Noisy Submodular Maximization via Adaptive Sampling with Applications to Crowdsourced Image Collection Summarization

We address the problem of maximizing an unknown submodular function that can only be accessed via noisy evaluations. Our work is motivated by the task of summarizing content, e.g., image collections, by leveraging users' feedback in form of clicks or ratings. For summarization tasks with the goal of maximizing coverage and diversity, submodular set functions are a natural choice. When the underlying submodular function is unknown, users' feedback can provide noisy evaluations of the function that we seek to maximize. We provide a generic algorithm -- \submM{} -- for maximizing an unknown submodular function under cardinality constraints. This algorithm makes use of a novel exploration module -- \blbox{} -- that proposes good elements based on adaptively sampling noisy function evaluations. \blbox{} is able to accommodate different kinds of observation models such as value queries and pairwise comparisons. We provide PAC-style guarantees on the quality and sampling cost of the solution obtained by \submM{}. We demonstrate the effectiveness of our approach in an interactive, crowdsourced image collection summarization application.Comment: Extended version of AAAI'16 pape

Manipulation of the Borda rule by introduction of a similar candidate

In an election contest, a losing candidate a can manipulate the election outcome in his favor by introducing a weak similar candidate WSC in the choice set, the WSC b being defined as an alternative which is ranked immediatly below a in the individual preferences. We characterize the voting situations where this manipulation is efficient for the Borda rule and express its vulnerability for a 3 alternative election.Borda rule, Manipulation, Strategic candidacy, Similar candidate

Multiwinner Voting with Fairness Constraints

Multiwinner voting rules are used to select a small representative subset of candidates or items from a larger set given the preferences of voters. However, if candidates have sensitive attributes such as gender or ethnicity (when selecting a committee), or specified types such as political leaning (when selecting a subset of news items), an algorithm that chooses a subset by optimizing a multiwinner voting rule may be unbalanced in its selection -- it may under or over represent a particular gender or political orientation in the examples above. We introduce an algorithmic framework for multiwinner voting problems when there is an additional requirement that the selected subset should be "fair" with respect to a given set of attributes. Our framework provides the flexibility to (1) specify fairness with respect to multiple, non-disjoint attributes (e.g., ethnicity and gender) and (2) specify a score function. We study the computational complexity of this constrained multiwinner voting problem for monotone and submodular score functions and present several approximation algorithms and matching hardness of approximation results for various attribute group structure and types of score functions. We also present simulations that suggest that adding fairness constraints may not affect the scores significantly when compared to the unconstrained case.Comment: The conference version of this paper appears in IJCAI-ECAI 201

Nash implementable domains for the Borda count

We characterize the preference domains on which the Borda count satisfies Maskin monotonicity. The basic concept is the notion of a "cyclic permutation domain" which arises by fixing one particular ordering of alternatives and including all its cyclic permutations. The cyclic permutation domains are exactly the maximal domains on which the Borda count is strategy-proof (when combined with every tie breaking rule). It turns out that the Borda count is monotonic on a larger class of domains. We show that the maximal domains on which the Borda count satisfies Maskin monotonicity are the "cyclically nested permutation domains." These are the preference domains which can be obtained from the cyclic permutation domains in an appropriate recursive way.Maskin monotonicity; Borda count; restricted preference domains

Weighted Heuristic Ensemble of Filters

Feature selection has become increasingly important in data mining in recent years due to the rapid increase in the dimensionality of big data. However, the reliability and consistency of feature selection methods (filters) vary considerably on different data and no single filter performs consistently well under various conditions. Therefore, feature selection ensemble has been investigated recently to provide more reliable and effective results than any individual one but all the existing feature selection ensemble treat the feature selection methods equally regardless of their performance. In this paper, we present a novel framework which applies weighted feature selection ensemble through proposing a systemic way of adding different weights to the feature selection methods-filters. Also, we investigate how to determine the appropriate weight for each filter in an ensemble. Experiments based on ten benchmark datasets show that theoretically and intuitively adding more weight to ‘good filters’ should lead to better results but in reality it is very uncertain. This assumption was found to be correct for some examples in our experiment. However, for other situations, filters which had been assumed to perform well showed bad performance leading to even worse results. Therefore adding weight to filters might not achieve much in accuracy terms, in addition to increasing complexity, time consumption and clearly decreasing the stability

Multicriterial ranking approach for evaluating bank branch performance

14 ranking methods based on multiple criteria are suggested for evaluating the performance of the bank branches. The methods are explained via an illustrative example, and some of them are applied to a real-life data for 23 retail bank branches in a large-scale private Turkish commercial bank