arXiv subjects

Yaniv Romano

Publications and source records attributed to Yaniv Romano.

At least 55 records · Page 3Linked to original sources

arXiv2023

Model-X Sequential Testing for Conditional Independence via Testing by Betting

This paper develops a model-free sequential test for conditional independence. The proposed test allows researchers to analyze an incoming i.i.d. data stream with any arbitrary dependency structure, and safely conclude whether a feature is conditionally associated with the response under study. We allow the processing of data points online, as soon as they arrive, and stop data acquisition once significant results are detected, rigorously controlling the type-I error rate. Our test can work with any sophisticated machine learning algorithm to enhance data efficiency to the extent possible. The developed method is inspired by two statistical frameworks. The first is the model-X conditional randomization test, a test for conditional independence that is valid in offline settings where the sample size is fixed in advance. The second is testing by betting, a ``game-theoretic'' approach for sequential hypothesis testing. We conduct synthetic experiments to demonstrate the advantage of our test over out-of-the-box sequential tests that account for the multiplicity of tests in the time horizon, and demonstrate the practicality of our proposal by applying it to real-world tasks.

stat.ME↗

arXiv2023

Learning to Increase the Power of Conditional Randomization Tests

The model-X conditional randomization test is a generic framework for conditional independence testing, unlocking new possibilities to discover features that are conditionally associated with a response of interest while controlling type-I error rates. An appealing advantage of this test is that it can work with any machine learning model to design powerful test statistics. In turn, the common practice in the model-X literature is to form a test statistic using machine learning models, trained to maximize predictive accuracy with the hope to attain a test with good power. However, the ideal goal here is to drive the model (during training) to maximize the power of the test, not merely the predictive accuracy. In this paper, we bridge this gap by introducing, for the first time, novel model-fitting schemes that are designed to explicitly improve the power of model-X tests. This is done by introducing a new cost function that aims at maximizing the test statistic used to measure violations of conditional independence. Using synthetic and real data sets, we demonstrate that the combination of our proposed loss function with various base predictive models (lasso, elastic net, and deep neural networks) consistently increases the number of correct discoveries obtained, while maintaining type-I error rates under control.

cs.LG↗

arXiv2023

Achieving Risk Control in Online Learning Settings

To provide rigorous uncertainty quantification for online learning models, we develop a framework for constructing uncertainty sets that provably control risk -- such as coverage of confidence intervals, false negative rate, or F1 score -- in the online setting. This extends conformal prediction to apply to a larger class of online learning problems. Our method guarantees risk control at any user-specified level even when the underlying data distribution shifts drastically, even adversarially, over time in an unknown fashion. The technique we propose is highly flexible as it can be applied with any base online learning algorithm (e.g., a deep neural network trained online), requiring minimal implementation effort and essentially zero additional computational cost. We further extend our approach to control multiple risks simultaneously, so the prediction sets we generate are valid for all given risks. To demonstrate the utility of our method, we conduct experiments on real-world tabular time-series data sets showing that the proposed method rigorously controls various natural risks. Furthermore, we show how to construct valid intervals for an online image-depth estimation problem that previous sequential calibration schemes cannot handle.

cs.LG↗

arXiv2022

Calibrated Multiple-Output Quantile Regression with Representation Learning

We develop a method to generate predictive regions that cover a multivariate response variable with a user-specified probability. Our work is composed of two components. First, we use a deep generative model to learn a representation of the response that has a unimodal distribution. Existing multiple-output quantile regression approaches are effective in such cases, so we apply them on the learned representation, and then transform the solution to the original space of the response. This process results in a flexible and informative region that can have an arbitrary shape, a property that existing methods lack. Second, we propose an extension of conformal prediction to the multivariate response setting that modifies any method to return sets with a pre-specified coverage level. The desired coverage is theoretically guaranteed in the finite-sample case for any distribution. Experiments conducted on both real and synthetic data show that our method constructs regions that are significantly smaller compared to existing techniques.

cs.LG↗

arXiv2022

Semantic uncertainty intervals for disentangled latent spaces

Meaningful uncertainty quantification in computer vision requires reasoning about semantic information -- say, the hair color of the person in a photo or the location of a car on the street. To this end, recent breakthroughs in generative modeling allow us to represent semantic information in disentangled latent spaces, but providing uncertainties on the semantic latent variables has remained challenging. In this work, we provide principled uncertainty intervals that are guaranteed to contain the true semantic factors for any underlying generative model. The method does the following: (1) it uses quantile regression to output a heuristic uncertainty interval for each element in the latent space (2) calibrates these uncertainties such that they contain the true value of the latent for a new, unseen input. The endpoints of these calibrated intervals can then be propagated through the generator to produce interpretable uncertainty visualizations for each semantic factor. This technique reliably communicates semantically meaningful, principled, and instance-adaptive uncertainty in inverse problems like image super-resolution and image completion.

cs.CV↗

arXiv2022

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 begin to address this problem in the context of multi-class classification by developing a novel training algorithm producing models with 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 can lead to smaller conformal prediction sets with higher conditional coverage, after exact calibration with hold-out data, compared to state-of-the-art alternatives.

stat.ML↗

arXiv2022

Quantum Sparse Coding

The ultimate goal of any sparse coding method is to accurately recover from a few noisy linear measurements, an unknown sparse vector. Unfortunately, this estimation problem is NP-hard in general, and it is therefore always approached with an approximation method, such as lasso or orthogonal matching pursuit, thus trading off accuracy for less computational complexity. In this paper, we develop a quantum-inspired algorithm for sparse coding, with the premise that the emergence of quantum computers and Ising machines can potentially lead to more accurate estimations compared to classical approximation methods. To this end, we formulate the most general sparse coding problem as a quadratic unconstrained binary optimization (QUBO) task, which can be efficiently minimized using quantum technology. To derive at a QUBO model that is also efficient in terms of the number of spins (space complexity), we separate our analysis into three different scenarios. These are defined by the number of bits required to express the underlying sparse vector: binary, 2-bit, and a general fixed-point representation. We conduct numerical experiments with simulated data on LightSolver's quantum-inspired digital platform to verify the correctness of our QUBO formulation and to demonstrate its advantage over baseline methods.

quant-ph↗

arXiv2022

An Asymptotic Test for Conditional Independence using Analytic Kernel Embeddings

We propose a new conditional dependence measure and a statistical test for conditional independence. The measure is based on the difference between analytic kernel embeddings of two well-suited distributions evaluated at a finite set of locations. We obtain its asymptotic distribution under the null hypothesis of conditional independence and design a consistent statistical test from it. We conduct a series of experiments showing that our new test outperforms state-of-the-art methods both in terms of type-I and type-II errors even in the high dimensional setting.

stat.ML↗

arXiv2022

Coordinated Double Machine Learning

Double machine learning is a statistical method for leveraging complex black-box models to construct approximately unbiased treatment effect estimates given observational data with high-dimensional covariates, under the assumption of a partially linear model. The idea is to first fit on a subset of the samples two non-linear predictive models, one for the continuous outcome of interest and one for the observed treatment, and then to estimate a linear coefficient for the treatment using the remaining samples through a simple orthogonalized regression. While this methodology is flexible and can accommodate arbitrary predictive models, typically trained independently of one another, this paper argues that a carefully coordinated learning algorithm for deep neural networks may reduce the estimation bias. The improved empirical performance of the proposed method is demonstrated through numerical experiments on both simulated and real data.

stat.ML↗

arXiv2022

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.

stat.ME↗

arXiv2022

Image-to-Image Regression with Distribution-Free Uncertainty Quantification and Applications in Imaging

Image-to-image regression is an important learning task, used frequently in biological imaging. Current algorithms, however, do not generally offer statistical guarantees that protect against a model's mistakes and hallucinations. To address this, we develop uncertainty quantification techniques with rigorous statistical guarantees for image-to-image regression problems. In particular, we show how to derive uncertainty intervals around each pixel that are guaranteed to contain the true value with a user-specified confidence probability. Our methods work in conjunction with any base machine learning model, such as a neural network, and endow it with formal mathematical guarantees -- regardless of the true unknown data distribution or choice of model. Furthermore, they are simple to implement and computationally inexpensive. We evaluate our procedure on three image-to-image regression tasks: quantitative phase microscopy, accelerated magnetic resonance imaging, and super-resolution transmission electron microscopy of a Drosophila melanogaster brain.

cs.LG↗

arXiv2021

Conformal Prediction using Conditional Histograms

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.

stat.ME↗

arXiv2021

Improving Conditional Coverage via Orthogonal Quantile Regression

We develop a method to generate prediction intervals that have a user-specified coverage level across all regions of feature-space, a property called conditional coverage. A typical approach to this task is to estimate the conditional quantiles with quantile regression -- it is well-known that this leads to correct coverage in the large-sample limit, although it may not be accurate in finite samples. We find in experiments that traditional quantile regression can have poor conditional coverage. To remedy this, we modify the loss function to promote independence between the size of the intervals and the indicator of a miscoverage event. For the true conditional quantiles, these two quantities are independent (orthogonal), so the modified loss function continues to be valid. Moreover, we empirically show that the modified loss function leads to improved conditional coverage, as evaluated by several metrics. We also introduce two new metrics that check conditional coverage by looking at the strength of the dependence between the interval size and the indicator of miscoverage.

cs.LG↗

arXiv2021

Searching for consistent associations with a multi-environment knockoff filter

This paper develops a method based on model-X knockoffs to find conditional associations that are consistent across diverse environments, controlling the false discovery rate. The motivation for this problem is that large data sets may contain numerous associations that are statistically significant and yet misleading, as they are induced by confounders or sampling imperfections. However, associations consistently replicated under different conditions may be more interesting. In fact, consistency sometimes provably leads to valid causal inferences even if conditional associations do not. While the proposed method is flexible and can be deployed in a wide range of applications, this paper highlights its relevance to genome-wide association studies, in which consistency across populations with diverse ancestries mitigates confounding due to unmeasured variants. The effectiveness of this approach is demonstrated by simulations and applications to the UK Biobank data.

stat.ME↗

arXiv2020

Achieving Equalized Odds by Resampling Sensitive Attributes

We present a flexible framework for learning predictive models that approximately satisfy the equalized odds notion of fairness. This is achieved by introducing a general discrepancy functional that rigorously quantifies violations of this criterion. This differentiable functional is used as a penalty driving the model parameters towards equalized odds. To rigorously evaluate fitted models, we develop a formal hypothesis test to detect whether a prediction rule violates this property, the first such test in the literature. Both the model fitting and hypothesis testing leverage a resampled version of the sensitive attribute obeying equalized odds, by construction. We demonstrate the applicability and validity of the proposed framework both in regression and multi-class classification problems, reporting improved performance over state-of-the-art methods. Lastly, we show how to incorporate techniques for equitable uncertainty quantification---unbiased for each group under study---to communicate the results of the data analysis in exact terms.

stat.ML↗

arXiv2020

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.

stat.ME↗

arXiv2019

With Malice Towards None: Assessing Uncertainty via Equalized Coverage

An important factor to guarantee a fair use of data-driven recommendation systems is that we should be able to communicate their uncertainty to decision makers. This can be accomplished by constructing prediction intervals, which provide an intuitive measure of the limits of predictive performance. To support equitable treatment, we force the construction of such intervals to be unbiased in the sense that their coverage must be equal across all protected groups of interest. We present an operational methodology that achieves this goal by offering rigorous distribution-free coverage guarantees holding in finite samples. Our methodology, equalized coverage, is flexible as it can be viewed as a wrapper around any predictive algorithm. We test the applicability of the proposed framework on real data, demonstrating that equalized coverage constructs unbiased prediction intervals, unlike competitive methods.

stat.ME↗

arXiv2019

Adversarial Noise Attacks of Deep Learning Architectures -- Stability Analysis via Sparse Modeled Signals

Despite their impressive performance, deep convolutional neural networks (CNNs) have been shown to be sensitive to small adversarial perturbations. These nuisances, which one can barely notice, are powerful enough to fool sophisticated and well performing classifiers, leading to ridiculous misclassification results. In this paper we analyze the stability of state-of-the-art deep-learning classification machines to adversarial perturbations, where we assume that the signals belong to the (possibly multi-layer) sparse representation model. We start with convolutional sparsity and then proceed to its multi-layered version, which is tightly connected to CNNs. Our analysis links between the stability of the classification to noise and the underlying structure of the signal, quantified by the sparsity of its representation under a fixed dictionary. In addition, we offer similar stability theorems for two practical pursuit algorithms, which are posed as two different deep-learning architectures - the layered Thresholding and the layered Basis Pursuit. Our analysis establishes the better robustness of the later to adversarial attacks. We corroborate these theoretical results by numerical experiments on three datasets: MNIST, CIFAR-10 and CIFAR-100.

stat.ML↗