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@INPROCEEDINGS{Bouss:1009719,
      author       = {Bouss, Peter and Nestler, Sandra and Fischer, Kirsten and
                      Merger, Claudia Lioba and Rene, Alexandre and Helias,
                      Moritz},
      title        = {{N}onlinear dimensionality reduction with normalizing flows
                      for analysis of electrophysiological recordings},
      reportid     = {FZJ-2023-02951},
      year         = {2023},
      abstract     = {Despite the large number of active neurons in the cortex,
                      the activity of neural populations for different brain
                      regions is expected to live on a low-dimensional manifold
                      [1]. Among the most common tools to estimate the mapping to
                      this manifold, along with its dimension, are variants of
                      principal component analysis. Although their success is
                      undisputed, these methods still have the disadvantage of
                      assuming that the data is well described by a Gaussian
                      distribution; any additional features such as skewness or
                      bimodality are neglected. Their performance when used as a
                      generative model is therefore often poor.To fully learn the
                      statistics of neural activity and to generate artificial
                      samples, we use Normalizing Flows (NFs) [2, 3]. These neural
                      networks learn a dimension-preserving estimator of the
                      probability distribution of the data (left part of Fig. 1).
                      They differ from generative adversarial networks (GANs) and
                      variational autoencoders (VAEs) by their simplicity – only
                      one bijective mapping is learned – and by their ability to
                      compute the likelihood exactly due to tractable Jacobians at
                      each building block.We adapt the training objective of NFs
                      to discriminate between relevant (in manifold) and noise
                      dimensions (out of manifold). To do this, we break the
                      original symmetry of the latent space by enforcing maximal
                      variance of the data to be encoded by as few dimensions as
                      possible (right part of Fig. 1) - the same idea underlying
                      PCA, a linear model, adapted here for nonlinear mappings.
                      This allows us to estimate the dimensionality of the neural
                      manifold and even to describe the underlying manifold
                      without discarding any information, a unique feature of
                      NFs.We prove the validity of our adaptation on artificial
                      datasets of varying complexity generated by a hidden
                      manifold model where the underlying dimensionality is known.
                      We illustrate the power of our approach by reconstructing
                      data using only a few latent NF dimensions. In this setting,
                      we show the advantage of such a nonlinear approach over
                      linear methods.Following this approach, we identify
                      manifolds in EEG recordings from a dataset featuring high
                      gamma activity. As described in [4], these recordings are
                      obtained from 128 electrodes during four movement tasks.
                      When plotted along the first principal components obtained
                      by PCA, these data show for some PCs a heavy-tailed
                      distribution. While linear models such as PCA are limited to
                      Gaussian statistics and hence suboptimal in such a case, the
                      nonlinearity of NFs enable to learn higher-order
                      correlations. Moreover, by flattening out the curvature in
                      latent space, we can better associate features with latent
                      dimensions. Especially, we have now a reduced set of latent
                      dimensions that explain most of the data
                      variance.References1. Gallego J, Perich M, Miller L, et al.
                      Neural manifolds for the control of movement. 2017. Neuron,
                      94(5), 978-984.2. Dinh L, Krueger D, Bengio Y. Nice:
                      Non-linear Independent Components Estimation. ICLR 2015.3.
                      Dinh L, Sohl-Dickstein J, Bengio S. Density estimation using
                      Real NVP. ICLR 2017.4. Schirrmeister R, Springenberg J,
                      Fiederer L, et al. Deep learning with convolutional neural
                      networks for EEG decoding and visualization. 2017. Hum Brain
                      Mapp, 38(11), 5391-5420.},
      month         = {Jul},
      date          = {2023-07-15},
      organization  = {32nd Annual Computational Neuroscience
                       Meeting, Leipzig (Germany), 15 Jul 2023
                       - 19 Jul 2023},
      subtyp        = {After Call},
      cin          = {INM-6 / IAS-6 / INM-10},
      cid          = {I:(DE-Juel1)INM-6-20090406 / I:(DE-Juel1)IAS-6-20130828 /
                      I:(DE-Juel1)INM-10-20170113},
      pnm          = {5231 - Neuroscientific Foundations (POF4-523) / 5232 -
                      Computational Principles (POF4-523) / 5234 - Emerging NC
                      Architectures (POF4-523) / GRK 2416 - GRK 2416:
                      MultiSenses-MultiScales: Neue Ansätze zur Aufklärung
                      neuronaler multisensorischer Integration (368482240) /
                      RenormalizedFlows - Transparent Deep Learning with
                      Renormalized Flows (BMBF-01IS19077A)},
      pid          = {G:(DE-HGF)POF4-5231 / G:(DE-HGF)POF4-5232 /
                      G:(DE-HGF)POF4-5234 / G:(GEPRIS)368482240 /
                      G:(DE-Juel-1)BMBF-01IS19077A},
      typ          = {PUB:(DE-HGF)24},
      doi          = {10.34734/FZJ-2023-02951},
      url          = {https://juser.fz-juelich.de/record/1009719},
}