Suvrit Sra (∯∐∇⊉I⊤ ∳⊋⟑)

Welcome to the geometric optimization webpage!

Geometric optimization refers broadly to the subject of optimizing a cost function subject to the parameters satisfying certain geometric properties. One familiar example is manifold optimization, where the geometric structure is that of a Riemannian or Finslerian manifold. Another key example is Conic geometric optimization, which includes geometric programming in its simplest (commutative) incarnation.

Software

Relevant Papers

On the matrix square root and geometric optimization 🍒 🍀
      Suvrit Sra
     (Version: Jul 2015)

@Article{sraRoot,
author = {Suvrit Sra},
title = {{On the matrix square root and geometric optimization}},
journal = {arXiv:1507.08366},
year = {2015},
note = {\it Preprint}
}

Riemannian dictionary learning and sparse coding for positive definite matrices 🍒
      Anoop Cherian, Suvrit Sra
     (Version of: July 2015)

@Article{cheSra15,
author = {Anoop Cherian and Suvrit Sra},
title = {{Riemannian Dictionary Learning and Sparse Coding for Positive Definite Matrices}},
journal = {arXiv:1507.02772},
mon     = {Jul.},
year = {2015},
}

Inference and mixture modelling with the Elliptical Gamma Distribution 🍒
      Reshad Hosseini, Suvrit Sra, Lucas Theis, Matthias Bethge
     (Submitted: Oct 2014; Revised: Jul. 2015)


@Article{hoSra14,
author = {Reshad Hosseini and Suvrit Sra and L. Theis and M. Bethge},
title = {Statistical inference with the Elliptical Gamma Distribution},
journal = {arXiv:1410.4812},
year = {2014},
note = {{\it Submitted}},
}

Positive Definite Matrices and the S-Divergence 🍀
      Suvrit Sra
     Proceedings of the American Mathematical Society (to appear)

@Article{srasdiv,
author = {Suvrit Sra},
title = {{Positive Definite Matrices and the S-Divergence}},
journal = {Proceedings of the American Mathematical Society},
year = {2015},
mon  = {Sep}
note = {arXiv:1110.1773v4}
}

Manifold optimization for mixture modeling 🍒
      Reshad Hosseini, Suvrit Sra
     Advances in Neural Information Processing Systems (NIPS 2015) (to appear)

@Article{hosSra15b,
author = {Reshad Hosseini and Suvrit Sra},
title = {{Manifold optimization for mixture modeling}},
journal = {arXiv:1506.07677},
year = {2015},
note = {\it Submitted}
}

Hlawka-Popoviciu inequalities on positive definite tensors 🍀
      Wolfgang Berndt, Suvrit Sra
      Linear Algebra and its Applications    (Accept: Feb 2015)

@Article{berSra15,
author = {Wolfgang Berndt and Suvrit Sra},
title = {{Hlawka-Popoviciu inequalities on positive definite tensors}},
journal = {Linear Algebra and its Applications},
volume = {486},
number = {1},
pages = {317--327},
year = {2015},
note = {arXiv:1411.0065}
}

Fixed-point algorithms for learning determinantal point processes 🍒
      Zelda Mariet, Suvrit Sra
      International Conf. on Machine Learning (ICML 2015);

@Inproceedings{marSra15,
author = {Zelda Mariet and Suvrit Sra},
title = {{Fixed-point algorithms for learning determinantal point processes}},
booktitle = {International Conference on Machine Learning (ICML)},
mon     = {Jun},
year = {2015},
}

Conic geometric optimisation on the manifold of positive definite matrices 🍀 🍒
      Suvrit Sra, Reshad Hosseini
      SIAM J. Optimization (SIOPT)   (Jan 2015)

@Article{sraHo15,
author = {Suvrit Sra and Reshad Hosseini},
title = {{Conic Geometric Optimization on the Manifold of Positive Definite Matrices}},
volume = {25},
number = {1},
pages  = {713--739},
journal = {SIAM J. Optimization (SIOPT)},
year = {2015},
note = {Accepted}
}

Data Modeling with the Elliptical Gamma Distribution 🍒
      Suvrit Sra, Reshad Hosseini, Lucas Theis, Matthias Bethge
      Artificial Intelligence and Statistics (AISTATS 2015)

@InProceedings{hoSra15,
author = {Reshad Hosseini and Suvrit Sra and L. Theis and M. Bethge},
title = {Statistical inference with the Elliptical Gamma Distribution},
booktitle = {Artificial Intelligence and Statistics (AISTATS)},
year = {2015},
volume = 18,
}

Riemannian sparse coding for positive definite matrices 🍒
      Anoop Cherian, Suvrit Sra
      European Conference on Computer Vision (ECCV)

@inproceedings{chSra14,
  title={Riemannian sparse coding for positive definite matrices},
  author={Anoop Cherian and Suvrit Sra},
  booktitle={ECCV 2014},
  pages={299--314},
  year={2014},
  publisher={Springer}
}

Geometric optimisation on positive definite matrices with application to elliptically contoured distributions 🍒
      Suvrit Sra and Reshad Hosseini
      Advances in Neural Information Processing Systems (NIPS)

@InProceedings{sraHo13,
  author =       {Suvrit Sra and Reshad Hosseini},
  title =        {{Geometric optimisation on positive definite matrices with application to elliptically contoured distributions}},
  booktitle =    {Advances in Neural Information Processing Systems (NIPS)},
  year =         2013,
  month =        dec,
}

Jensen-Bregman LogDet Divergence for Efficient Similarity Computations on Positive Definite Tensors🍒
      Anoop Cherian, Suvrit Sra, Arindam Banerjee, and Nikos Papanikolopoulos
      IEEE Tran. Pattern. Analy. Mach. Intell. (TPAMI) Dec. 2012;

@Article{chSra.pami,
  author =       {Anoop Cherian and Suvrit Sra and Arindam Banerjee and Nikolaos Papanikolopoulos},
  title =        {{Jensen-Bregman LogDet Divergence with Application to Efficient Similarity  Search for Covariance Matrices}},
  journal =      {IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI)},
  year =         2012,
  month =        {Dec.},
  note =         {14 pages},
}

A new metric on the manifold of kernel matrices with application to matrix geometric means 🍒🍀
      Suvrit Sra
      Advances of Neural Information Processing Systems (NIPS) 2012;

@inproceedings{sra12.nips,
  title={A new metric on the manifold of kernel matrices with application to matrix geometric means},
  author={Suvrit Sra},
  booktitle={Advances in Neural Information Processing Systems},
  pages={144--152},
  year={2012}
}

People

Reshad Hosseini (U. Tehran)
Suvrit Sra (MIT)

Students

Hongyi Zhang (MIT)

Collaborators

Anoop Cherian (INRIA)

Under construction