相关论文: Sample and Computationally Efficient Robust Learni…

Delineation of cancerous regions in gigapixel whole slide images (WSIs) is a crucial diagnostic procedure in digital pathology. This process is time-consuming because of the large search space in the gigapixel WSIs, causing chances of…

We study the problem of learning a single neuron $\mathbf{x}\mapsto \sigma(\mathbf{w}^T\mathbf{x})$ with gradient descent (GD). All the existing positive results are limited to the case where $\sigma$ is monotonic. However, it is recently…

We provide an algorithm for properly learning mixtures of two single-dimensional Gaussians without any separability assumptions. Given $\tilde{O}(1/\varepsilon^2)$ samples from an unknown mixture, our algorithm outputs a mixture that is…

A Gaussian quantum theory of bosonic modes has been widely used to describe quantum optical systems, including coherent Ising machines (CIMs) that consist of $\chi^{(2)}$ degenerate optical parametric oscillators (DOPOs) as nonlinear…

This paper investigates the problem of recovering missing samples using methods based on sparse representation adapted especially for image signals. Instead of $l_2$-norm or Mean Square Error (MSE), a new perceptual quality measure is used…

The performance of Bayesian detection of Gaussian signals using noisy observations is investigated via the error exponent for the average error probability. Under unknown signal correlation structure or limited processing capability it is…

Learning and decision-making in domains with naturally high noise-to-signal ratio, such as Finance or Healthcare, is often challenging, while the stakes are very high. In this paper, we study the problem of learning and acting under a…

We prove that $\tilde{\Theta}(k d^2 / \varepsilon^2)$ samples are necessary and sufficient for learning a mixture of $k$ Gaussians in $\mathbb{R}^d$, up to error $\varepsilon$ in total variation distance. This improves both the known upper…

Consider estimating a structured signal $\mathbf{x}_0$ from linear, underdetermined and noisy measurements $\mathbf{y}=\mathbf{A}\mathbf{x}_0+\mathbf{z}$, via solving a variant of the lasso algorithm: $\hat{\mathbf{x}}=\arg\min_\mathbf{x}\{…

Learning in the presence of label noise is a challenging yet important task: it is crucial to design models that are robust in the presence of mislabeled datasets. In this paper, we discover that a new class of loss functions called the…

As an example of the recently-introduced concept of rate of innovation, signals that are linear combinations of a finite number of Diracs per unit time can be acquired by linear filtering followed by uniform sampling. However, in reality,…

The decomposition of a sample of images on a relevant subspace is a recurrent problem in many different fields from Computer Vision to medical image analysis. We propose in this paper a new learning principle and implementation of the…

The conventional success of textual classification relies on annotated data, and the new paradigm of pre-trained language models (PLMs) still requires a few labeled data for downstream tasks. However, in real-world applications, label noise…

Identification of a linear time-invariant dynamical system from partial observations is a fundamental problem in control theory. Particularly challenging are systems exhibiting long-term memory. A natural question is how learn such systems…

What is the optimal number of independent observations from which a sparse Gaussian Graphical Model can be correctly recovered? Information-theoretic arguments provide a lower bound on the minimum number of samples necessary to perfectly…

While subspace identification methods (SIMs) are appealing due to their simple parameterization for MIMO systems and robust numerical realizations, a comprehensive statistical analysis of SIMs remains an open problem, especially in the…

In this work, we show, for the well-studied problem of learning parity under noise, where a learner tries to learn $x=(x_1,\ldots,x_n) \in \{0,1\}^n$ from a stream of random linear equations over $\mathrm{F}_2$ that are correct with…

We describe a general technique that yields the first {\em Statistical Query lower bounds} for a range of fundamental high-dimensional learning problems involving Gaussian distributions. Our main results are for the problems of (1) learning…

In the standard Gaussian linear measurement model $Y=X\mu_0+\xi \in \mathbb{R}^m$ with a fixed noise level $\sigma>0$, we consider the problem of estimating the unknown signal $\mu_0$ under a convex constraint $\mu_0 \in K$, where $K$ is a…

We propose a new partial-observability model for online learning problems where the learner, besides its own loss, also observes some noisy feedback about the other actions, depending on the underlying structure of the problem. We represent…