We propose a distributionally robust classification model with a fairness constraint that encourages the classifier to be fair in view of the equality of opportunity criterion. We use a type-$\infty$ Wasserstein ambiguity set centered at the empirical distribution to model distributional uncertainty and derive a conservative reformulation for the worst-case equal opportunity unfairness measure. We establish that the model is equivalent to a mixed binary optimization problem, which can be solved by standard off-the-shelf solvers. To improve scalability, we further propose a convex, hinge-loss-based model for large problem instances whose reformulation does not incur any binary variables. Moreover, we also consider the distributionally robust learning problem with a generic ground transportation cost to hedge against the uncertainties in the label and sensitive attribute. Finally, we numerically demonstrate that our proposed approaches improve fairness with negligible loss of predictive accuracy.
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In this paper, we study a distributed learning problem constrained by constant communication bits. Specifically, we consider the distributed hypothesis testing (DHT) problem where two distributed nodes are constrained to transmit a constant number of bits to a central decoder. In such cases, we show that in order to achieve the optimal error exponents, it suffices to consider the empirical distributions of observed data sequences and encode them to the transmission bits. With such a coding strategy, we develop a geometric approach in the distribution spaces and characterize the optimal schemes. In particular, we show the optimal achievable error exponents and coding schemes for the following cases: (i) both nodes can transmit $\log_23$ bits; (ii) one of the nodes can transmit $1$ bit, and the other node is not constrained; (iii) the joint distribution of the nodes are conditionally independent given one hypothesis. Furthermore, we provide several numerical examples for illustrating the theoretical results. Our results provide theoretical guidance for designing practical distributed learning rules, and the developed approach also reveals new potentials for establishing error exponents for DHT with more general communication constraints.
In many applications, it is of interest to assess the relative contribution of features (or subsets of features) toward the goal of predicting a response -- in other words, to gauge the variable importance of features. Most recent work on variable importance assessment has focused on describing the importance of features within the confines of a given prediction algorithm. However, such assessment does not necessarily characterize the prediction potential of features, and may provide a misleading reflection of the intrinsic value of these features. To address this limitation, we propose a general framework for nonparametric inference on interpretable algorithm-agnostic variable importance. We define variable importance as a population-level contrast between the oracle predictiveness of all available features versus all features except those under consideration. We propose a nonparametric efficient estimation procedure that allows the construction of valid confidence intervals, even when machine learning techniques are used. We also outline a valid strategy for testing the null importance hypothesis. Through simulations, we show that our proposal has good operating characteristics, and we illustrate its use with data from a study of an antibody against HIV-1 infection.
Chance constrained optimization problems allow to model problems where constraints involving stochastic components should only be violated with a small probability. Evolutionary algorithms have recently been applied to this scenario and shown to achieve high quality results. With this paper, we contribute to the theoretical understanding of evolutionary algorithms for chance constrained optimization. We study the scenario of stochastic components that are independent and Normally distributed. By generalizing results for the class of linear functions to the sum of transformed linear functions, we show that the (1+1)~EA can optimize the chance constrained setting without additional constraints in time O(n log n). However, we show that imposing an additional uniform constraint already leads to local optima for very restricted scenarios and an exponential optimization time for the (1+1)~EA. We therefore propose a multi-objective formulation of the problem which trades off the expected cost and its variance. We show that multi-objective evolutionary algorithms are highly effective when using this formulation and obtain a set of solutions that contains an optimal solution for any possible confidence level imposed on the constraint. Furthermore, we show that this approach can also be used to compute a set of optimal solutions for the chance constrained minimum spanning tree problem.
This paper investigates an unmanned aerial vehicle (UAV)-assisted wireless powered mobile-edge computing (MEC) system, where the UAV powers the mobile terminals by wireless power transfer (WPT) and provides computation service for them. We aim to maximize the computation rate of terminals while ensuring fairness among them. Considering the random trajectories of mobile terminals, we propose a soft actor-critic (SAC)-based UAV trajectory planning and resource allocation (SAC-TR) algorithm, which combines off-policy and maximum entropy reinforcement learning to promote the convergence of the algorithm. We design the reward as a heterogeneous function of computation rate, fairness, and reaching of destination. Simulation results show that SAC-TR can quickly adapt to varying network environments and outperform representative benchmarks in a variety of situations.
Ensuring fairness in machine learning algorithms is a challenging and important task. We consider the problem of clustering a set of points while ensuring fairness constraints. While there have been several attempts to capture group fairness in the k-clustering problem, fairness at an individual level is not well-studied. We introduce a new notion of individual fairness in k-clustering based on features that are not necessarily used for clustering. We show that this problem is NP-hard and does not admit a constant factor approximation. We then design a randomized algorithm that guarantees approximation both in terms of minimizing the clustering distance objective as well as individual fairness under natural restrictions on the distance metric and fairness constraints. Finally, our experimental results validate that our algorithm produces lower clustering costs compared to existing algorithms while being competitive in individual fairness.
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible while commonly constrained to match empirically estimated feature expectations. We seek to generalize this principle to scenarios where the empirical feature expectations cannot be computed because the model variables are only partially observed, which introduces a dependency on the learned model. Extending and generalizing the principle of latent maximum entropy, we introduce uncertain maximum entropy and describe an expectation-maximization based solution to approximately solve these problems. We show that our technique generalizes the principle of maximum entropy and latent maximum entropy and discuss a generally applicable regularization technique for adding error terms to feature expectation constraints in the event of limited data.
Semi-supervised learning on class-imbalanced data, although a realistic problem, has been under studied. While existing semi-supervised learning (SSL) methods are known to perform poorly on minority classes, we find that they still generate high precision pseudo-labels on minority classes. By exploiting this property, in this work, we propose Class-Rebalancing Self-Training (CReST), a simple yet effective framework to improve existing SSL methods on class-imbalanced data. CReST iteratively retrains a baseline SSL model with a labeled set expanded by adding pseudo-labeled samples from an unlabeled set, where pseudo-labeled samples from minority classes are selected more frequently according to an estimated class distribution. We also propose a progressive distribution alignment to adaptively adjust the rebalancing strength dubbed CReST+. We show that CReST and CReST+ improve state-of-the-art SSL algorithms on various class-imbalanced datasets and consistently outperform other popular rebalancing methods.
Optimizing ranking systems based on user interactions is a well-studied problem. State-of-the-art methods for optimizing ranking systems based on user interactions are divided into online approaches - that learn by directly interacting with users - and counterfactual approaches - that learn from historical interactions. Existing online methods are hindered without online interventions and thus should not be applied counterfactually. Conversely, counterfactual methods cannot directly benefit from online interventions. We propose a novel intervention-aware estimator for both counterfactual and online Learning to Rank (LTR). With the introduction of the intervention-aware estimator, we aim to bridge the online/counterfactual LTR division as it is shown to be highly effective in both online and counterfactual scenarios. The estimator corrects for the effect of position bias, trust bias, and item-selection bias by using corrections based on the behavior of the logging policy and on online interventions: changes to the logging policy made during the gathering of click data. Our experimental results, conducted in a semi-synthetic experimental setup, show that, unlike existing counterfactual LTR methods, the intervention-aware estimator can greatly benefit from online interventions.
Developing classification algorithms that are fair with respect to sensitive attributes of the data has become an important problem due to the growing deployment of classification algorithms in various social contexts. Several recent works have focused on fairness with respect to a specific metric, modeled the corresponding fair classification problem as a constrained optimization problem, and developed tailored algorithms to solve them. Despite this, there still remain important metrics for which we do not have fair classifiers and many of the aforementioned algorithms do not come with theoretical guarantees; perhaps because the resulting optimization problem is non-convex. The main contribution of this paper is a new meta-algorithm for classification that takes as input a large class of fairness constraints, with respect to multiple non-disjoint sensitive attributes, and which comes with provable guarantees. This is achieved by first developing a meta-algorithm for a large family of classification problems with convex constraints, and then showing that classification problems with general types of fairness constraints can be reduced to those in this family. We present empirical results that show that our algorithm can achieve near-perfect fairness with respect to various fairness metrics, and that the loss in accuracy due to the imposed fairness constraints is often small. Overall, this work unifies several prior works on fair classification, presents a practical algorithm with theoretical guarantees, and can handle fairness metrics that were previously not possible.
Methods that align distributions by minimizing an adversarial distance between them have recently achieved impressive results. However, these approaches are difficult to optimize with gradient descent and they often do not converge well without careful hyperparameter tuning and proper initialization. We investigate whether turning the adversarial min-max problem into an optimization problem by replacing the maximization part with its dual improves the quality of the resulting alignment and explore its connections to Maximum Mean Discrepancy. Our empirical results suggest that using the dual formulation for the restricted family of linear discriminators results in a more stable convergence to a desirable solution when compared with the performance of a primal min-max GAN-like objective and an MMD objective under the same restrictions. We test our hypothesis on the problem of aligning two synthetic point clouds on a plane and on a real-image domain adaptation problem on digits. In both cases, the dual formulation yields an iterative procedure that gives more stable and monotonic improvement over time.
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