9.520/6.860: Statistical Learning Theory and Applications, Fall 2016

Units: 3-0-9 H,G
Class Times: Monday and Wednesday: 1:00 pm - 2:30 pm
Location: 46-3310

Tomaso Poggio (TP), Lorenzo Rosasco (LR)


Hongyi Zhang, Max Kleiman-Weiner, Jon Malmaud, Brando Miranda, Xavier Boix, Georgios Evangelopoulos

Office Hours: Thursday 3-4 pm, 46-5156 (Poggio Lab lounge)
Email Contact: 9.520@mit.edu
Previous Class: FALL 2015, lecture videos
Further Info: 9.520/6.860 is currently NOT using the Stellar system
Registration: Please register to 9.520/6.860 by filing this registration form
Mailing list: Registered students will be added in the course mailing list (9520students)

Course description

The course covers foundations and recent advances of Machine Learning from the point of view of Statistical Learning and Regularization Theory.

Understanding intelligence and how to replicate it in machines is arguably one of the greatest problems in science. Learning, its principles and computational implementations, is at the very core of intelligence. During the last decade, for the first time, we have been able to develop artificial intelligence systems that can solve complex tasks, previously considered out of reach: Cameras recognize faces, smartphones understand your voice and cars can see and avoid obstacles.

The machine learning algorithms that are at the roots of these success stories are trained with labeled examples rather than programmed to solve a task. Among the approaches in modern machine learning, the course focuses on regularization techniques, that provide a theoretical foundation to high-dimensional supervised learning. Besides classic approaches such as Support Vector Machines, the course covers state of the art techniques exploiting data geometry (aka manifold learning), sparsity and a variety of algorithms for supervised learning (batch and online), feature selection, structured prediction and multitask learning. Concepts from optimization theory useful for machine learning are covered in some detail (first order methods, proximal/splitting techniques,...).

The final part of the course will focus on deep learning networks. It will introduce a theoretical framework connecting the computations within the layers of deep learning networks to kernel machines. It will study an extension of convolutional layers in order to deal with more general invariance properties and to learn them from implicitly supervised data. It will describe new theorems characterizing the class of learning problems for which deep networks -- but not shallow networks -- can avoid the curse of dimensionality. This emerging theory of hierarchical architectures may explain how the visual cortex learns, in an implicitly supervised way, a data representation that can lower the sample complexity of a final supervised learning stage.

The goal of this course is to provide students with the theoretical knowledge and the basic intuitions needed to use and develop effective machine learning solutions to challenging problems.


We will make extensive use of basic notions of calculus, linear algebra and probability. The essentials are covered in class and during the Math Camp. We will introduce a few concepts in functional/convex analysis and optimization. Note that this is an advanced graduate course and some exposure on introductory Machine Learning concepts or courses is expected. Students are also expected to be familiar with MATLAB/Octave.


Requirements for grading are attending lectures/participation (10%), four problems sets (60%) and a final project (30%).

Slides with grading policies and anticiptated dates: (pdf).

Problem Sets

Problem Set 1, out: Sep. 21, due: Sun., Oct. 02 (Class 08).
Problem Set 2, out: Oct. 13, due: Mon., Oct. 24 (Class 13).
Problem Set 3, out: Oct. 27, due: Mon., Nov. 07 (Class 17).
Problem Set 4, out: Nov. 17, due: Tue., Nov. 29 (Class 24).

Submission instructions: Follow the instructions included with each problem set. Use the provided latex template for the writeup (there is a maximum page limit). Submit your writeup online (including code if applicable) by the due date/time and a printout in the first class after the due date.


Course projects should be individual research projects, focusing, typically, on one or more of the following: theory, comparisons/critical evaluations, applications, review or implementation.

Guidelines and key dates. Online form for project proposal (complete by Oct. 31).

Poster, due: Sun., Dec. 11, Poster presentations Mon., Dec. 12, Final report, due: Thu., Dec. 15

Reports should follow NIPS format and style files: template files

Projects archive

List of Wikipedia entries, created or edited as part of projects during previous course offerings.


Follow the link for each class to find a detailed description, suggested readings, and class slides. Some of the later classes may be subject to reordering or rescheduling.

Class Date Title Instructor(s)

Reading List

Notes covering the classes will be provided in the form of independent chapters of a book currently in draft format. Additional information will be given through the slides associated with classes (where applicable). The books/papers listed below are useful general reference reading, especially from the theoretical viewpoint. A list of additional suggested readings will also be provided separately for each class.

Book (draft)

Primary References

Resources and links