This course aims to teach a suite of algorithms and concepts to a diverse set of participants interested in the general concept of fitting data to models. It starts with mostly simple linear algebra and computational methods, and introduces some more difficult mathematical concepts towards the end. This method also, by design, fits in with our approach of morning lectures and afternoon practice on personal computers. The combined teaching system provides opportunities for much hands-on learning and participants leave the course with practical knowledge of the basic algorithms.
Applied data science enjoys widespread application in nearly every industry today. It lies at the intersection of the quantitative (statistics and optimization), the computational (programming and IT), and the domanial (business knowledge).
Unfortunately, Data Science Education presently seems to overemphasize nonparametric methods, like Artificial Intelligence and Machine Learning (more on this below), perhaps because such methods seem irresistibly powerful and arcane.
AI and ML certainly can be powerful, but only the practitioner with a firm grasp of the fundamentals of data and models can leverage such methods with a sure hand, knowing when and how to use them and, importantly, when not to.
The present class is such a foundational course in data and models. Through the lens of regression analysis, a far-reaching discipline with roots in mathematics, statistics, and optimization, Foundations of Data and Models introduces students to the quantitative and (to a lesser degree) computational realms of data science.
One way to unpack the field of data and models is to bisect it into two general categories:
In these approaches, a reasonable mathematical model of the system under consideration is proposed, and the “regression task” is to determine the parameters of that mathematical model as uniquely and as accurately as possible. Typical methods for doing so include Least Squares, Simulated Annealing, Genetic Algorithms, Quasi-Random and Grid Search, etc.
Here no mathematical model is assumed, though this doesn’t mean a mathematical model is not used. Rather, the mathematical model is usually baked into the method and is sufficiently general that it can mimic a wide variety of possibly very nonlinear behaviors arising from the system under consideration. Typical methods are the Principal Components, Neural Networks or Deep Learning, Artificial Intelligence (AI), Machine Learning (ML), etc.
There are pros and cons to each method.
Foundations of Data and Models is a course in parametric methods of regression, which provides the student an intuitive understanding of the quantitative principles needed to excel when their data science journey arrives at AI and ML.
The course covers such topics as Statistics, Least Squares, Bacchus-Gilbert Methods, Simple Random and Grid Search algorithms, Annealing and Genetic Algorithms, Errors in Nonlinear Regression, Solving Large Systems, Robust Regression with Regularization, Neural Networks and an Introduction to Artificial Intelligence.
We strongly suggest that students take this (or a similar) course before embarking into the world of Artificial Intelligence and Machine Learning.
Laptops for which you have administrative privileges are required for this course. PCs are recommended. Tablets will not be sufficient for the computing activities performed in this course.
Participants are encouraged to study a basic text prior to attendance. Two suggestions are:
- Data Reduction and Error Analysis for the Physical Sciences, P. R. Bevington and D. K. Robinson, McGraw-Hill, Inc., 2nd ed., 1992.
- Applied Regression Analysis, N. R. Draper and H. Smith, John Wiley and Sons, Inc., 2nd ed., 1981.
This course was previously titled "Data and Models in Engineering, Science, and Business."
It is highly recommended that you apply for a course at least 6-8 weeks before the start date to guarantee there will be space available. After that date you may be placed on a waitlist. Courses with low enrollment may be cancelled up to 4 weeks before start date if sufficient enrollments are not met. If you are able to access the online application form, then registration for that particular course is still open.
Takeaways from this course include:
- Examining how to fit data to models
- Defining linear least squares, non-linear least squares, singular value decomposition, sensitivity analysis, experiment design, and parameter error estimation
- Appreciating grid search, random search, simulated annealing, genetic algorithms, neural networks, and large inverse systems
- Investigating principles leading to rapid application of methods
- Evaluating the results of pre-programmed computer exercises
Who Should Attend:
This course is ideal for anyone who fits data to models. This course is truly broad-based and participants from vastly differing fields are envisioned and encouraged to attend. Some of these fields are engineering, business, natural sciences, geoscience, medicine, statistics, and economics.
Familiarity with computing and statistics is desirable. A fair background in linear algebra is highly recommended. The course is a condensed version of a regular MIT class with the same title, taught by Professor Morgan. The course has also been given at NASA, the University of the West Indies in Barbados, Sakarya University in Turkey, Stanford University, University of Science and Technology of China,the Cyprus Institute, and Texas A&M University.
Recent and past participants in this course have come from: Air Force Office of Scientific Research (AFOSR), Amgen Inc., AT&T, BAE Systems, Bank of America, Boeing, Boehringer Ingelheim Pharmaceuticals, BP America, Cisco Systems, Cox Communications, Delphi, Draper Laboratory, Dupont, EMC, Environmental Protection Agency, ExxonMobil Chemical, General Motors, Hitachi (Japan), Intel, Johnson & Johnson, Korea Power Co., Kraft Foods, Los Alamos Labs, Mathworks, Mayo Clinic, Merck & Co Inc, Merrill Lynch, Motorola, Naval Research Laboratory, New York University, NTT (Japan), Nokia Research Center, Phillips Exeter Academy, Philips North America, Pioneer Investments, Polaroid Corporation, Salesforce, Sandia National Labs, Saudi Arabian Monetary Agency, Toshiba Corporation, University of Pennsylvania, University of West Indies, the U.S. Air Force, and Verizon Wireless.
The format of each day is generally the same: mornings are devoted to lectures while participants spend the afternoons running pre-programmed software based on the morning lectures. During the afternoons, we stop the class often to have a discussion of progress and to give helpful tips and suggestions. Participants can work singly or in pairs at the computer.
Individual lectures will address the following topics:
- Philosophy of Data and Models
- Straight Line Data Analysis
- Least Squares
- Levenberg-Marquardt and Ridge Regression Algorithms
- Damped Least Squares Comparison
- Stochastic Inverse
- Singular Value Decomposition
- Random and Grid-Search Methods
- Simulated Annealing and Genetic Algorithms
- Neural Networks
- Parameter Error Estimates
- Large Inverse Problems
- Experimental Design
Note that the order of the lectures can vary from that given above. A bound copy (and an electronic version) of all PowerPoint lecture notes is given to each participant, to follow lectures and make notes.
View 2020 schedule (pdf)
Class runs 9:00 am to 5:00 pm Monday-Friday.
9:00 am - 12:00 pm - Lecture
12:00 pm - 1:00 pm - Lunch Break
1:00 pm - 5:00 pm - Lab Exercises
DEPUTY CHIEF SCIENTIST, AIR FORCE OFFICE OF SCIENTIFIC RESEARCH
“The course efficiently provided a broad understanding of a wide variety of methods to a very varied and interesting group of students.”
ASSOCIATE PROFESSOR, UNIVERSITY OF THE PACIFIC
“Course was well designed. Lab work was very helpful. Application to real-world problems was well illustrated.”
ELECTRICAL & CONTROLS ENGINEER, BP AMERICA
"I enjoyed the courses taken at MIT this summer. They combined a large amount of theory with lab work in an accelerated fashion. These courses have been the best post-bachelor's courses I have taken thus far."
POSTDOCTORAL RESEARCH FELLOW, BRIGHAM AND WOMEN'S HOSPITAL
“I found it to be a very stimulating and exciting environment. I felt that the instructors were very knowledgeable in the area and were willing to discuss issues related to applications beyond the classroom. Overall, I would attend courses at MIT Professional Education - Short Programs in the future and would recommend the program to colleagues.”
SENIOR MECHANICAL ENGINEER, BAE SYSTEMS
“The lab portions of the class were thoughtfully planned and very instructive.”
PROGRAM MANAGER, UNIVERSITY OF ARKANSAS FOR MEDICAL SCIENCES
“The instructors were excellent, and the in-lab reviews with other participants were enlightening.”
ENGINEERING SPECIALIST, BAXTER HEALTHCARE
“To remain competitive, we need to implement process improvements across the organization to greatly improve efficiency while simultaneously increasing the robustness and efficacy of our products. This knowledge provides additional tools to accomplish this.”
DIRECTOR OF RESEARCH AND DEVELOPMENT, PRESCIENT RIDGE MANAGEMENT
“Definitely a good balance between the lectures in the morning which gave the theory and the labs in the afternoon which allowed time to work on the practical application.”
SIMULATION CONSULTANT, DEMATIC
“The knowledge will help me to better analyze customer data and build more sophisticated simulation models.”
Frank Dale Morgan obtained his BSc (Math/Physics, 1970) and his MSc (Theoretical Solid State Physics, 1972) from the University of the West Indies, Trinidad, where he was a Lecturer in Physics from 1970-1975. From 1975 to 1981, he completed a PhD in Geophysics at MIT. He returned to the University of the West Indies, Trinidad, as a Research Fellow in the Seismic Research Unit. From 1983 to 1985 he was a Research Associate in the Geophysics Department at Stanford University. In 1985, he joined the faculty of the Geophysics Department at Texas A&M University. He is now a Professor of Geophysics at the Massachusetts Institute of Technology in the Department of Earth, Atmospheric, and Planetary Sciences and associated with the Earth Resources Laboratory. His current interests are in rock physics, geoelectromagnetism, applied seismology, inverse theory, environmental and engineering geophysics, electrochemistry, and electronic instrumentation. He teaches courses on the physics and chemistry of rocks, environmental and engineering geophysics, alternative energy, and inverse theory. He is the organizer and principal instructor for the course.
Darrell Coles obtained his BA in Pure Mathematics from the University of Rochester (1994), and his MSc in Geosystems (1998) and PhD in Geophysics (2008) from the Massachusetts Institute of Technology. He worked from 2008 to 2010 in Scotland as a research geophysicist in a joint posting between Total Exploration & Production and the GeoSciences School of University of Edinburgh on cutting edge theory and application of the design of industrial seismic experiments and 4D seismic data analysis (leading to an international patent and several peer-reviewed articles). Since 2010, he has worked as a senior research geophysicist at Schlumberger in Cambridge, MA and Houston, TX. His research efforts have been in optimal experimental design for industrial-scale geoscientific applications, inverse and optimization theory, uncertainty characterization and control, all in the context of seismic data acquisition and analysis. He has obtained several additional patents and written several peer-reviewed publications since joining Schlumberger and is currently branching into commercial software development and data science.
This course takes place on the MIT campus in Cambridge, Massachusetts. We can also offer this course for groups of employees at your location. Please complete the Custom Programs request form for further details.
|Fundamentals: Core concepts, understandings, and tools (75%)||75|
|Latest Developments: Recent advances and future trends (25%)||25|
|Lecture: Delivery of material in a lecture format (40%)||40|
|Discussion: Guided discussion reinforcing lectures and computer lab work (15%)||15|
|Labs: Demonstrations, experiments, simulations (45%)||45|
|Introductory: Appropriate for a general audience (30%)||30|
|Specialized: Assumes experience in practice area or field (50%)||50|
|Advanced: In-depth explorations at the graduate level (20%)||20|