Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userUnfolding with Gaussian Processes
94
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
A method to perform unfolding with Gaussian processes (GPs) is presented. Using Bayesian regression, we define an estimator for the underlying truth distribution as the mode of the posterior. We show that in the case where the bin contents are distributed approximately according to a Gaussian, this estimator is equivalent to the mean function of a GP conditioned on the maximum likelihood estimator. Regularisation is introduced via the kernel function of the GP, which has a natural interpretation as the covariance of the underlying distribution. This novel approach allows for the regularisation to be informed by prior knowledge of the underlying distribution, and for it to be varied along the spectrum. In addition, the full statistical covariance matrix for the estimator is obtained as part of the result. The method is applied to two examples: a double-peaked bimodal distribution and a falling spectrum.
rate research
Read More
Autonomous experiments are excellent tools to increase the efficiency of material discovery. Indeed, AI and ML methods can help optimizing valuable experimental resources as, for example, beam time in neutron scattering experiments, in addition to scientists knowledge and experience. Active learning methods form a particular class of techniques that acquire knowledge on a specific quantity of interest by autonomous decisions on what or where to investigate next based on previous measurements. For instance, Gaussian Process Regression (GPR) is a well-known technique that can be exploited to accomplish active learning tasks for scattering experiments as was recently demonstrated. Gaussian processes are not only capable to approximate functions by their posterior mean function, but can also quantify uncertainty about the approximation itself. Hence, if we perform function evaluations at locations of highest uncertainty, the function can be optimally learned in an iterative manner. We suggest the use of log-Gaussian processes, being a natural approach to successfully conduct autonomous neutron scattering experiments in general and TAS experiments with the instrument PANDA at MLZ in particular.
In this paper we describe RooFitUnfold, an extension of the RooFit statistical software package to treat unfolding problems, and which includes most of the unfolding methods that commonly used in particle physics. The package provides a common interface to these algorithms as well as common uniform methods to evaluate their performance in terms of bias, variance and coverage. In this paper we exploit this common interface of RooFitUnfold to compare the performance of unfolding with the Richardson-Lucy, Iterative Dynamically Stabilized, Tikhonov, Gaussian Process, Bin-by-bin and inversion methods on several example problems.
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. Two procedures to choose the strength of the regularisation are tested, namely the L-curve scan and a scan of global correlation coefficients. The advantages and disadvantages of the unfolding methods and choices of the regularisation strength are discussed using a toy example.
PyUnfold is a Python package for incorporating imperfections of the measurement process into a data analysis pipeline. In an ideal world, we would have access to the perfect detector: an apparatus that makes no error in measuring a desired quantity. However, in real life, detectors have finite resolutions, characteristic biases that cannot be eliminated, less than full detection efficiencies, and statistical and systematic uncertainties. By building a matrix that encodes a detectors smearing of the desired true quantity into the measured observable(s), a deconvolution can be performed that provides an estimate of the true variable. This deconvolution process is known as unfolding. The unfolding method implemented in PyUnfold accomplishes this deconvolution via an iterative procedure, providing results based on physical expectations of the desired quantity. Furthermore, tedious book-keeping for both statistical and systematic errors produces precise final uncertainty estimates.
Unfolding is a well-established tool in particle physics. However, a naive application of the standard regularization techniques to unfold the momentum spectrum of protons ejected in the process of negative muon nuclear capture led to a result exhibiting unphysical artifacts. A finite data sample limited the range in which unfolding can be performed, thus introducing a cutoff. A sharply falling true distribution led to low data statistics near the cutoff, which exacerbated the regularization bias and produced an unphysical spike in the resulting spectrum. An improved approach has been developed to address these issues and is illustrated using a toy model. The approach uses full Poisson likelihood of data, and produces a continuous, physically plausible, unfolded distribution. The new technique has a broad applicability since spectra with similar features, such as sharply falling spectra, are common.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
