Statistical Learning Theory and Applications
Covers foundations and recent advances in statistical machine learning theory, with the dual goals of providing students with the theoretical knowledge to use machine learning and preparing more advanced students to contribute to progress in the field. The content is roughly divided into three parts. The first part is about classical regularization, margin, stochastic gradient methods, overparametrization, implicit regularization, and stability. The second part is about deep networks: approximation and optimization theory plus roots of generalization. The third part is about the connections between learning theory and the brain. Occasional talks by leading researchers on advanced research topics. Emphasis on current research topics.
Spring 2006
Topics
- The Course at a Glance
- The Learning Problem in Perspective
- Reproducing Kernel Hilbert Spaces
- Regression and Least-Squares Classification
- Support Vector Machines for Classification
- Manifold Regularization
- Unsupervised Learning Techniques
- Multiclass
- Ranking
- Boosting and Bagging
- Computer Vision
- Online Learning
- Loose Ends
- Generalization Bounds
- Stability of Tikhonov Regularization
- Uniform Convergence Over Function Classes
- Uniform Convergence for Classification
- Neuroscience
- Symmetrization
- Fenchel Duality
- Speech / Audio
- Active Learning
- Morphable Models for Video
- Bioinformatics
- Project Presentations
- Project Presentations (cont.)
- Math Camp 1: Functional Analysis
- Math Camp 2: Probability Theory
Readings
- There is no textbook for this course. All the required information will be presented in the slides associated with each class. The books/papers listed below are useful general reference reading, especially from the theoretical viewpoint. A list of suggested readings is also provided for each class separately.
- Vapnik, V. The Nature of Statistical Learning Theory . New York, NY: John Wiley & Sons, 1995. ISBN: 0387987800.
- ———. Statistical Learning Theory . New York, NY: John Wiley & Sons, 1998. ISBN: 0471030031.
- Devroye, L., L. Gyorfi, and G. Lugosi. A Probabilistic Theory of Pattern Recognition . New York, NY: Springer, 1997. ISBN: 0387946187.
- Cristianini, N., and J. Shawe-Taylor. Introduction To Support Vector Machines . Cambridge, UK: Cambridge University Press, 2000. ISBN: 0521780195.
- SES #: 2 · TOPICS: The Learning Problem in Perspective · READINGS: Cucker, F., and S. Smale. “On The Mathematical Foundations of Learning.” Bulletin of the American Mathematical Society 39, no. 1 (2002): 1-49.
- Evgeniou, P., and T. Poggio. “Regularization Networks and Support Vector Machines.” Advances in Computational Mathematics 13, no. 1 (2000): 1-50.
- SES #: 3 · TOPICS: Reproducing Kernel Hilbert Spaces · READINGS: Aronszajn, N. “Theory of Reproducing Kernels.” Transactions of the American Mathematical Society 68, no. 3 (1950): 337-404.
- Cucker, F., and S. Smale. “On The Mathematical Foundations of Learning.” Bulletin of the American Mathematical Society 39, no. 1 (2002): 1-49.
- Girosi, F. “An Equivalence Between Sparse Approximation and Support Vector Machines.” Neural Computation 10, no. 6 (1998): 1455-1480.
- Wahba, G. “Spline Models for Observational Data Series in Applied Mathematics.” SIAM 59 (1990). Philadelphia, PA: CBMS-NSF Regional Conference Series in Applied Mathematics.
- SES #: 4 · TOPICS: Regression and Least-Squares Classification · READINGS: Rifkin, R. “Everything Old Is New Again: A Fresh Look at Historical Approaches in Machine Learning.” Ph.D. Thesis, Massachusetts Institute of Technology, 2002.
- SES #: 5 · TOPICS: Support Vector Machines for Classification · READINGS: Rifkin, R. “Everything Old Is New Again: A Fresh Look at Historical Approaches in Machine Learning.” Ph.D. Thesis, Massachusetts Institute of Technology, 2002.
- SES #: 6 · TOPICS: Manifold Regularization · READINGS: Belkin, M., and P. Niyogi. “Semi-supervised Learning on Riemannian Manifolds.” Machine Learning 56, no. 1-3 (2004): 209-239.
- Belkin, M., P. Niyogi, and V. Sindhwani. “On Manifold Regularization.” In Proceedings of the Tenth International Workshop on Artificial Intelligence and Statistics . Barbados: University College London, 2005.
- SES #: 7 · TOPICS: Unsupervised Learning Techniques · READINGS: Hastie, T., R. Tibshirani, and J. Friedman. The Elements of Statistical Learning: Data Mining, Inference, and Prediction . New York, NY: Springer-Verlag, 2001. ISBN: 0387952845.
- Tenenbaum, J., Vin de Silva, and J. Langford. “A Global Geometric Framework for Nonlinear Dimensionality Reduction.” Science 290, no. 5500 (2000): 2319-2323.
- Donoho, G. “Hessian Eigenmaps: Locally Linear Embedding Techniques for High-dimensional Data.” PNAS 100, no. 10 (2003): 5591-5596.
- Belkin, M., and P. Niyogi. “Laplacian Eigenmaps for Dimensionality Reduction and Data Representation.” Neural Computation 15, no. 6 (2003): 1373-1396.
- SES #: 8 · TOPICS: Multiclass · READINGS: Rifkin, R., and A. Klautau. “In Defense of One-Vs-All Classification.” Journal of Machine Learning Research 5 (2004): 101-141.
- SES #: 9 · TOPICS: Ranking · READINGS: Caruana, R., and T. Joachims, eds. Proceedings of NIPS 2002 Workshop: Beyond Classification and Regression: Learning Rankings, Preferences, Equality Predicates, and Other Structures . Cornell, NY: Cornell University, 2002.
- Saul, L., Y. Weiss, and L. Bottou, eds. Proceedings of the NIPS 2005 Workshop: Learning to Rank . Whistler, BC: Cornell University, 2005.
- SES #: 10 · TOPICS: Boosting and Bagging · READINGS: Freund, Y., and R. E. Schapire. “A Short Introduction to Boosting.” Journal of Japanese Society for Artificial Intelligence 14, no. 5 (1999): 771-780.
- SES #: 12 · TOPICS: Online Learning · READINGS: Duda, R., P. Hart, and D. Stork. Pattern Classification . New York, NY: John Wiley & Sons, 2001. ISBN: 9814126020.
- Smale, S., and Y. Yao. “Online Learning Algorithms.” Foundations of Computational Mathematics 6, no. 2 (2006): 145-170.
- Intro to Stability Vapnik, V. Statistical Learning Theory . New York, NY: John Wiley & Sons, 1998. ISBN: 0471030031.
- Bousquet, O., and A. Elisseeff. “Stability and Generalization.” Journal of Machine Learning Research 2 (2002): 499-527.
- SES #: 15 · TOPICS: Stability of Tikhonov Regularization · READINGS: Bousquet, O., and A. Elisseeff. “Stability and Generalization.” Journal of Machine Learning Research 2 (2002): 499-527.
- SES #: 16 · TOPICS: Uniform Convergence Over Function Classes · READINGS: Vapnik, V. The Nature of Statistical Learning Theory . New York, NY: John Wiley & Sons, 1995. ISBN: 0387987800.
- Zhou, Ding-Xuan. “Capacity of Reproducing Kernel Spaces in Learning Theory.” IEEE Trans on Info Theory 49, no. 7 (2003): 1743-1752.
- Vapnik, V., and A. Chervonenkis. “Necessary and Sufficient Conditions for the Uniform Convergence of the Means to Their Expectations.” Probability Theory and Applications 26 (1981): 532-553.
- VC-dimension Alon, N., S. Ben-David, N. Cesa-Bianchi, and D. Haussler. “Scale-sensitive Dimensions, Uniform Convergence, and Learnability.” Journal of the ACM 44, no. 4 (1997): 615-631.
- SES #: 18 · TOPICS: Neuroscience · READINGS: Serre, T. “Learning a Dictionary of Shape-components in Visual Cortex: Comparison with Neurons, Humans and Machines.” PhD Thesis, Massachusetts Institute of Technology, 2006.
- Serre, T., L. Wolf, and T. Poggio. “Object Recognition with Features Inspired by Visual Cortex.” In Proceedings of 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR 2005) . San Diego, CA: IEEE Computer Society Press, 2005.
- Serre, T., M. Kouh, C. Cadieu, U. Knoblich, G. Kreiman, and T. Poggio. “A Theory of Object Recognition: Computations and Circuits in the Feedforward Path of the Ventral Stream in Primate Visual Cortex.” CBCL Paper #259/AI Memo #2005-036. Cambridge, MA: Massachusetts Institute of Technology, 2005.
Spring 2003
Topics
- The Course at a Glance
- The Learning Problem in Perspective
- Regularization and Reproducing Kernel Hilbert Spaces
- Regression and Least-Squares Classification
- Support Vector Machines for Classification
- Generalization Bounds, Intro to Stability
- Stability of Tikhonov Regularization
- Consistency and Uniform Convergence over Function Classes
- Necessary and Sufficient Conditions for Uniform Convergence
- Bagging and Boosting
- Computer Vision, Object Detection
- Loose Ends
- Approximation Theory
- RKHS, Mercer Thm, Unbounded Domains, Frames and Wavelets
- Bioinformatics
- Text
- Regularization Networks
- Morphable Models for Video
- Leave-One-Out Approximations
- Bayesian Interpretations
- Multiclass Classification
- Stability and Glivenko-Cantelli Classes
- Symmetrization, Rademacher Averages
- Project Presentations
- Lagrange Multipliers/Convex Optimization
- Functional Analysis
- SVM Rules of Thumb
Readings
- Cristianini, N., and J. Shawe-Taylor. Introduction To Support Vector Machines . Cambridge, 2000.
- Cucker, F., and S. Smale. “On The Mathematical Foundations of Learning.” Bulletin of the American Mathematical Society. 2002.
- Devroye, L., L. Gyorfi, and G. Lugosi. A Probabilistic Theory of Pattern Recognition . Springer, 1997.
- Evgeniou, T., M. Pontil, and T. Poggio. “Regularization Networks and Support Vector Machines.” Advances in Computational Mathematics . 2000.
- Poggio, T., and S. Smale. “The Mathematics of Learning: Dealing with Data.” Notices of the AMS. 2003.
- Vapnik, V. N. The Nature of Statistical Learning Theory . Springer, 1995.
- ———. Statistical Learning Theory . Wiley, 1998.
Prerequisites & course information
Same subject as 6.7910J Prereq: 6.3700 , 6.7900 , 18.06 , or permission of instructor G (Fall) 3-0-9 units
Sources
- Course catalogue ↗2026–2027
- MIT OpenCourseWare ↗Spring 2006
- MIT OCW calendar ↗
- MIT OCW readings ↗
- MIT OCW syllabus ↗
- MIT OpenCourseWare ↗Spring 2003
- MIT OCW readings ↗
- MIT OCW calendar ↗
- MIT OCW syllabus ↗
- Historical MIT OpenCourseWare offering. Named reading entries and schedule topics are automatically extracted from the linked source pages.
- Historical MIT OpenCourseWare offering. Named reading entries and schedule topics are automatically extracted from the linked source pages.