Related papers: Sinusoidal Frequency Estimation by Gradient Descen…

The estimation of the frequencies of multiple superimposed exponentials in noise is an important research problem due to its various applications from engineering to chemistry. In this paper, we propose an efficient and accurate algorithm…

Increasing effort is put into the development of methods for learning mechanistic models from data. This task entails not only the accurate estimation of parameters but also a suitable model structure. Recent work on the discovery of…

Traditional nonparametric estimation methods often lead to a slow convergence rate in large dimensions and require unrealistically enormous sizes of datasets for reliable conclusions. We develop an approach based on partial derivatives,…

Stochastic gradient descent (SGD) has been a go-to algorithm for nonconvex stochastic optimization problems arising in machine learning. Its theory however often requires a strong framework to guarantee convergence properties. We hereby…

In this paper, we investigate the theoretical properties of stochastic gradient descent (SGD) for statistical inference in the context of nonconvex optimization problems, which have been relatively unexplored compared to convex settings.…

Online decision making aims to learn the optimal decision rule by making personalized decisions and updating the decision rule recursively. It has become easier than before with the help of big data, but new challenges also come along.…

It seems that in the current age, computers, computation, and data have an increasingly important role to play in scientific research and discovery. This is reflected in part by the rise of machine learning and artificial intelligence,…

Line spectral estimation is the problem of recovering the frequencies and amplitudes of a mixture of a few sinusoids from equispaced samples. However, in a variety of signal processing problems arising in imaging, radar, and localization we…

A significantly low cost and tractable progressive learning approach is proposed and discussed for efficient spatiotemporal monitoring of a completely unknown, two dimensional correlated signal distribution in localized wireless sensor…

Stochastic gradient descent (SGD) is widely believed to perform implicit regularization when used to train deep neural networks, but the precise manner in which this occurs has thus far been elusive. We prove that SGD minimizes an average…

Robust online estimation of oscillation frequency belongs to classical problems of system identification and adaptive control. The given harmonic signal can be noisy and with varying amplitude at the same time, as in the case of damped…

We are interested in the development of surrogate models for uncertainty quantification and propagation in problems governed by stochastic PDEs using a deep convolutional encoder-decoder network in a similar fashion to approaches considered…

This paper studies the problem of parameter estimation in resonant, acoustic fluid-structure interaction problems over a wide frequency range. Problems with multiple resonances are known to be subjected to local minima, which represents a…

Gaussian processes are an important regression tool with excellent analytic properties which allow for direct integration of derivative observations. However, vanilla GP methods scale cubically in the amount of observations. In this work,…

In this paper we are concerned with fully automatic and locally adaptive estimation of functions in a "signal + noise"-model where the regression function may additionally be blurred by a linear operator, e.g. by a convolution. To this end,…

The analysis of signals created by a variety of instruments involves calculating the phase of a sinusoidal type signal. One widely used method to extract this information is through the use of Fourier transforms, but it is known that…

Recent works have shown that high probability metrics with stochastic gradient descent (SGD) exhibit informativeness and in some cases advantage over the commonly adopted mean-square error-based ones. In this work we provide a formal…

Generalization theory has been established for sparse deep neural networks under high-dimensional regime. Beyond generalization, parameter estimation is also important since it is crucial for variable selection and interpretability of deep…

Existing work has linked properties of a function's gradient to the difficulty of function approximation. Motivated by these insights, we study how gradient information can be leveraged to improve neural network's ability to approximate…

We consider a model applicable in many communication systems where the sum of n stochastic sinusoidal signals of the same frequency, but with random amplitudes as well as phase angles is present. The exact probability distribution of the…