Training Uncertainty-Aware Classifiers with Conformalized Deep Learning

Deep neural networks are powerful tools to detect hidden patterns in data and leverage them to make predictions, but they are not designed to understand uncertainty and estimate reliable probabilities. In particular, they tend to be overconfident. We address this problem by developing a novel training algorithm that can lead to more dependable uncertainty estimates, without sacrificing predictive power. The idea is to mitigate overconfidence by minimizing a loss function, inspired by advances in conformal inference, that quantifies model uncertainty by carefully leveraging hold-out data. Experiments with synthetic and real data demonstrate this method leads to smaller conformal prediction sets with higher conditional coverage, after exact calibration with hold-out data, compared to state-of-the-art alternatives.

Conformalized Frequency Estimation from Sketched Data

A flexible conformal inference method is developed to construct confidence intervals for the frequencies of queried objects in a very large data set, based on the information contained in a much smaller sketch of those data. The approach is completely data-adaptive and makes no use of any knowledge of the population distribution or of the inner workings of the sketching algorithm; instead, it constructs provably valid frequentist confidence intervals under the sole assumption of data exchangeability. Although the proposed solution is much more broadly applicable, this paper explicitly demonstrates its use in combination with the famous count-min sketch algorithm and a non-linear variation thereof to facilitate the exposition. The performance is compared to that of existing frequentist and Bayesian alternatives through several experiments with synthetic data as well as with real data sets consisting of SARS-CoV-2 DNA sequences and classic English literature.

Conformal histogram regression

This paper develops a conformal method to compute prediction intervals for non-parametric regression that can automatically adapt to skewed data. Leveraging black-box machine learning algorithms to estimate the conditional distribution of the outcome using histograms, it translates their output into the shortest prediction intervals with approximate conditional coverage. The resulting prediction intervals provably have marginal coverage in finite samples, while asymptotically achieving conditional coverage and optimal length if the black-box model is consistent. Numerical experiments with simulated and real data demonstrate improved performance compared to state-of-the-art alternatives, including conformalized quantile regression and other distributional conformal prediction approaches.

Testing for Outliers with Conformal p-values

This paper studies the construction of p-values for nonparametric outlier detection, taking a multiple-testing perspective. The goal is to test whether new independent samples belong to the same distribution as a reference data set or are outliers. We propose a solution based on conformal inference, a broadly applicable framework which yields p-values that are marginally valid but mutually dependent for different test points. We prove these p-values are positively dependent and enable exact false discovery rate control, although in a relatively weak marginal sense. We then introduce a new method to compute p-values that are both valid conditionally on the training data and independent of each other for different test points; this paves the way to stronger type-I error guarantees. Our results depart from classical conformal inference as we leverage concentration inequalities rather than combinatorial arguments to establish our finite-sample guarantees. Furthermore, our techniques also yield a uniform confidence bound for the false positive rate of any outlier detection algorithm, as a function of the threshold applied to its raw statistics. Finally, the relevance of our results is demonstrated by numerical experiments on real and simulated data.

Interpretable Signal Analysis with Knockoffs Enhances Classification of Bacterial Raman Spectra

Interpretability is important for many applications of machine learning to signal data, covering aspects such as how well a model fits the data, how accurately explanations are drawn from it, and how well these can be understood by people. Feature extraction and selection can improve model interpretability by identifying structures in the data that are both informative and intuitively meaningful. To this end, we propose a signal classification framework that combines feature extraction with feature selection using the knockoff filter, a method which provides guarantees on the false discovery rate (FDR) amongst selected features. We apply this to a dataset of Raman spectroscopy measurements from bacterial samples. Using a wavelet-based feature representation of the data and a logistic regression classifier, our framework achieves significantly higher predictive accuracy compared to using the original features as input. Benchmarking was also done with features obtained through principal components analysis, as well as the original features input into a neural network-based classifier. Our proposed framework achieved better predictive performance at the former task and comparable performance at the latter task, while offering the advantage of a more compact and human-interpretable set of features.

Classification with Valid and Adaptive Coverage

Conformal inference, cross-validation+, and the jackknife+ are hold-out methods that can be combined with virtually any machine learning algorithm to construct prediction sets with guaranteed marginal coverage. In this paper, we develop specialized versions of these techniques for categorical and unordered response labels that, in addition to providing marginal coverage, are also fully adaptive to complex data distributions, in the sense that they perform favorably in terms of approximate conditional coverage compared to alternative methods. The heart of our contribution is a novel conformity score, which we explicitly demonstrate to be powerful and intuitive for classification problems, but whose underlying principle is potentially far more general. Experiments on synthetic and real data demonstrate the practical value of our theoretical guarantees, as well as the statistical advantages of the proposed methods over the existing alternatives.

A comparison of some conformal quantile regression methods

We compare two recently proposed methods that combine ideas from conformal inference and quantile regression to produce locally adaptive and marginally valid prediction intervals under sample exchangeability (Romano et al., 2019; Kivaranovic et al., 2019). First, we prove that these two approaches are asymptotically efficient in large samples, under some additional assumptions. Then we compare them empirically on simulated and real data. Our results demonstrate that the method in Romano et al. (2019) typically yields tighter prediction intervals in finite samples. Finally, we discuss how to tune these procedures by fixing the relative proportions of observations used for training and conformalization.

Deep Knockoffs

This paper introduces a machine for sampling approximate model-X knockoffs for arbitrary and unspecified data distributions using deep generative models. The main idea is to iteratively refine a knockoff sampling mechanism until a criterion measuring the validity of the produced knockoffs is optimized; this criterion is inspired by the popular maximum mean discrepancy in machine learning and can be thought of as measuring the distance to pairwise exchangeability between original and knockoff features. By building upon the existing model-X framework, we thus obtain a flexible and model-free statistical tool to perform controlled variable selection. Extensive numerical experiments and quantitative tests confirm the generality, effectiveness, and power of our deep knockoff machines. Finally, we apply this new method to a real study of mutations linked to changes in drug resistance in the human immunodeficiency virus.