On the Bayes-optimality of F-measure maximizers

The F-measure, which has originally been introduced in information retrieval, is nowadays routinely used as a performance metric for problems such as binary classification, multi-label classification, and structured output prediction. Optimizing this measure is a statistically and computationally challenging problem, since no closed-form solution exists. Adopting a decision-theoretic perspective, this article provides a formal and experimental analysis of different approaches for maximizing the F-measure. We start with a Bayes-risk analysis of related loss functions, such as Hamming loss and subset zero-one loss, showing that optimizing such losses as a surrogate of the F-measure leads to a high worst-case regret. Subsequently, we perform a similar type of analysis for F-measure maximizing algorithms, showing that such algorithms are approximate, while relying on additional assumptions regarding the statistical distribution of the binary response variables. Furthermore, we present a new algorithm which is not only computationally efficient but also Bayes-optimal, regardless of the underlying distribution. To this end, the algorithm requires only a quadratic (with respect to the number of binary responses) number of parameters of the joint distribution. We illustrate the practical performance of all analyzed methods by means of experiments with multi-label classification problems

Optimal Voting Rules

We study dominant strategy incentive compatible (DIC) and deterministic mechanisms in a social choice setting with several alternatives. The agents are privately informed about their preferences, and have single-crossing utility functions. Monetary transfers are not feasible. We use an equivalence between deterministic, DIC mechanisms and generalized median voter schemes to construct the constrained-efficient, optimal mechanism for an utilitarian planner. Optimal schemes for other welfare criteria such as, say, a Rawlsian maximin can be analogously obtained

Proposal Rights and Political Power

In a canonical model of sequential collective bargaining over a divisible good we show that equilibrium expected payoffs are not restricted by players’ voting rights or their impatience. For all monotonic voting rules and discount factors, and for all divisions of the good among players, there exists a stationary proposal-making rule such that this division represents players’ expected payoffs in a Stationary Subgame Perfect Nash equilibrium in pure strategies. The result attests to the significance of proposal rights in determining political power in collective deliberations.Power, Proposal Rights, Voting Rights.

Probabilistic Opacity for Markov Decision Processes

Opacity is a generic security property, that has been defined on (non probabilistic) transition systems and later on Markov chains with labels. For a secret predicate, given as a subset of runs, and a function describing the view of an external observer, the value of interest for opacity is a measure of the set of runs disclosing the secret. We extend this definition to the richer framework of Markov decision processes, where non deterministic choice is combined with probabilistic transitions, and we study related decidability problems with partial or complete observation hypotheses for the schedulers. We prove that all questions are decidable with complete observation and $\omega$-regular secrets. With partial observation, we prove that all quantitative questions are undecidable but the question whether a system is almost surely non opaque becomes decidable for a restricted class of $\omega$-regular secrets, as well as for all $\omega$-regular secrets under finite-memory schedulers

A dynamic model of democratic elections in multidimensional policy spaces

We propose a general model of repeated elections. In each period, a challenger is chosen from the electorate to run against an incumbent politician in a majority-rule election, and the winner then selects a policy from a multidimensional policy space. Individual policy preferences are private information, whereas policy choices are publicly observable. We prove existence and continuity of equilibria in "simple" voting and policy strategies; we provide examples to show the variety of possible equilibrium patterns in multiple dimensions; we analyze the effects of patience and office-holding benefits on the persistence of policies over time; and we identify relationships between equilibrium policies and the core of the underlying voting game. As a byproduct of our analysis, we show how equilibrium incentives maylead elected representatives to make policy compromises, even when binding commitments are unavailable. We provide an informational story for incumbency advantage. Finally, we give an asymptotic version of the median voter theorem for the one-dimensional model as voters become-arbitrarily patient

Graph Summarization

The continuous and rapid growth of highly interconnected datasets, which are both voluminous and complex, calls for the development of adequate processing and analytical techniques. One method for condensing and simplifying such datasets is graph summarization. It denotes a series of application-specific algorithms designed to transform graphs into more compact representations while preserving structural patterns, query answers, or specific property distributions. As this problem is common to several areas studying graph topologies, different approaches, such as clustering, compression, sampling, or influence detection, have been proposed, primarily based on statistical and optimization methods. The focus of our chapter is to pinpoint the main graph summarization methods, but especially to focus on the most recent approaches and novel research trends on this topic, not yet covered by previous surveys.Comment: To appear in the Encyclopedia of Big Data Technologie