Related papers: An iterative, dynamically stabilized method of dat…
In performative learning, the data distribution reacts to the deployed model - for example, because strategic users adapt their features to game it - which creates a more complex dynamic than in classical supervised learning. One should…
We address the problem of constructing varying-coefficient models based on basis expansions along with the technique of regularization. A crucial point in our modeling procedure is the selection of smoothing parameters in the regularization…
The analysis of surface wave dispersion curves is a way to infer the vertical distribution of shear-wave velocity. The range of applicability is extremely wide going, for example, from seismological studies to geotechnical characterizations…
Deep learning requires regularization mechanisms to reduce overfitting and improve generalization. We address this problem by a new regularization method based on distributional robust optimization. The key idea is to modify the…
We propose a novel method for modeling data by using structural models based on economic theory as regularizers for statistical models. We show that even if a structural model is misspecified, as long as it is informative about the…
Inverse problems arise in a variety of imaging applications including computed tomography, non-destructive testing, and remote sensing. The characteristic features of inverse problems are the non-uniqueness and instability of their…
Correlation functions in one-dimensional complex scalar field theory provide a toy model for phase fluctuations, sign problems, and signal-to-noise problems in lattice field theory. Phase unwrapping techniques from signal processing are…
We present a novel technique to parametrize experimental data, based on the construction of a probability measure in the space of functions, which retains the full experimental information on errors and correlations. This measure is…
We introduce a construction of multiscale tight frames on general domains. The frame elements are obtained by spectral filtering of the integral operator associated with a reproducing kernel. Our construction extends classical wavelets as…
This paper develops a large-scale inference approach for the regularization of stock return covariance matrices. The framework allows for the presence of heavy tails and multivariate GARCH-type effects of unknown form among the stock…
Accounting for inaccuracies in Monte Carlo simulations is a crucial step in any high energy physics analysis. It becomes especially important when training machine learning models, which can amplify simulation inaccuracies and introduce…
In order to understand the dynamical mechanism of the friction phenomena, we heavily rely on the numerical analysis using various methods: molecular dynamics, Langevin equation, lattice Boltzmann method, Monte Carlo, e.t.c.. We propose a…
The importance of regularization has been well established in image reconstruction -- which is the computational inversion of imaging forward model -- with applications including deconvolution for microscopy, tomographic reconstruction,…
This paper is concerned with the inverse problem of determining the shape of penetrable periodic scatterers from scattered field data. We propose a sampling method with a novel indicator function for solving this inverse problem. This…
Spectral methods are popular in detecting global structures in the given data that can be represented as a matrix. However when the data matrix is sparse or noisy, classic spectral methods usually fail to work, due to localization of…
The focus of this book is on the analysis of regularization methods for solving \emph{nonlinear inverse problems}. Specifically, we place a strong emphasis on techniques that incorporate supervised or unsupervised data derived from prior…
Sequential Monte Carlo methods have been a major breakthrough in the field of numerical signal processing for stochastic dynamical state-space systems with partial and noisy observations. However, these methods still present certain…
Techniques for approximately contracting tensor networks are limited in how efficiently they can make use of parallel computing resources. In this work we demonstrate and characterize a Monte Carlo approach to the tensor network…
A selection of unfolding methods commonly used in High Energy Physics is compared. The methods discussed here are: bin-by-bin correction factors, matrix inversion, template fit, Tikhonov regularisation and two examples of iterative methods.…
Conventional sampling and interpolation commonly rely on discrete measurements. In this paper, we develop a theoretical framework for extrapolation of signals in higher dimensions from knowledge of the continuous waveform on bounded…