Resources
Continuous optimization books
- Numerical Optimization (Springer Series in Operations
Research
and Financial Engineering) by Jorge Nocedal and Stephen Wright, 2006
- Convex Optimization by Stephen Boyd and Lieven
Vandenberghe, Cambridge, 2004
- Understanding and Using Linear Programming, J. Matousek and B. Gartner, Springer, 2007
- Introduction to Optimization, P. Pedregal, Springer, 2004
- Optimization for Machine Learning, Sra, Nowozin and Wright, MIT Press, 2011
- Foundations of Optimization, Guler, Springer, 2010
- Nonlinear Programming by Dimitri P. Bertsekas, Athena, 1999
- Practical Methods of Optimization by R. Fletcher,
Wiley, 2000
- Practical Optimization by Philip E. Gill, Walter
Murray, Margaret H. Wright, Academic, 1982
- The EM Algorithm and Extensions 2nd Edition
by Geoffrey McLachlan (Author), Thriyambakam Krishnan (Author)
Useful papers
- Sean Borman The Expectation Maximization Algorithm A short tutorial
- Yihua Chen and Maya Gupta EM Demystified: An Expectation-Maximization Tutorial
- Johathan Shewchuk, An
Introduction to the conjugate gradient method without the agonizing
pain, 1994
- F.A. Potra, S.J. Wright, "Interior point methods", Journal of Computational and Applied Mathematics
Volume 124, Issues 1-2, 1 December 2000, Pages 281-302 (find it here from a computer inside UIUC VPN)
- S. Shalev-Shwartz and Y. Singer, "Logarithmic regret algorithms for strongly convex repeated games", TR, Hebrew University, 2007
Striking behavior of Gradient Descent
- The Implicit Bias of Gradient Descent on Separable Data
D Soudry, E Hoffer, MS Nacson, S Gunasekar, N Srebro
- Implicit regularization in matrix factorization
S Gunasekar, BE Woodworth, S Bhojanapalli, B Neyshabur, N Srebro
- Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview
Yuejie Chi, Yue M. Lu, Yuxin Chen
- Implicit Regularization in Nonconvex Statistical Estimation: Gradient Descent Converges Linearly for Phase Retrieval, Matrix Completion and Blind Deconvolution
Cong Ma, Kaizheng Wang, Yuejie Chi, Yuxin Chen
Graphical Models
-
Variational inference in graphical models: The view from the marginal polytope
Martin J .Wainwright, Michael I. Jordan
Appeared in:
Allerton Conference on Control, Communication and Computing
October 1--3, 2003 Quick and to the point; takes some work
- An introduction to LP relaxations for MAP inference slides by Adrial Weller, 2017
- Graphical Models, Exponential Families, and Variational Inference MJ Wainwright and MIJordan, Foundations and trends in Machine Learning, 2008 The mother lode; everything is here, done rigorously, but quite hard work.
-
Understanding Belief Propagation and its Generalizations
Jonathan S. Yedidia, William T. Freeman, and Yair Weiss, IJCAI 2001 another mother lode, for bp and loopy bp
Decomposition
- S. Boyd, L. Xiao, A. Mutapcic, J. Mattingley, Notes on Decomposition methods, 2008
- Alexander M. Rush and Michael Collins. A tutorial on Lagrangian relaxation and dual decomposition for NLP.
In Journal of Artificial Intelligence Research, 2012
- Introduction to Dual Decomposition for Inference David Sontag, Amir Globerson and Tommi Jaakkola
Book chapter in Optimization for Machine Learning, editors S. Sra, S. Nowozin, and S. J. Wright: MIT Press, 2011 .
Alternating Direction Method of Multipliers
- Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein
Foundations and Trends in Machine Learning, 3(1):1–122, 2011.
- André F. T. Martins, Mário A. T. Figueiredo, Pedro M. Q. Aguiar, Noah A. Smith, and Eric P. Xing.
"An Augmented Lagrangian Approach to Constrained MAP Inference."
International Conference on Machine Learning (ICML'11), Bellevue, Washington, USA, June 2011.
- J. Duchi, S. Shalev-Shwartz, Y. Singer, T. Chandra, "Efficient projections onto the l1-ball for learning in high dimensions", ICML 08
- S. Shalev-Shwartz, Y. Singer, "Efficient Learning of Label Ranking by Soft Projections onto Polyhedra", JMLR, 2006
- André F. T. Martins, Noah A. Smith, Mário A. T. Figueiredo, Pedro M. Q. Aguiar.
"Dual Decomposition With Many Overlapping Components."
Empirical Methods in Natural Language Processing (EMNLP'11), Edinburgh, UK, July 2011.
- Efficient projections onto the l 1-ball for learning in high dimensions, John Duchi, Shai Shalev-Shwartz, Yoram Singer, Tushar Chandra, Proceedings of the 25th international conference on Machine learning, 2008
L1 Logistic Regression and regularization paths
- J. Mairal, B. Yu. Complexity Analysis of the Lasso Regularization Path. International Conference on Machine Learning, 2012
- Osborne, M., Presnell, B., and Turlach, B. A new approach to variable selection in least squares prob- lems. IMA J. Numer. Anal., 20(3):389–403, 2000
- Bradley Efron, Trevor Hastie, Iain Johnstone and Robert Tibshirani, Least Angle Regression Annals of Statistics (with discussion) (2004) 32(2), 407-499.
- Trevor Hastie, Saharon Rosset, Rob Tibshirani and Ji Zhu, The Entire Regularization Path for the Support Vector Machine, NIPS 2004
Gradient Boost
- Jerome H. Friedman, Greedy Function Approximation: A Gradient Boosting Machine , The Annals of Statistics, Vol. 29, No. 5 (Oct., 2001), pp. 1189-1232
Neat MRF algorithm cheat-sheet
- Which Energy Minimization for my MRF/CRF? A Cheat-Sheet, Bogdan Alexe, Thomas Deselaers, Marcin Eicher, Vittorio Ferrari, Peter Gehler, Alain Lehmann, Stefano Pellegrini, Alessandro Prest
Submodular function applications
- Submodular function tutorial slides (Krause, Guestrin, 2008)
- Batch Mode Active Learning and Its Application to Medical Image Classification, Hoi, Jin, Zhu and Lyu, ICML 08
Bilevel Optimization notes
- An Introduction to Bilevel Programming (Fricke, ND)
- Classfication model selection via bilevel programming, Kunapuli, Bennet, Hu and Pang, Optimization Methods and Software, 2008
Papers
Continuous optimization applications
Iterative scaling and the
like
- The improved
iterative scaling algorithm: A gentle introduction
A Berger - Unpublished manuscript, 1997
- Iain Bancarz, M. Osborne, Improved iterative scaling can
yield multiple globally optimal models with radically differing
performance levels, Proceedings of the 19th international
conference on Computational linguistics, 1 - 7, 2002
- Robert Malouf, A
comparison of algorithms for maximum entropy parameter estimation,
proceeding of the 6th conference on Natural language learning - Volume
20, 1 - 7, 2002
- F. Sha and F. Pereira, Shallow
parsing with conditional random fields, Proc HLT-NAACL, Main
papers, pp 134-141, 2003
- Hanna Wallach, Efficient
Training of Conditional Random Fields, University of
Edinburgh, 2002.
Boosting
- Jerome H. Friedman, Greedy Function Approximation: A Gradient Boosting Machine , The Annals of Statistics, Vol. 29, No. 5 (Oct., 2001), pp. 1189-1232
Bundle adjustment
- Bill Triggs, Philip F. McLauchlan,
Richard I. Hartley and Andrew W. Fitzgibbon, Bundle Adjustment -- A Modern
Synthesis,
Vision Algorithms: Theory and Practice: International Workshop on
Vision Algorithms, Corfu, Greece, September 1999, pp153-177,
Matrix factorization
- Buchanan, A.M.; Fitzgibbon, A.W., Damped Newton algorithms for
matrix factorization with missing data, Computer Vision and
Pattern Recognition, 2005, 316 - 322
- Fast Maximum Margin Matrix Factorization for Collaborative Prediction, Jason D. M. Rennie, Nati Srebro, in Luc De Raedt, Stefan Wrobel (Eds.) Proceedings of the 22nd International Machine Learning Conference, ACM Press, 2005
- Scene Discovery by Matrix Factorization, N.Loeff, A. Farhadi, ECCV 2008
- T. Finley and T.Joachims, Supervised clustering with support vector machines, Proceedings of the 22nd international conference on Machine learning, 217 - 224, 2005
Registration
- A.W. Fitzgibbon, Robust
registration of 2D and 3D point sets, Image and Vision
Computing, Volume 21, Issues 13-14, 1 December 2003, Pages 1145-1153
SVM's
- C.J.C. Burges, ``A
Tutorial on Support Vector Machines for Pattern
Recognition, '' Data Mining and Knowledge Discovery, 2,
121-167 (1998)
- Sequential minimal
optimization: A fast algorithm for training support vector machines J Platt - Advances in Kernel Methods-Support Vector Learning, 1999
- S. S. Keerthi, S. K. Shevade,C. Bhattacharyya, K. R. K.
Murthy, Improvements to
Platt's SMO Algorithm for SVM Classifier Design, Neural Computation. 2001;13:637-649, 2001
- Dynamic visual category learning, T.Yeh and T. Darrell, CVPR, 2008
- K. Zhang, I.W. Tsang, J.T. Kwok, Maximum margin clustering made practical, Proceedings of the 24th international conference on Machine learning, 1119 - 1126, 2007
- Pegasos: Primal Estimated sub-GrAdient SOlver for SVM, S. Shalev-Shwartz, Y. Singer, N. Srebro, ICML 2008
Structure learning
- I. Tsochantaridis, T. Joachims, T. Hofmann, and Y. Altun, Large Margin Methods for Structured and Interdependent Output Variables, Journal of Machine Learning Research (JMLR), 6(Sep):1453-1484, 2005.
- Subgradient Methods for Maximum Margin Structured Learning Nathan D. Ratliff
J. Andrew Bagnell
Martin A. Zinkevich
- Learning to localize objects with structured output regression, Blaschko and Lamport, ECCV 2008
Efficient use of subgradients
- Smooth minimization of non-smooth functions (Nesterov; Math. Prog 2005).
Discrete Optimization
Resources
- M. Goemans and D.P Williamson, Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming, Journal of the ACM, Volume 42 , Issue 6, 1115 - 1145, 1995
- L.Vandenberghe and S.Boyd, Semidefinite programming, SIAM review, 38, 1, 49-95, 1996
- A Tutorial on Dual Decomposition and Lagrangian Relaxation for Inference in Natural Language Processing, A.M. Rush and M. Collins, JMLR,
Applications
Matching
- Y Rubner, C Tomasi, LJ Guibas, The Earth Mover's Distance as a Metric for Image Retrieval, International Journal of Computer Vision, 2000
- Grauman, K. Darrell, T., Fast contour matching using approximate earth mover's distance. CVPR 2004
- E Levina, P Bickel, The earth mover’s distance is the Mallows distance: Some insights from statistics, Proc. ICCV, 2001
- S Belongie, J Malik, J Puzicha, Matching shapes, Proc. of ICCV, 2001
- Maciel, J.; Costeira, J.P.; A global solution to sparse correspondence problems, Pattern Analysis and Machine Intelligence, IEEE Transactions on, Volume 25, Issue 2, Feb. 2003 Page(s):187 - 19
- A.Berg, T. Berg and J. Malik, Shape matching and object recognition using low distortion correspondence, CVPR, 2005
Markov Random Fields
- Boykov, Y. and O. Veksler, Graph cuts in vision and graphics: theories and applications, Handbook of Math. Models of Computer Vision, Paragios, Chen, Faugeras (eds)
- Boykov, Y. Veksler, O. Zabih, R. Fast approximate energy minimization via graph cuts, PAMI, 23, 11, 1222-1239, 2001
- Boykov, Y. Veksler, O. Zabih, R., Markov random fields with efficient approximations, CVPR, 1998
- P. Kohli and M. Pawan Kumar and P.H.S. Torr, P^3 and Beyond: Solving Energies with Higher Order Cliques, CVPR 2007
- C.Olsson A.P. Eriksson and F. Kahl, Solving Large Scale Binary Quadratic Problems: Spectral Methods vs Semidefinite Programming, CVPR 2007
- Accelerated dual decomposition for MAP inference (Jojic, Gould, Koller; ICML 2010).
- MRF Energy Minimization and Beyond via Dual Decomposition (Komodakis, Paragios; PAMI 2010)
- A Comparative Study of Energy Minimization Methods for Markov Random Fields, R. Szeliski, R. Zabih, D. Scharstein, O. Veksler, V. Kolmogorov, A. Agarwala, M.Tappen, and C. Rother, ECCV 2006
- Minimizing Nonsubmodular Functions with Graph Cuts—A Review, V. Kolmogorov and C. Rother, PAMI 2007
- Convergent Tree-Reweighted Message Passing for Energy Minimization, V. Kolmogorov, PAMI 2006
- Approximate labeling via graph cuts based on linear programming, N Komodakis… - Pattern Analysis and Machine Intelligence, 2007
- Dynamic graph cuts for efficient inference in markov random fields, P Kohli… - Pattern Analysis and Machine Intelligence,
2007
Submodular functions
- Kang, Jin, Sukthankar, Correlated label propagation with application to multi-label learning, CVPR 2006