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Discrete Sparse Coding.

Georgios Exarchakis1, Jörg Lücke2

  • 1Machine Learning Lab, Cluster of Excellence Hearing4all and Department for Medical Physics and Acoustics, Carl-von-Ossietzky University Oldenburg, 26111 Oldenburg, Germany georgios.exarchakis@uol.de.

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This study introduces discrete sparse coding, a novel approach for analyzing data with discrete latent variables. The method efficiently learns data structures and offers new insights into complex datasets.

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Area of Science:

  • Machine Learning
  • Computational Neuroscience
  • Signal Processing

Background:

  • Sparse coding typically uses continuous latent variables, largely overlooking discrete alternatives.
  • Discrete latent spaces offer a powerful framework for modeling data with inherent categorical structures.

Purpose of the Study:

  • To investigate sparse coding with discrete prior distributions instead of continuous ones.
  • To develop and evaluate an efficient training method for probabilistic generative models with discrete latents.
  • To demonstrate the applicability of discrete sparse coding across diverse data types.

Main Methods:

  • Developed a sparse coding model utilizing discrete prior distributions.
  • Employed a modified truncated expectation-maximization (expectation truncation) algorithm for efficient parameter training.
  • Learned prior probabilities directly from data, avoiding assumptions on functional forms.

Main Results:

  • Successfully recovered generating parameters from artificial data.
  • Demonstrated effective component extraction from natural image patches.
  • Presented a novel analysis method for neural spiking data using discretization.
  • Applied the algorithm to encode human speech audio waveforms.

Conclusions:

  • Discrete sparse coding algorithms are efficient and scalable for realistic datasets.
  • The approach provides novel statistical measures for data structure analysis.
  • This work opens new avenues for analyzing data generated by discrete causes.