Related papers: The Geometry of Over-parameterized Regression and …

Recent work has shown that additive threat models, which only permit the addition of bounded noise to the pixels of an image, are insufficient for fully capturing the space of imperceivable adversarial examples. For example, small rotations…

The reliability of a learning model is key to the successful deployment of machine learning in various industries. Creating a robust model, particularly one unaffected by adversarial attacks, requires a comprehensive understanding of the…

We study multivariate linear regression under Gaussian covariates in two settings, where data may be erased or corrupted by an adversary under a coordinate-wise budget. In the incomplete data setting, an adversary may inspect the dataset…

A novel framework is introduced to formalize identifiability in well-specified but ill-posed linear regression models. The framework is distribution-free and accommodates highly correlated features that may or may not relate to the…

Adversarial examples are often cited by neuroscientists and machine learning researchers as an example of how computational models diverge from biological sensory systems. Recent work has proposed adding biologically-inspired components to…

Over the past decade, Deep Learning has emerged as a useful and efficient tool to solve a wide variety of complex learning problems ranging from image classification to human pose estimation, which is challenging to solve using statistical…

A common approach in neuroscience is to study neural representations as a means to understand a system -- increasingly, by relating the neural representations to the internal representations learned by computational models. However, a…

Many statistical estimators for high-dimensional linear regression are M-estimators, formed through minimizing a data-dependent square loss function plus a regularizer. This work considers a new class of estimators implicitly defined…

Graph alignment, the problem of identifying corresponding nodes across multiple graphs, is fundamental to numerous applications. Most existing unsupervised methods embed node features into latent representations to enable cross-graph…

Understanding generalization in overparameterized neural networks hinges on the interplay between the data geometry, neural architecture, and training dynamics. In this paper, we theoretically explore how data geometry controls this…

Benign overfitting, the phenomenon where interpolating models generalize well in the presence of noisy data, was first observed in neural network models trained with gradient descent. To better understand this empirical observation, we…

A main puzzle of deep networks revolves around the absence of overfitting despite large overparametrization and despite the large capacity demonstrated by zero training error on randomly labeled data. In this note, we show that the dynamics…

The brittleness of deep image classifiers to small adversarial input perturbations has been extensively studied in the last several years. However, the main objective of existing perturbations is primarily limited to change the correctly…

We study inference on a low-dimensional functional $\beta$ in the presence of infinite-dimensional nuisance parameters. Classical inferential methods are typically based on Wald intervals, whose large-sample validity rests on asymptotic…

Modern machine learning models are often trained in a setting where the number of parameters exceeds the number of training samples. To understand the implicit bias of gradient descent in such overparameterized models, prior work has…

In this review article we consider linear regression analysis from a geometric perspective, looking at standard methods and outputs in terms of the lengths of the relevant vectors and the angles between these vectors. We show that standard…

Adversarial examples are known as carefully perturbed images fooling image classifiers. We propose a geometric framework to generate adversarial examples in one of the most challenging black-box settings where the adversary can only…

Artificial neural networks (ANNs) have become the de facto standard for modeling the human visual system, primarily due to their success in predicting neural responses. However, with many models now achieving similar predictive accuracy, we…

Deep neural networks have been shown to suffer from a surprising weakness: their classification outputs can be changed by small, non-random perturbations of their inputs. This adversarial example phenomenon has been explained as originating…

The problem of prediction in functional linear regression is conventionally addressed by reducing dimension via the standard principal component basis. In this paper we show that an alternative basis chosen through weighted least-squares,…