Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Tropical geometry of statistical models.

Lior Pachter1, Bernd Sturmfels

  • 1Department of Mathematics, University of California, Berkeley, CA 94720, USA.

Proceedings of the National Academy of Sciences of the United States of America
|November 10, 2004
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

TCIA Radiology Image Processing for AI and Radiomics.

medRxiv : the preprint server for health sciences·2026
Same author

Transcriptomic responses to endurance exercise training in rats.

BMC genomic data·2026
Same author

Systems genetics reveals ITIH5 as a key mediator of adipocyte-Endothelial crosstalk.

Molecular metabolism·2026
Same author

The Rayleigh Quotient and Contrastive Principal Component Analysis II.

bioRxiv : the preprint server for biology·2026
Same author

Hybrid crosses reveal a cell-type-specific landscape of mouse regulatory variation.

bioRxiv : the preprint server for biology·2026
Same author

The impact of package selection and versioning on single-cell RNA-seq analysis.

Cell systems·2026

This study introduces a geometric framework for graphical model inference, viewing models as algebraic varieties. It reveals how inference solutions depend on parameters using tropical algebraic geometry and Newton polytopes.

Area of Science:

  • Statistics
  • Algebraic Geometry
  • Machine Learning

Background:

  • Graphical models are widely used for representing complex systems.
  • Inference in these models often relies on algorithms like sum-product.
  • Understanding parameter dependencies in inference is crucial.

Purpose of the Study:

  • To develop a unified mathematical framework for inference in graphical models.
  • To investigate the dependence of inference solutions on model parameters.
  • To leverage geometric and tropical algebraic geometry perspectives.

Main Methods:

  • Representing graphical models as algebraic varieties.
  • Utilizing the sum-product algorithm for coordinate evaluation.
  • Applying tropical algebraic geometry and Newton polytopes.

Related Experiment Videos

Main Results:

  • A novel geometric viewpoint for graphical model inference.
  • Solutions to inference problems are shown to depend on model parameters.
  • The Newton polytope is identified as a key component.

Conclusions:

  • The proposed framework offers a unified approach to graphical model inference.
  • Tropical algebraic geometry provides powerful tools for analyzing parameter dependencies.
  • The methods are applicable to models like Hidden Markov Models.