arXiv subjects

Teemu Härkönen

Publications and source records attributed to Teemu Härkönen.

8 recordsLinked to original sources

arXiv2026

Bayesian estimation of optical constants using mixtures of Gaussian process experts

We propose modeling absorption spectrum measurements as mixtures of Gaussian process experts. This enables us to construct a flexible statistical model for interpolating and extrapolating measurements, facilitating statistical integration of Kramers-Kronig relations to estimate the whole complex refractive index. Additionally, we statistically model the anchoring points used in subtractive Kramers-Kronig relations to account for possible measurement errors of the anchor point. In addition to flexible statistical modeling, the mixtures of Gaussian process formulation enables automatic selection of measurement points to use for extrapolation. We apply the method to experimental absorption spectrum measurements of gallium arsenide, potassium chloride, and transparent wood.

stat.AP↗

arXiv2026

Estimation of log-Gaussian gamma processes with iterated posterior linearization and Hamiltonian Monte Carlo

Stochastic processes are a flexible and widely used family of models for statistical modeling. While stochastic processes offer attractive properties such as inclusion of uncertainty properties, their inference is typically intractable, with the notable exception of Gaussian processes. Inference of models with non-Gaussian errors typically involves estimation of a high-dimensional latent variable. We propose two methods that use iterated posterior linearization followed by Hamiltonian Monte Carlo to sample the posterior distributions of such latent models with a particular focus on log-Gaussian gamma processes. The proposed methods are validated with two synthetic datasets generated from the log-Gaussian gamma process and a multiscale biocomposite stiffness model. In addition, we apply the methodology to an experimental Raman spectrum of argentopyrite.

stat.ME↗

arXiv2025

Mixtures of Gaussian Process Experts with SMC$^2$

Gaussian processes are a key component of many flexible statistical and machine learning models. However, they exhibit cubic computational complexity and high memory constraints due to the need of inverting and storing a full covariance matrix. To circumvent this, mixtures of Gaussian process experts have been considered where data points are assigned to independent experts, reducing the complexity by allowing inference based on smaller, local covariance matrices. Moreover, mixtures of Gaussian process experts substantially enrich the model's flexibility, allowing for behaviors such as non-stationarity, heteroscedasticity, and discontinuities. In this work, we construct a novel inference approach based on nested sequential Monte Carlo samplers to simultaneously infer both the gating network and Gaussian process expert parameters. This greatly improves inference compared to importance sampling, particularly in settings when a stationary Gaussian process is inappropriate, while still being thoroughly parallelizable.

stat.ML↗

arXiv2024

Statistical Estimation of Mean Lorentzian Line Width in Spectra by Gaussian Processes

We propose a statistical approach for estimating the mean line width in spectra comprising Lorentzian, Gaussian, or Voigt line shapes. Our approach uses Gaussian processes in two stages to jointly model a spectrum and its Fourier transform. We generate statistical samples for the mean line width by drawing realizations for the Fourier transform and its derivative using Markov chain Monte Carlo methods. In addition to being fully automated, our method enables well-calibrated uncertainty quantification of the mean line width estimate through Bayesian inference. We validate our method using a simulation study and apply it to an experimental Raman spectrum of $β$-carotene.

stat.AP↗

arXiv2023

Log-Gaussian Gamma Processes for Training Bayesian Neural Networks in Raman and CARS Spectroscopies

We propose an approach utilizing gamma-distributed random variables, coupled with log-Gaussian modeling, to generate synthetic datasets suitable for training neural networks. This addresses the challenge of limited real observations in various applications. We apply this methodology to both Raman and coherent anti-Stokes Raman scattering (CARS) spectra, using experimental spectra to estimate gamma process parameters. Parameter estimation is performed using Markov chain Monte Carlo methods, yielding a full Bayesian posterior distribution for the model which can be sampled for synthetic data generation. Additionally, we model the additive and multiplicative background functions for Raman and CARS with Gaussian processes. We train two Bayesian neural networks to estimate parameters of the gamma process which can then be used to estimate the underlying Raman spectrum and simultaneously provide uncertainty through the estimation of parameters of a probability distribution. We apply the trained Bayesian neural networks to experimental Raman spectra of phthalocyanine blue, aniline black, naphthol red, and red 264 pigments and also to experimental CARS spectra of adenosine phosphate, fructose, glucose, and sucrose. The results agree with deterministic point estimates for the underlying Raman and CARS spectral signatures.

stat.AP↗

arXiv2023

A Log-Gaussian Cox Process with Sequential Monte Carlo for Line Narrowing in Spectroscopy

We propose a statistical model for narrowing line shapes in spectroscopy that are well approximated as linear combinations of Lorentzian or Voigt functions. We introduce a log-Gaussian Cox process to represent the peak locations thereby providing uncertainty quantification for the line narrowing. Bayesian formulation of the method allows for robust and explicit inclusion of prior information as probability distributions for parameters of the model. Estimation of the signal and its parameters is performed using a sequential Monte Carlo algorithm followed by an optimization step to determine the peak locations. Our method is validated using a simulation study and applied to a mineralogical Raman spectrum.

stat.AP↗

arXiv2023

Interpolated inverse discrete wavelet transforms in additive and non-additive spectral background correction

We demonstrate the applicability of using interpolated inverse discrete wavelet transforms as a general tool for modeling additive or multiplicative background or error signals in spectra. Additionally, we propose an unsupervised way of estimating the optimal wavelet basis along with the model parameters. We apply the method to experimental Raman spectra of phthalocyanine blue, aniline black, naphthol red, pigment yellow 150, and pigment red 264 pigments to remove their additive background and to CARS spectra of adenosine phosphate, fructose, glucose, and sucrose to remove their multiplicative background signals.

physics.data-an↗

arXiv2020

Bayesian quantification for coherent anti-Stokes Raman scattering spectroscopy

We propose a Bayesian statistical model for analyzing coherent anti-Stokes Raman scattering (CARS) spectra. Our quantitative analysis includes statistical estimation of constituent line-shape parameters, underlying Raman signal, error-corrected CARS spectrum, and the measured CARS spectrum. As such, this work enables extensive uncertainty quantification in the context of CARS spectroscopy. Furthermore, we present an unsupervised method for improving spectral resolution of Raman-like spectra requiring little to no \textit{a priori} information. Finally, the recently-proposed wavelet prism method for correcting the experimental artefacts in CARS is enhanced by using interpolation techniques for wavelets. The method is validated using CARS spectra of adenosine mono-, di-, and triphosphate in water, as well as, equimolar aqueous solutions of D-fructose, D-glucose, and their disaccharide combination sucrose.

stat.AP↗