Related papers: Robust Matrix Regression
In the last a few decades, deep neural networks have achieved remarkable success in machine learning, computer vision, and pattern recognition. Recent studies however show that neural networks (both shallow and deep) may be easily fooled by…
Graph is a fundamental mathematical structure in characterizing relations between different objects and has been widely used on various learning tasks. Most methods implicitly assume a given graph to be accurate and complete. However, real…
In this paper we consider the trace regression model. Assume that we observe a small set of entries or linear combinations of entries of an unknown matrix $A_0$ corrupted by noise. We propose a new rank penalized estimator of $A_0$. For…
While generalizing well over natural inputs, neural networks are vulnerable to adversarial inputs. Existing defenses against adversarial inputs have largely been detached from the real world. These defenses also come at a cost to accuracy.…
Deep neural networks give state-of-the-art accuracy for reconstructing images from few and noisy measurements, a problem arising for example in accelerated magnetic resonance imaging (MRI). However, recent works have raised concerns that…
Convolutional and Recurrent, deep neural networks have been successful in machine learning systems for computer vision, reinforcement learning, and other allied fields. However, the robustness of such neural networks is seldom apprised,…
Challenges with data in the big-data era include (i) the dimension $p$ is often larger than the sample size $n$ (ii) outliers or contaminated points are frequently hidden and more difficult to detect. Challenge (i) renders most conventional…
Machine learning has demonstrated remarkable performance over finite datasets, yet whether the scores over the fixed benchmarks can sufficiently indicate the model's performance in the real world is still in discussion. In reality, an ideal…
Regression neural networks (NNs) are most commonly trained by minimizing the mean squared prediction error, which is highly sensitive to outliers and data contamination. Existing robust training methods for regression NNs are often limited…
This thesis addresses challenges related to data and parameter efficiency in neural language models, with a focus on representation analysis and the introduction of new optimization techniques. The first part examines the properties and…
Neural networks have become increasingly popular in controller design due to their versatility and efficiency. However, their integration into feedback systems can pose stability challenges, particularly in the presence of uncertainties.…
Supervised classification methods often assume that evaluation data is drawn from the same distribution as training data and that all classes are present for training. However, real-world classifiers must handle inputs that are far from the…
This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank…
Deep learning has gained broad interest in remote sensing image scene classification thanks to the effectiveness of deep neural networks in extracting the semantics from complex data. However, deep networks require large amounts of training…
We consider the problem of robust matrix completion, which aims to recover a low rank matrix $L_*$ and a sparse matrix $S_*$ from incomplete observations of their sum $M=L_*+S_*\in\mathbb{R}^{m\times n}$. Algorithmically, the robust matrix…
This paper gives two theoretical results on estimating low-rank parameter matrices for linear models with multivariate responses. We first focus on robust parameter estimation of low-rank multi-task learning with heavy-tailed data and…
In this paper, a robust optimization framework is developed to train shallow neural networks based on reachability analysis of neural networks. To characterize noises of input data, the input training data is disturbed in the description of…
Precision matrix estimation is a fundamental topic in multivariate statistics and modern machine learning. This paper proposes an adversarially perturbed precision matrix estimation framework, motivated by recent developments in adversarial…
Gradient boosting algorithms construct a regression predictor using a linear combination of ``base learners''. Boosting also offers an approach to obtaining robust non-parametric regression estimators that are scalable to applications with…
In the past five years, deep learning methods have become state-of-the-art in solving various inverse problems. Before such approaches can find application in safety-critical fields, a verification of their reliability appears mandatory.…