of player attributes. We conclude by highlighting envisioned downstream impacts, including possibilities for extensions to other sports (real and virtual)

TRPA1 Contributes to the Acute Inflammatory Response and Mediates Carrageenan-Induced Paw Edema in the Mouse

Transient receptor potential ankyrin 1 (TRPA1) is an ion channel involved in thermosensation and nociception. TRPA1 is activated by exogenous irritants and also by oxidants formed in inflammatory reactions. However, our understanding of its role in inflammation is limited. Here, we tested the hypothesis that TRPA1 is involved in acute inflammatory edema. The TRPA1 agonist allyl isothiocyanate (AITC) induced inflammatory edema when injected intraplantarly to mice, mimicking the classical response to carrageenan. Interestingly, the TRPA1 antagonist HC-030031 and the cyclo-oxygenase (COX) inhibitor ibuprofen inhibited not only AITC but also carrageenan-induced edema. TRPA1-deficient mice displayed attenuated responses to carrageenan and AITC. Furthermore, AITC enhanced COX-2 expression in HEK293 cells transfected with human TRPA1, a response that was reversed by HC-030031. This study demonstrates a hitherto unknown role of TRPA1 in carrageenan-induced inflammatory edema. The results also strongly suggest that TRPA1 contributes, in a COX-dependent manner, to the development of acute inflammation

TRPA1 is essential for the vascular response to environmental cold exposure

This work was supported by the British Heart Foundation and a Capacity Building Award in Integrative Mammalian Biology. It was also supported by Arthritis Research UK and XK is supported by a British Pharmacological Society AJ Clark studentship