Related papers: Beyond Tsybakov: Model Margin Noise and $\mathcal{…
Understanding generalization in deep neural networks is an active area of research. A promising avenue of exploration has been that of margin measurements: the shortest distance to the decision boundary for a given sample or that sample's…
Ill-posed linear inverse problems appear frequently in various signal processing applications. It can be very useful to have theoretical characterizations that quantify the level of ill-posedness for a given inverse problem and the degree…
Vacuum stability implies a lower limit on the mass of the higgs boson in the Standard Model (SM). In contrast, an upper limit on the lightest higgs mass can be calculated in supersymmetric (susy) models. The main uncertainty in each limit…
We test the robustness of a maximum-likelihood (ML) based classifier where sequential data as observation is corrupted by noise. The hypothesis is that a generative model, that combines the state transitions of a hidden Markov model (HMM)…
We introduce a noise-aware extension to the parametric maximum-likelihood framework for component separation by modeling correlated $1/f^\alpha$ noise as a harmonic-space power law. This approach addresses a key limitation of existing…
Robust gauge conditions are critically important to the stability and accuracy of numerical relativity (NR) simulations involving compact objects. Most of the NR community use the highly robust---though decade-old---moving-puncture (MP)…
We consider the regression model with observation error in the design: y=X\theta* + e, Z=X+N. Here the random vector y in R^n and the random n*p matrix Z are observed, the n*p matrix X is unknown, N is an n*p random noise matrix, e in R^n…
This paper examines fundamental error characteristics for a general class of matrix completion problems, where the matrix of interest is a product of two a priori unknown matrices, one of which is sparse, and the observations are noisy. Our…
This paper examines the performance of ridge regression in reproducing kernel Hilbert spaces in the presence of noise that exhibits a finite number of higher moments. We establish excess risk bounds consisting of subgaussian and polynomial…
This paper presents uniform-in-time finite-sample bounds for regularized linear regression with vector-valued outputs and conditionally zero-mean subgaussian noise. By revisiting classical self-normalized martingale arguments, we obtain…
In supervised learning, automatically assessing the quality of the labels before any learning takes place remains an open research question. In certain particular cases, hypothesis testing procedures have been proposed to assess whether a…
In nonlinear deterministic parameter estimation, the maximum likelihood estimator (MLE) is unable to attain the Cramer-Rao lower bound at low and medium signal-to-noise ratios (SNR) due the threshold and ambiguity phenomena. In order to…
We study the efficient PAC learnability of halfspaces in the presence of Tsybakov noise. In the Tsybakov noise model, each label is independently flipped with some probability which is controlled by an adversary. This noise model…
Class-conditional noise commonly exists in machine learning tasks, where the class label is corrupted with a probability depending on its ground-truth. Many research efforts have been made to improve the model robustness against the…
We consider the least-squares regression problem with unknown noise variance, where the observed data points are allowed to be corrupted by outliers. Building on the median-of-means (MOM) method introduced by Lecue and Lerasle…
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 analyse the interpolator with minimal $\ell_2$-norm $\hat{\beta}$ in a general high dimensional linear regression framework where $\mathbb Y=\mathbb X\beta^*+\xi$ where $\mathbb X$ is a random $n\times p$ matrix with independent…
In the Minimal Supersymmetric Model (MSSM) and the Next to Minimal Supersymmetric Model [(M+1)SSM], an upper bound on the lightest higgs mass can be calculated. On the other hand, vacuum stability implies a lower limit on the mass of the…
After a general introduction about the regularization by noise phenomenon in the degenerate setting, the first part of this PhD thesis focuses at establishing the Schauder estimates, a useful analytical tool to prove also the well-posedness…
This paper studies binary classification in robust one-bit compressed sensing with adversarial errors. It is assumed that the model is overparameterized and that the parameter of interest is effectively sparse. AdaBoost is considered, and,…