Related papers: Sharp bounds for population recovery
This paper presents a novel information-theoretic perspective on generalization in machine learning by framing the learning problem within the context of lossy compression and applying finite blocklength analysis. In our approach, the…
Extracting meaning from uncertain, noisy data is a fundamental problem across time series analysis, pattern recognition, and language modeling. This survey presents a unified mathematical framework that connects classical estimation theory,…
We provide high probability finite sample complexity guarantees for hidden non-parametric structure learning of tree-shaped graphical models, whose hidden and observable nodes are discrete random variables with either finite or countable…
Compressive sampling offers a new paradigm for acquiring signals that are compressible with respect to an orthonormal basis. The major algorithmic challenge in compressive sampling is to approximate a compressible signal from noisy samples.…
Random instances of Constraint Satisfaction Problems (CSP's) appear to be hard for all known algorithms, when the number of constraints per variable lies in a certain interval. Contributing to the general understanding of the structure of…
In the field of medical image analysis, deep learning models have demonstrated remarkable success in enhancing diagnostic accuracy and efficiency. However, the reliability of these models is heavily dependent on the quality of training…
In this article, we discuss a novel greedy algorithm for the recovery of compressive sampled signals under noisy conditions. Most of the greedy recovery algorithms proposed in the literature require sparsity of the signal to be known or…
We consider the problem of robust polynomial regression, where one receives samples $(x_i, y_i)$ that are usually within $\sigma$ of a polynomial $y = p(x)$, but have a $\rho$ chance of being arbitrary adversarial outliers. Previously, it…
We study the problem of clustering a set of items from binary user feedback. Such a problem arises in crowdsourcing platforms solving large-scale labeling tasks with minimal effort put on the users. For example, in some of the recent…
This work explores the fundamental problem of the recoverability of a sparse tensor being reconstructed from its compressed embodiment. We present a generalized model of block-sparse tensor recovery as a theoretical foundation, where…
We consider approximation or recovery of functions based on a finite number of function evaluations. This is a well-studied problem in optimal recovery, machine learning, and numerical analysis in general, but many fundamental insights were…
The effectiveness of using model sparsity as a priori information when solving linear inverse problems is studied. We investigate the reconstruction quality of such a method in the non-idealized case and compute some typical recovery errors…
We provide high-probability sample complexity guarantees for exact structure recovery and accurate predictive learning using noise-corrupted samples from an acyclic (tree-shaped) graphical model. The hidden variables follow a…
We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…
In this paper, we consider the group testing problem with adaptive test designs and noisy outcomes. We propose a computationally efficient four-stage procedure with components including random binning, identification of bins containing…
We consider the problem of mixed sparse linear regression with two components, where two real $k$-sparse signals $\beta_1, \beta_2$ are to be recovered from $n$ unlabelled noisy linear measurements. The sparsity is allowed to be sublinear…
With the rise of smartphones and the internet-of-things, data is increasingly getting generated at the edge on local, personal devices. For privacy, latency and energy saving reasons, this shift is causing machine learning algorithms to…
Reconstruction of signals from undersampled and noisy measurements is a topic of considerable interest. Sharpness conditions directly control the recovery performance of restart schemes for first-order methods without the need for…
Recovering an unknown but structured signal from its measurements is a challenging problem with significant applications in fields such as imaging restoration, wireless communications, and signal processing. In this paper, we consider the…
Common problem in signal processing is reconstruction of the missing signal samples. Missing samples can occur by intentionally omitting signal coefficients to reduce memory requirements, or to speed up the transmission process. Also, noisy…