Related papers: Learning a mixture of two subspaces over finite fi…
Learning from data in the presence of outliers is a fundamental problem in statistics. In this work, we study robust statistics in the presence of overwhelming outliers for the fundamental problem of subspace recovery. Given a dataset where…
Over-parameterized deep neural networks (DNNs) with sufficient capacity to memorize random noise can achieve excellent generalization performance, challenging the bias-variance trade-off in classical learning theory. Recent studies claimed…
We study the problem of PAC learning halfspaces with Massart noise. Given labeled samples $(x, y)$ from a distribution $D$ on $\mathbb{R}^{d} \times \{ \pm 1\}$ such that the marginal $D_x$ on the examples is arbitrary and the label $y$ of…
This paper is concerned with computationally efficient learning of homogeneous sparse halfspaces in $\mathbb{R}^d$ under noise. Though recent works have established attribute-efficient learning algorithms under various types of label noise…
The low-degree polynomial framework has been highly successful in predicting computational versus statistical gaps for high-dimensional problems in average-case analysis and machine learning. This success has led to the low-degree…
Deep learning has demonstrated strong potential for MRI reconstruction. However, conventional supervised learning requires high-quality, high-SNR references for network training, which are often difficult or impossible to obtain in…
Adversarial perturbations are noise-like patterns that can subtly change the data, while failing an otherwise accurate classifier. In this paper, we propose to use such perturbations within a novel contrastive learning setup to build…
In this paper, we study the adversarial robustness of subspace learning problems. Different from the assumptions made in existing work on robust subspace learning where data samples are contaminated by gross sparse outliers or small dense…
Nonlinear manifold learning from unorganized data points is a very challenging unsupervised learning and data visualization problem with a great variety of applications. In this paper we present a new algorithm for manifold learning and…
With recent deep learning based approaches showing promising results in removing noise from images, the best denoising performance has been reported in a supervised learning setup that requires a large set of paired noisy images and ground…
We study the problem of finding elements in the intersection of an arbitrary conic variety in $\mathbb{F}^n$ with a given linear subspace (where $\mathbb{F}$ can be the real or complex field). This problem captures a rich family of…
In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by Poisson noise. A proper data fidelity term (log-likelihood) is introduced to reflect the Poisson statistics of the noise. On…
Low-light raw denoising is an important and valuable task in computational photography where learning-based methods trained with paired real data are mainstream. However, the limited data volume and complicated noise distribution have…
The current dominant approach for neural speech enhancement is based on supervised learning by using simulated training data. The trained models, however, often exhibit limited generalizability to real-recorded data. To address this, this…
We consider the problem of learning a mixture of linear regressions (MLRs). An MLR is specified by $k$ nonnegative mixing weights $p_1, \ldots, p_k$ summing to $1$, and $k$ unknown regressors $w_1,...,w_k\in\mathbb{R}^d$. A sample from the…
The goal of subspace learning is to find a $k$-dimensional subspace of $\mathbb{R}^d$, such that the expected squared distance between instance vectors and the subspace is as small as possible. In this paper we study subspace learning in a…
Based on the predictive map theory of spatial learning in animals, this study delves into the dynamics of Successor Feature (SF) and Predecessor Feature (PF) algorithms within noisy environments. Utilizing Q-learning and Q($\lambda$)…
In this paper, we consider the mixture of sparse linear regressions model. Let ${\beta}^{(1)},\ldots,{\beta}^{(L)}\in\mathbb{C}^n$ be $ L $ unknown sparse parameter vectors with a total of $ K $ non-zero coefficients. Noisy linear…
We introduce a new model of membership query (MQ) learning, where the learning algorithm is restricted to query points that are \emph{close} to random examples drawn from the underlying distribution. The learning model is intermediate…
Smoothed analysis is a powerful paradigm in overcoming worst-case intractability in unsupervised learning and high-dimensional data analysis. While polynomial time smoothed analysis guarantees have been obtained for worst-case intractable…