David Frich Hansen

PhD Student at DTU Compute, section for Cognitive systems.
I research Bayesian modeling of spectral data (mostly Raman spectra) and Bayesian inference methods.


I have a M.Sc. in Mathematical Modeling and Computing from DTU Compute, where I specialized in approximate Bayesian inference and Machine Learning in general. My thesis was on stochastic gradient Markov chain Monte Carlo, where I used SGMCMC for Bayesian learning in neural networks for robust uncertainty estimation on predictions (download thesis).
My résumé can be downloaded here .
Besides, I enjoy bicycling (both recreationally, as a means of transportation and as a professional sport, which I follow intensely), skiing and playing board games!

PhD Project

My PhD project is titled "Towards real time Raman molecular imaging of living organisms" and is revolved around performing rapid inference on Raman 'videos' such that biological or chemical processes such as fermentation or drug delivery can be monitored in real time in a non-destructive, non-invasive manner. To achieve this, I am developing an end-to-end statistical procedure to map the Raman map inputs to desired outputs, such as analyte concentration. This requires a probabilistic model for extracting features of relevance from the Raman maps (ie. peak shapes, peak locations etc.), baseline (ie. background signal) and calibration (ie. modeling the properties of the spectrometer). We are also investigating amortizing the inference procedure for faster future inferences. Thank you to Mikkel N. Schmidt for providing the graphic to the left.
A popular scientific summary of the project is available here.

Research interests

For a list of publications, see this page.

Bayesian modeling of Raman spectroscopy

Raman spectroscopy is a powerful non-invasive method of identifying and characterizing molecules of interest. It involves illuminating a sample with a laser and observing the wavelengths of the scattered light. The difference in wavelengths of the laser light and the scattered light can reveal important properties of the molecules, as the energy (and thus the wavelength) is dependent on the molecular structure of the sample at hand. We model these spectra in a probabilistic way to obtain information about the sample, while capturing uncertainty in an elegant way.

Bayesian inference

Bayesian statistics is a popular approach to modeling complex phenomena due to its' high flexibility and elegant uncertainty estimation. Inference in Bayesian models, however, is computationally demanding and (often) analytically intractable. Thus approximate inference procedures such as Markov chain Monte Carlo (MCMC) or Variational Bayesian (VB) are needed. I study mainly MCMC for big-data settings, where we simulate a dynamical system to achieve proposals for new samples of the Bayesian posterior distribution. These samples can be used to estimate global properties of the posterior distribution. Specifically, I study stochastic gradient MCMC, where stochastic estimates are used instead of true gradients, which speeds up computations when a lot of data is available.

Non-stationary Gaussian processes

Gaussian processes are an extremely flexible class of stochastic processes, used in almost all areas of statistical science. I have studied GP's with non-stationary covariance functions for source separation where we are interested in separating some signal of interest from measurement noise and background signals. The non-stationarity of the GP's are interesting especially when the noise is correlated over time. I have also investigated learning a suitable covariance function from data with mixed results.

Amortized inference

Amortizing inference is the procedure of using a statistical model (often a neural network - specifically variational autoencoders) to mimic a more complicated inference procedure. I study this in the context of spectral data (Raman spectroscopy), as parameter estimation in Bayesian models of Raman spectroscopy is computationally intensive. The general idea is to train a neural network at the same time as the parameters of a specific statistical model of the phenomenon is estimated. The neural network then learns a (fast to compute) foward map of the inputs directy to the output of interest (in the context of Raman spectroscopy, this could be analyte concentrations), thus eliminating the need to re-estimate parameters when new data is presented.

  • Address

    Technical University of Denmark, Dept. of Applied Mathematics and Computer Science (DTU Compute)
    Richard Petersens Plads 321, room 112
    2800 Kongens Lyngby
  • Email

  • Phone

    (+45) 50 57 56 60
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