Related papers: Linear minimum-variance approximants for noisy dat…
At its core, machine learning seeks to train models that reliably generalize beyond noisy observations; however, the theoretical vacuum in which state-of-the-art universal approximation theorems (UATs) operate isolates them from this goal,…
Subsampling is an efficient method to deal with massive data. In this paper, we investigate the optimal subsampling for linear quantile regression when the covariates are functions. The asymptotic distribution of the subsampling estimator…
High-dimensional data often lie in low-dimensional subspaces corresponding to different classes they belong to. Finding sparse representations of data points in a dictionary built using the collection of data helps to uncover…
This paper investigates system identification problems with Gaussian inputs and quantized observations under fixed thresholds. By reinterpreting the nonlinear effects induced by quantization as the product of the unknown parameter and an…
Linear Least Squares is a very well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required.…
We propose a penalized least-squares method to fit the linear regression model with fitted values that are invariant to invertible linear transformations of the design matrix. This invariance is important, for example, when practitioners…
We consider fitting a bivariate spline regression model to data using a weighted least-squares cost function, with weights that sum to one to form a discrete probability distribution. By applying the principle of maximum entropy, the weight…
It is well-known that the noise associated with the collection of an astronomical image by a CCD camera is, in large part, Poissonian. One would expect, therefore, that computational approaches that incorporate this a priori information…
We consider stochastic approximation for the least squares regression problem in the non-strongly convex setting. We present the first practical algorithm that achieves the optimal prediction error rates in terms of dependence on the noise…
Reconstructing noise-driven nonlinear networks from time series of output variables is a challenging problem, which turns to be very difficult when nonlinearity of dynamics, strong noise impacts and low measurement frequencies jointly…
Finding a sparse representation of a possibly noisy signal can be modeled as a variational minimization with l_q-sparsity constraints for q less than one. Especially for real-time, on-line, or iterative applications, in which problems of…
This work studies an experimental design problem where {the values of a predictor variable, denoted by $x$}, are to be determined with the goal of estimating a function $m(x)$, which is observed with noise. A linear model is fitted to…
We consider the problem of approximating an unknown function $u\in L^2(D,\rho)$ from its evaluations at given sampling points $x^1,\dots,x^n\in D$, where $D\subset \mathbb{R}^d$ is a general domain and $\rho$ is a probability measure. The…
Consider linear regression where the examples are generated by an unknown distribution on $R^d\times R$. Without any assumptions on the noise, the linear least squares solution for any i.i.d. sample will typically be biased w.r.t. the least…
We pose the approximation problem for scalar nonnegative input-output systems via impulse response convolutions of finite order, i.e. finite order moving averages, based on repeated observations of input/output signal pairs. The problem is…
With an ever-expanding ecosystem of noisy and intermediate-scale quantum devices, exploring their possible applications is a rapidly growing field of quantum information science. In this work, we demonstrate that variational quantum…
This paper proposes an estimation framework to assess the performance of sorting over perturbed/noisy data. In particular, the recovering accuracy is measured in terms of Minimum Mean Square Error (MMSE) between the values of the sorting…
This work develops a robust diffusion recursive least squares algorithm to mitigate the performance degradation often experienced in networks of agents in the presence of impulsive noise. This algorithm minimizes an exponentially weighted…
Presented is a new algorithm for estimating the frequency of a single-tone noisy signal using linear least squares (LLS). Frequency estimation is a nonlinear problem, and typically, methods such as Nonlinear Least Squares (NLS) (batch) or a…
In approximation of functions based on point values, least-squares methods provide more stability than interpolation, at the expense of increasing the sampling budget. We show that near-optimal approximation error can nevertheless be…