Kernel functions based on triplet comparisons

Given only information in the form of similarity triplets "Object A is more similar to object B than to object C" about a data set, we propose two ways of defining a kernel function on the data set. While previous approaches construct a low-dimensional Euclidean embedding of the data set that reflects the given similarity triplets, we aim at defining kernel functions that correspond to high-dimensional embeddings. These kernel functions can subsequently be used to apply any kernel method to the data set

Are Two Heads the Same as One? Identifying Disparate Treatment in Fair Neural Networks

We show that deep neural networks that satisfy demographic parity do so through a form of race or gender awareness, and that the more we force a network to be fair, the more accurately we can recover race or gender from the internal state of the network. Based on this observation, we propose a simple two-stage solution for enforcing fairness. First, we train a two-headed network to predict the protected attribute (such as race or gender) alongside the original task, and second, we enforce demographic parity by taking a weighted sum of the heads. In the end, this approach creates a single-headed network with the same backbone architecture as the original network. Our approach has near identical performance compared to existing regularization-based or preprocessing methods, but has greater stability and higher accuracy where near exact demographic parity is required. To cement the relationship between these two approaches, we show that an unfair and optimally accurate classifier can be recovered by taking a weighted sum of a fair classifier and a classifier predicting the protected attribute. We use this to argue that both the fairness approaches and our explicit formulation demonstrate disparate treatment and that, consequentially, they are likely to be unlawful in a wide range of scenarios under the US law

Active Sampling for Min-Max Fairness

We propose simple active sampling and reweighting strategies for optimizing min-max fairness that can be applied to any classification or regression model learned via loss minimization. The key intuition behind our approach is to use at each timestep a datapoint from the group that is worst off under the current model for updating the model. The ease of implementation and the generality of our robust formulation make it an attractive option for improving model performance on disadvantaged groups. For convex learning problems, such as linear or logistic regression, we provide a fine-grained analysis, proving the rate of convergence to a min-max fair solution

Individual Preference Stability for Clustering

In this paper, we propose a natural notion of individual preference (IP) stability for clustering, which asks that every data point, on average, is closer to the points in its own cluster than to the points in any other cluster. Our notion can be motivated from several perspectives, including game theory and algorithmic fairness. We study several questions related to our proposed notion. We first show that deciding whether a given data set allows for an IP-stable clustering in general is NP-hard. As a result, we explore the design of efficient algorithms for finding IP-stable clusterings in some restricted metric spaces. We present a polytime algorithm to find a clustering satisfying exact IP-stability on the real line, and an efficient algorithm to find an IP-stable 2-clustering for a tree metric. We also consider relaxing the stability constraint, i.e., every data point should not be too far from its own cluster compared to any other cluster. For this case, we provide polytime algorithms with different guarantees. We evaluate some of our algorithms and several standard clustering approaches on real data sets.Comment: Accepted to ICML'22. This is a full version of the ICML version as well as a substantially improved version of arXiv:2006.0496