F-measure Maximization in Multi-Label Classification with Conditionally Independent Label Subsets

We discuss a method to improve the exact F-measure maximization algorithm called GFM, proposed in (Dembczynski et al. 2011) for multi-label classification, assuming the label set can be can partitioned into conditionally independent subsets given the input features. If the labels were all independent, the estimation of only $m$ parameters ($m$ denoting the number of labels) would suffice to derive Bayes-optimal predictions in $O(m^2)$ operations. In the general case, $m^2+1$ parameters are required by GFM, to solve the problem in $O(m^3)$ operations. In this work, we show that the number of parameters can be reduced further to $m^2/n$, in the best case, assuming the label set can be partitioned into $n$ conditionally independent subsets. As this label partition needs to be estimated from the data beforehand, we use first the procedure proposed in (Gasse et al. 2015) that finds such partition and then infer the required parameters locally in each label subset. The latter are aggregated and serve as input to GFM to form the Bayes-optimal prediction. We show on a synthetic experiment that the reduction in the number of parameters brings about significant benefits in terms of performance

A theory of unstructured bargaining using distribution-valued solution concepts

In experiments it is typically found that many joint utility outcomes arise in any given unstructured bargaining game. This suggests using a positive unstructured bargaining concept that maps a bargaining game to a probability distribution over outcomes rather than to a single outcome. We show how to "translate" Nash's bargaining axioms to apply to such distributional bargaining concepts. We then prove that a subset of those axioms forces the distribution over outcomes to be a power-law. Unlike Nash's original result, our result holds even if the feasible set is finite. When the feasible set is convex and comprehensive, the mode of the power law distribution is the Harsanyi bargaining solution, and if we require symmetry it is the Nash bargaining solution. However in general these modes of the joint utility distribution are not Bayes-optimal predictions for the joint uitlity, nor are the bargains corresponding to those outcomes the most likely bargains. We then show how an external regulator can use distributional solution concepts to optimally design an unstructured bargaining scenario. Throughout we demonstrate our analysis in computational experiments involving flight rerouting negotiations in the National Airspace System.JEL Codes:

A Sandbox Tool to Bias(Stress)-Test Fairness Algorithms

Motivated by the growing importance of reducing unfairness in ML predictions, Fair-ML researchers have presented an extensive suite of algorithmic "fairness-enhancing" remedies. Most existing algorithms, however, are agnostic to the sources of the observed unfairness. As a result, the literature currently lacks guiding frameworks to specify conditions under which each algorithmic intervention can potentially alleviate the underpinning cause of unfairness. To close this gap, we scrutinize the underlying biases (e.g., in the training data or design choices) that cause observational unfairness. We present a bias-injection sandbox tool to investigate fairness consequences of various biases and assess the effectiveness of algorithmic remedies in the presence of specific types of bias. We call this process the bias(stress)-testing of algorithmic interventions. Unlike existing toolkits, ours provides a controlled environment to counterfactually inject biases in the ML pipeline. This stylized setup offers the distinct capability of testing fairness interventions beyond observational data and against an unbiased benchmark. In particular, we can test whether a given remedy can alleviate the injected bias by comparing the predictions resulting after the intervention in the biased setting with true labels in the unbiased regime -- that is, before any bias injection. We illustrate the utility of our toolkit via a proof-of-concept case study on synthetic data. Our empirical analysis showcases the type of insights that can be obtained through our simulations

Hedging predictions in machine learning

Recent advances in machine learning make it possible to design efficient prediction algorithms for data sets with huge numbers of parameters. This paper describes a new technique for "hedging" the predictions output by many such algorithms, including support vector machines, kernel ridge regression, kernel nearest neighbours, and by many other state-of-the-art methods. The hedged predictions for the labels of new objects include quantitative measures of their own accuracy and reliability. These measures are provably valid under the assumption of randomness, traditional in machine learning: the objects and their labels are assumed to be generated independently from the same probability distribution. In particular, it becomes possible to control (up to statistical fluctuations) the number of erroneous predictions by selecting a suitable confidence level. Validity being achieved automatically, the remaining goal of hedged prediction is efficiency: taking full account of the new objects' features and other available information to produce as accurate predictions as possible. This can be done successfully using the powerful machinery of modern machine learning.Comment: 24 pages; 9 figures; 2 tables; a version of this paper (with discussion and rejoinder) is to appear in "The Computer Journal

On Aggregation in Ensembles of Multilabel Classifiers

While a variety of ensemble methods for multilabel classification have been proposed in the literature, the question of how to aggregate the predictions of the individual members of the ensemble has received little attention so far. In this paper, we introduce a formal framework of ensemble multilabel classification, in which we distinguish two principal approaches: "predict then combine" (PTC), where the ensemble members first make loss minimizing predictions which are subsequently combined, and "combine then predict" (CTP), which first aggregates information such as marginal label probabilities from the individual ensemble members, and then derives a prediction from this aggregation. While both approaches generalize voting techniques commonly used for multilabel ensembles, they allow to explicitly take the target performance measure into account. Therefore, concrete instantiations of CTP and PTC can be tailored to concrete loss functions. Experimentally, we show that standard voting techniques are indeed outperformed by suitable instantiations of CTP and PTC, and provide some evidence that CTP performs well for decomposable loss functions, whereas PTC is the better choice for non-decomposable losses.Comment: 14 pages, 2 figure