Related papers: A Statistical Framework to Investigate the Optimal…
We address the inverse problem of reconstructing both the structure and dynamics of a network from mean-field measurements, which are linear combinations of node states. This setting arises in applications where only a few aggregated…
Broadband wireless channels usually have the sparse nature. Based on the assumption of Gaussian noise model, adaptive filtering algorithms for reconstruction sparse channels were proposed to take advantage of channel sparsity. However,…
This paper concerns the problem of recovering an unknown but structured signal $x \in R^n$ from $m$ quadratic measurements of the form $y_r=|<a_r,x>|^2$ for $r=1,2,...,m$. We focus on the under-determined setting where the number of…
We study the problem of reconstructing a signal from its projection on a subspace. The proposed signal reconstruction algorithms utilize a guiding subspace that represents desired properties of reconstructed signals. We show that optimal…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
This paper provides a least squares formulation for the training of a 2-layer convolutional neural network using quadratic activation functions, a 2-norm loss function, and no regularization term. Using this method, an analytic expression…
Many regularization schemes for high-dimensional regression have been put forward. Most require the choice of a tuning parameter, using model selection criteria or cross-validation schemes. We show that a simple non-negative or…
The standard approach to compressive sampling considers recovering an unknown deterministic signal with certain known structure, and designing the sub-sampling pattern and recovery algorithm based on the known structure. This approach…
Iteratively reweighted least square (IRLS) is a popular approach to solve sparsity-enforcing regression problems in machine learning. State of the art approaches are more efficient but typically rely on specific coordinate pruning schemes.…
Motivated by the need for efficient estimation of conditional expectations, we consider a least-squares function approximation problem with heavily polluted data. Existing methods that are effective in the small-noise regime are suboptimal…
We present an online algorithm for reconstructing a signal from a set of non-uniform samples. By representing the signal using compactly supported basis functions, we show how estimating the expansion coefficients using least-squares can be…
This paper considers the linear inverse problem where we wish to estimate a structured signal $x$ from its corrupted observations. When the problem is ill-posed, it is natural to make use of a convex function $f(\cdot)$ that exploits the…
Consider a collection of competing machine learning algorithms. Given their performance on a benchmark of datasets, we would like to identify the best performing algorithm. Specifically, which algorithm is most likely to rank highest on a…
Subsampling algorithms for various parametric regression models with massive data have been extensively investigated in recent years. However, all existing studies on subsampling heavily rely on clean massive data. In practical…
Bagging, a powerful ensemble method from machine learning, improves the performance of unstable predictors. Although the power of Bagging has been shown mostly in classification problems, we demonstrate the success of employing Bagging in…
We present a novel probabilistic framework for the recovery of discrete signals with missing data, extending classical Fourier-based methods. While prior results, such as those of Donoho and Stark; see also Logan's method, guarantee exact…
In signal processing and data recovery, reconstructing a signal from quadratic measurements poses a significant challenge, particularly in high-dimensional settings where measurements $m$ is far less than the signal dimension $n$ (i.e., $m…
Reconstruction tasks in computer vision aim fundamentally to recover an undetermined signal from a set of noisy measurements. Examples include super-resolution, image denoising, and non-rigid structure from motion, all of which have seen…
Even though image signals are typically defined on a regular two-dimensional grid, there also exist many scenarios where this is not the case and the amplitude of the image signal only is available for a non-regular subset of pixel…
We analyze statistical features of the ``optimization landscape'' in a random version of one of the simplest constrained optimization problems of the least-square type: finding the best approximation for the solution of an overcomplete…