Brett Mullins

Cecilia Ferrando, Miguel Fuentes, Brett Mullins et al.

We propose PACE-GGM, a data-adaptive differentially private method for covariance estimation that concentrates its privacy budget on the most informative entries of the empirical covariance matrix, rather than perturbing all entries. This applies in the natural setting where the modeler supplies separate bounds for each variable, so that individual entries can be measured with less noise than the full matrix. In each round, our method selects a poorly approximated entry, measures it using the Gaussian mechanism, and then reconstructs a full covariance matrix using a maximum-entropy reconstruction objective, leading to a Gaussian graphical model structure. Experiments on diverse real-world datasets demonstrate consistent improvements in estimation error with respect to the Gaussian mechanism and other baselines, particularly in high-dimensional and low-to-moderate privacy regimes.

Brett Mullins

Rule-based explanations provide simple reasons explaining the behavior of machine learning classifiers at given points in the feature space. Several recent methods (Anchors, LORE, etc.) purport to generate rule-based explanations for arbitrary or black-box classifiers. But what makes these methods work in general? We introduce a topological framework for rule-based explanation methods and provide a characterization of explainability in terms of the definability of a classifier relative to an explanation scheme. We employ this framework to consider various explanation schemes and argue that the preferred scheme depends on how much the user knows about the domain and the probability measure over the feature space.

Miguel Fuentes, Brett Mullins, Ryan McKenna et al.

Mechanisms for generating differentially private synthetic data based on marginals and graphical models have been successful in a wide range of settings. However, one limitation of these methods is their inability to incorporate public data. Initializing a data generating model by pre-training on public data has shown to improve the quality of synthetic data, but this technique is not applicable when model structure is not determined a priori. We develop the mechanism jam-pgm, which expands the adaptive measurements framework to jointly select between measuring public data and private data. This technique allows for public data to be included in a graphical-model-based mechanism. We show that jam-pgm is able to outperform both publicly assisted and non publicly assisted synthetic data generation mechanisms even when the public data distribution is biased.

Brett Mullins

We introduce the notion of pointwise coverage to measure the explainability properties of machine learning classifiers. An explanation for a prediction is a definably simple region of the feature space sharing the same label as the prediction, and the coverage of an explanation measures its size or generalizability. With this notion of explanation, we investigate whether or not there is a natural characterization of the most explainable classifier. According with our intuitions, we prove that the binary linear classifier is uniquely the most explainable classifier up to negligible sets.