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

Distributed Online Big Data Classification Using Context Information

Distributed, online data mining systems have emerged as a result of applications requiring analysis of large amounts of correlated and high-dimensional data produced by multiple distributed data sources. We propose a distributed online data classification framework where data is gathered by distributed data sources and processed by a heterogeneous set of distributed learners which learn online, at run-time, how to classify the different data streams either by using their locally available classification functions or by helping each other by classifying each other's data. Importantly, since the data is gathered at different locations, sending the data to another learner to process incurs additional costs such as delays, and hence this will be only beneficial if the benefits obtained from a better classification will exceed the costs. We model the problem of joint classification by the distributed and heterogeneous learners from multiple data sources as a distributed contextual bandit problem where each data is characterized by a specific context. We develop a distributed online learning algorithm for which we can prove sublinear regret. Compared to prior work in distributed online data mining, our work is the first to provide analytic regret results characterizing the performance of the proposed algorithm

A sparse multinomial probit model for classification

A recent development in penalized probit modelling using a hierarchical Bayesian approach has led to a sparse binomial (two-class) probit classifier that can be trained via an EM algorithm. A key advantage of the formulation is that no tuning of hyperparameters relating to the penalty is needed thus simplifying the model selection process. The resulting model demonstrates excellent classification performance and a high degree of sparsity when used as a kernel machine. It is, however, restricted to the binary classification problem and can only be used in the multinomial situation via a one-against-all or one-against-many strategy. To overcome this, we apply the idea to the multinomial probit model. This leads to a direct multi-classification approach and is shown to give a sparse solution with accuracy and sparsity comparable with the current state-of-the-art. Comparative numerical benchmark examples are used to demonstrate the method

The Measure and Mismeasure of Fairness: A Critical Review of Fair Machine Learning

The nascent field of fair machine learning aims to ensure that decisions guided by algorithms are equitable. Over the last several years, three formal definitions of fairness have gained prominence: (1) anti-classification, meaning that protected attributes---like race, gender, and their proxies---are not explicitly used to make decisions; (2) classification parity, meaning that common measures of predictive performance (e.g., false positive and false negative rates) are equal across groups defined by the protected attributes; and (3) calibration, meaning that conditional on risk estimates, outcomes are independent of protected attributes. Here we show that all three of these fairness definitions suffer from significant statistical limitations. Requiring anti-classification or classification parity can, perversely, harm the very groups they were designed to protect; and calibration, though generally desirable, provides little guarantee that decisions are equitable. In contrast to these formal fairness criteria, we argue that it is often preferable to treat similarly risky people similarly, based on the most statistically accurate estimates of risk that one can produce. Such a strategy, while not universally applicable, often aligns well with policy objectives; notably, this strategy will typically violate both anti-classification and classification parity. In practice, it requires significant effort to construct suitable risk estimates. One must carefully define and measure the targets of prediction to avoid retrenching biases in the data. But, importantly, one cannot generally address these difficulties by requiring that algorithms satisfy popular mathematical formalizations of fairness. By highlighting these challenges in the foundation of fair machine learning, we hope to help researchers and practitioners productively advance the area

Ethical Adversaries: Towards Mitigating Unfairness with Adversarial Machine Learning

Machine learning is being integrated into a growing number of critical systems with far-reaching impacts on society. Unexpected behaviour and unfair decision processes are coming under increasing scrutiny due to this widespread use and its theoretical considerations. Individuals, as well as organisations, notice, test, and criticize unfair results to hold model designers and deployers accountable. We offer a framework that assists these groups in mitigating unfair representations stemming from the training datasets. Our framework relies on two inter-operating adversaries to improve fairness. First, a model is trained with the goal of preventing the guessing of protected attributes' values while limiting utility losses. This first step optimizes the model's parameters for fairness. Second, the framework leverages evasion attacks from adversarial machine learning to generate new examples that will be misclassified. These new examples are then used to retrain and improve the model in the first step. These two steps are iteratively applied until a significant improvement in fairness is obtained. We evaluated our framework on well-studied datasets in the fairness literature -- including COMPAS -- where it can surpass other approaches concerning demographic parity, equality of opportunity and also the model's utility. We also illustrate our findings on the subtle difficulties when mitigating unfairness and highlight how our framework can assist model designers.Comment: 15 pages, 3 figures, 1 tabl

The Utility of Text: The Case of Amicus Briefs and the Supreme Court

We explore the idea that authoring a piece of text is an act of maximizing one's expected utility. To make this idea concrete, we consider the societally important decisions of the Supreme Court of the United States. Extensive past work in quantitative political science provides a framework for empirically modeling the decisions of justices and how they relate to text. We incorporate into such a model texts authored by amici curiae ("friends of the court" separate from the litigants) who seek to weigh in on the decision, then explicitly model their goals in a random utility model. We demonstrate the benefits of this approach in improved vote prediction and the ability to perform counterfactual analysis.Comment: Working draf