Related papers: $p$-adic Linear Regression for Random Sampling wit…
Dynamical sampling deals with signals that evolve in time under the action of a linear operator. The purpose of the present paper is to analyze the performance of the basic dynamical sampling algorithms in the finite dimensional case and…
A method for approximating continuous functions $\mathbb{Z}_{p}^{n}\rightarrow\mathbb{Z}_{p}$ by a linear superposition of continuous functions $\mathbb{Z}_{p}\rightarrow\mathbb{Z}_{p}$ is presented and a polynomial regression model is…
Accurate noise modelling is important for training of deep learning reconstruction algorithms. While noise models are well known for traditional imaging techniques, the noise distribution of a novel sensor may be difficult to determine a…
Adaptive randomized pivoting (ARP) is a recently proposed and highly effective algorithm for column subset selection. This paper reinterprets the ARP algorithm by drawing connections to the volume sampling distribution and active learning…
Randomized smoothing has achieved great success for certified robustness against adversarial perturbations. Given any arbitrary classifier, randomized smoothing can guarantee the classifier's prediction over the perturbed input with…
We propose a novel probabilistic method for detection of objects in noisy images. The method uses results from percolation and random graph theories. We present an algorithm that allows to detect objects of unknown shapes in the presence of…
Adding noises to artificial neural network(ANN) has been shown to be able to improve robustness in previous work. In this work, we propose a new technique to compute the pathwise stochastic gradient estimate with respect to the standard…
$p$-adic linear regression is the problem of finding coefficients $\beta$ that minimise $\sum_i |y_i - x_i^\top\beta|_p$. We prove that computing an optimal solution is NP-hard via a polynomial-time reduction from Max Cut using a…
Dynamic mode decomposition (DMD) is an efficient tool for decomposing spatio-temporal data into a set of low-dimensional modes, yielding the oscillation frequencies and the growth rates of physically significant modes. In this paper, we…
We develop a computational procedure to estimate the covariance hyperparameters for semiparametric Gaussian process regression models with additive noise. Namely, the presented method can be used to efficiently estimate the variance of the…
We propose an adaptive ridge (AR) estimation scheme for a heteroscedastic linear regression model with log-linear noise in data. We simultaneously estimate the mean and variance parameters, demonstrating new asymptotic distributional and…
This paper reports on a new algorithm to compute the asymptotic solutions of a linear differential system. A feature of the algorithm is the ability to accommodate periodic coefficients.
A new algorithm is presented for reconstructing stochastic nonlinear dynamical models from noisy time-series data. The approach is analytical; consequently, the resulting algorithm does not require an extensive global search for the model…
In this paper, we propose a novel class of Piecewise Deterministic Markov Processes (PDMPs) that are designed to sample from probability distributions $\pi$ supported on a convex set $\mathcal{M}$. This class of PDMPs adapts the concept of…
In this paper, we propose projected gradient descent (PGD) algorithms for signal estimation from noisy nonlinear measurements. We assume that the unknown $p$-dimensional signal lies near the range of an $L$-Lipschitz continuous generative…
We propose an algorithm to actively estimate the parameters of a linear dynamical system. Given complete control over the system's input, our algorithm adaptively chooses the inputs to accelerate estimation. We show a finite time bound…
The autoregressive time series model is a popular second-order stationary process, modeling a wide range of real phenomena. However, in applications, autoregressive signals are often corrupted by additive noise. Further, the autoregressive…
Deep Neural Networks (DNNs) have been shown to be susceptible to memorization or overfitting in the presence of noisily-labelled data. For the problem of robust learning under such noisy data, several algorithms have been proposed. A…
In this paper, we introduce a new algorithm to deal with the stalling effect in the LMS algorithm used in adaptive filters. We modify the update rule of the tap weight vectors by adding noise, generated by a noise generator. The properties…
Modulo sampling is a promising technology to preserve amplitude information that exceeds the observable range of analog-to-digital converters during the digitization of analog signals. Since conventional methods typically reconstruct the…