Related papers: Mismatch in the Classification of Linear Subspaces…
This paper studies the classification of high-dimensional Gaussian signals from low-dimensional noisy, linear measurements. In particular, it provides upper bounds (sufficient conditions) on the number of measurements required to drive the…
In many real-world classification problems, the labels of training examples are randomly corrupted. Most previous theoretical work on classification with label noise assumes that the two classes are separable, that the label noise is…
We study the estimation capacity of the generalized Lasso, i.e., least squares minimization combined with a (convex) structural constraint. While Lasso-type estimators were originally designed for noisy linear regression problems, it has…
It is a common practice in the machine learning community to assume that the observed data are noise-free in the input attributes. Nevertheless, scenarios with input noise are common in real problems, as measurements are never perfectly…
We consider the problem of estimating how well a model class is capable of fitting a distribution of labeled data. We show that it is often possible to accurately estimate this "learnability" even when given an amount of data that is too…
We present fundamental limits on the reliable classification of linear and affine subspaces from noisy, linear features. Drawing an analogy between discrimination among subspaces and communication over vector wireless channels, we propose…
We pose a fundamental question in computational learning theory: can we efficiently test whether a training set satisfies the assumptions of a given noise model? This question has remained unaddressed despite decades of research on learning…
We consider the problem of linear fitting of noisy data in the case of broad (say $\alpha$-stable) distributions of random impacts ("noise"), which can lack even the first moment. This situation, common in statistical physics of small…
We study ``selective'' or ``conditional'' classification problems under an agnostic setting. Classification tasks commonly focus on modeling the relationship between features and categories that captures the vast majority of data. In…
This paper derives fundamental limits on the performance of compressive classification when the source is a mixture of Gaussians. It provides an asymptotic analysis of a Bhattacharya based upper bound on the misclassification probability…
We give the first efficient algorithm for learning halfspaces in the testable learning model recently defined by Rubinfeld and Vasilyan (2023). In this model, a learner certifies that the accuracy of its output hypothesis is near optimal…
In this paper we revisit some classic problems on classification under misspecification. In particular, we study the problem of learning halfspaces under Massart noise with rate $\eta$. In a recent work, Diakonikolas, Goulekakis, and Tzamos…
We study the algorithmic task of testably learning general Massart halfspaces under the Gaussian distribution. In the testable learning setting, the aim is the design of a tester-learner pair satisfying the following properties: (1) if the…
With the explosion of massive, widely available unlabeled data in the past years, finding label and time efficient, robust learning algorithms has become ever more important in theory and in practice. We study the paradigm of active…
Deep neural networks generalize well despite being exceedingly overparameterized and being trained without explicit regularization. This curious phenomenon has inspired extensive research activity in establishing its statistical principles:…
We prove bounds on the population risk of the maximum margin algorithm for two-class linear classification. For linearly separable training data, the maximum margin algorithm has been shown in previous work to be equivalent to a limit of…
Understanding and dealing with inference biases in gravitational-wave (GW) parameter estimation when a plethora of signals are present in the data is one of the key challenges for the analysis of data from future GW detectors. Working…
We study the problem of signal estimation from non-linear observations when the signal belongs to a low-dimensional set buried in a high-dimensional space. A rough heuristic often used in practice postulates that non-linear observations may…
When is optimal estimation linear? It is well known that, when a Gaussian source is contaminated with Gaussian noise, a linear estimator minimizes the mean square estimation error. This paper analyzes, more generally, the conditions for…
This paper provides theoretical insights into high-dimensional binary classification with class-conditional noisy labels. Specifically, we study the behavior of a linear classifier with a label noisiness aware loss function, when both the…