ELEC301x – Discrete Time Signals and Systems (Part 1 – Time Domain)
ELEC301x – Discrete Time Signals and Systems (Part 2 – Frequency Domain)
Enter the world of signal processing: analyze and extract meaning from the signals around us!
About the Course: Technological innovations have revolutionized the way we view and interact with the world around us. Editing a photo, re-mixing a song, automatically measuring and adjusting chemical concentrations in a tank: each of these tasks requires real-world data to be captured by a computer and then manipulated digitally to extract the salient information. Ever wonder how signals from the physical world are sampled, stored, and processed without losing the information required to make predictions and extract meaning from the data? Students will find out in this rigorous mathematical introduction to the engineering field of signal processing: the study of signals and systems that extract information from the world around us. This course will teach students to analyze discrete-time signals and systems in both the time and frequency domains. Students will learn convolution, discrete Fourier transforms, the z-transform, and digital filtering. Students will apply these concepts to build a digital audio synthesizer in MATLAB. Prerequisites include strong problem solving skills, the ability to understand mathematical representations of physical systems, and advanced mathematical background (one-dimensional integration, matrices, vectors, basic linear algebra, imaginary numbers, and sum and series notation). This course is an excerpt from an advanced undergraduate class at Rice University taught to all electrical and computer engineering majors.
This offering of the course is split into two convenient mini-courses. Part 1 covers signals and systems from a time-domain perspective, while Part 2 takes a frequency-domain perspective.
Sign up now for Part 1 and Part 2 and join in the fun!
T. Goldstein, C. Studer, and R. G. Baraniuk, “A Field Guide to Forward-Backward Splitting with a FASTA Implementation,” arXiv preprint, arxiv.org/abs/1411.3406, December 2014
Non-differentiable and constrained optimization play a key role in machine learning, signal and image processing, communications, and beyond. For high-dimensional minimization problems involving large datasets or many unknowns, the forward-backward splitting (FBS) method (also called the proximal gradient method) provides a simple, practical solver. Despite its apparently simplicity, the performance of the forward-backward splitting is highly sensitive to implementation details. Our research explores FBS with a special emphasis on practical implementation concerns and considering issues such as stepsize selection, acceleration, stopping conditions, and initialization. Our new solver FASTA (short for Fast Adaptive Shrinkage/Thresholding Algorithm) incorporates many variations of forward-backward splitting and provides a simple interface for applying FBS to a broad range of problems.
Software for FASTA is available here
Example: “Two Moons” data set for testing machine learning (classification) algorithms
Convergence of FASTA (red) on Two Moons versus more conventional forward-backward splitting (FBS) techniques
A. Lan, D. Vats, A. Waters, and R. G. Baraniuk, “Mathematical Language Processing: Automatic Grading and Feedback for Open Response Mathematical Questions,”
ACM Conference on Learning at Scale, Vancouver, March 2015.
Abstract: While computer and communication technologies have provided effective means to scale up many aspects of education, the submission and grading of assessments such as homework assignments and tests remains a weak link. In this paper, we study the problem of automatically grading the kinds of open response mathematical questions that figure prominently in STEM (science, technology, engineering, and mathematics) courses. Our data-driven framework for mathematical language processing (MLP) leverages solution data from a large number of learners to evaluate the correctness of their solutions, assign partial-credit scores, and provide feedback to each learner on the likely locations of any errors.
MLP takes inspiration from the success of natural language processing for text data and comprises three main steps. First, we convert each solution to an open response mathematical question into a series of numerical features. Second, we cluster the features from several solutions to uncover the structures of correct, partially correct, and incorrect solutions. We develop two different clustering approaches, one that leverages
generic clustering algorithms and one based on Bayesian nonparametrics. Third, we automatically grade the remaining (potentially large number of) solutions based on their assigned cluster and one instructor-provided grade per cluster. As a bonus, we can track the cluster assignment of each step of a multistep solution and determine when it departs from a cluster of correct solutions, which enables us to indicate the likely locations of errors to learners. We test and validate MLP on real-world MOOC data to demonstrate how it can substantially reduce the human effort required in large-scale educational platforms.
The figure below illustrates the clusters obtained by MLP to the solutions of 100 learners to four different mathematical questions (two from algebra and two from Fourier analysis). Each node corresponds to a solution. Nodes with the same color correspond to solutions that are estimated to be in the same cluster. The thickness of the edge between two solutions is proportional to their similarity score. Boxed solutions are correct; others have varying degrees of correctness.
The examples below demonstrate the generation of real-time feedback generation by MLP while learners enter their solutions. After each expression, we compute both the probability that the learner’s solution belongs to a cluster that does not have full credit (3 points) and the learner’s expected grade. An alert is generated when the expected credit is less than full credit.
A. Waters, D. Tinapple, and R. G. Baraniuk, “BayesRank: A Bayesian Approach to Ranked Peer Grading,” ACM Conference on Learning at Scale, Vancouver, March 2015.
Abstract: Advances in online and computer supported education afford exciting opportunities to revolutionize the classroom, while also presenting a number of new challenges not faced in traditional educational settings. Foremost among these challenges is the problem of accurately and efficiently evaluating learner work as the class size grows, which is directly related to the larger goal of providing quality, timely, and actionable formative feedback. Recently there has been a surge in interest in using peer grading methods coupled with machine learning to accurately and fairly evaluate learner work while alleviating the instructor bottleneck and grading overload. Prior work in peer grading almost exclusively focuses on numerically scored grades – either real-valued or ordinal. In this work, we consider the implications of peer ranking in which learners rank a small subset of peer work from strongest to weakest, and propose new types of computational analyses that can be applied to this ranking data. We adopt a Bayesian approach to the ranked peer grading problem and develop a novel model and method for utilizing ranked peer-grading data. We additionally develop a novel procedure for adaptively identifying which work should be ranked by particular peers in order to dynamically resolve ambiguity in the data and rapidly resolve a clearer picture of learner performance. We showcase our results on both synthetic and several real-world educational datasets.
The figures below compares BayesRank to the known ground truth item ordering in a synthetic experiment using Kendall’s tau metric, which measures the general agreement between two ordered sets. Kendall’s tau metric looks at each pair in one ranking and compares the same items in the second ranking to check for consistency. D_tau = +1/-1 corresponds to perfect agreement/disagreement. The two curves correspond to BayesRank with observations generated using adaptive assignment (red) and random item assignment (blue); we plot the tau metric as a function of the size of the class N (left) and as a function of the number of items K assigned to each grader. In all cases, BayesRank random assignment achieves significantly better performance than traditional random assignment.
Richard Baraniuk, the Victor E. Cameron Professor of Electrical and Computer Engineering at Rice University, has been named recipient of the 2014 IEEE Signal Processing Society Technical Achievement Award for “contributions to the theory and applications of sparsity and compressive sensing.”
The Technical Achievement Award honors a person who, over a period of years, has made outstanding technical contributions to theory and/or practice as demonstrated by publications, patents, or recognized impact on the field. The award will be presented at ICASSP 2015 in Brisbane, Australia, where Baraniuk is also a plenary speaker presenting his work on machine learning for open education.
Richard Baraniuk, the founder and director of OpenStax College and Rice’s Victor E. Cameron Professor of Electrical and Computer Engineering, has been named recipient of the 2015 IEEE James H. Mulligan Jr. Education Medal.
The medal, presented annually since 1956 by the former Institute of Electrical and Electronics Engineers, is given for outstanding contributions to education in the fields of interest to the organization. Baraniuk was specifically cited for his “fundamental contributions to open educational resources for electrical engineering and beyond.” The medal will be presented at the IEEE Honors Ceremony June 20 in New York City. Mulligan is a former president of IEEE.
Baraniuk founded Rice-based Connexions in 1999 to bring textbooks and other learning materials to the Internet. OpenStax grew from that effort as a way to provide high-quality, peer-reviewed, college-level textbooks to students worldwide. The books are free to download and can be printed at low cost. The OpenStax library includes textbooks for college physics, sociology, economics, anatomy and physiology, and separate biology books for majors and nonmajors. Since its launch in 2012, OpenStax books have been selected for use by more than 1,100 college courses and downloaded nearly a million times, saving students more than $30 million.
A. Waters, C. Studer, and R. G. Baraniuk, “Collaboration-Type Identification in Educational Datasets,” Journal of Educational Data Mining, Vol. 6, No. 1, 2014.
Abstract: Identifying collaboration between learners in a course is an important challenge in education for two reasons: First, depending on the courses rules, collaboration can be considered a form of cheating. Second, it helps one to more accurately evaluate each learners competence. While such collaboration identification is already challenging in traditional classroom settings consisting of a small number of learners, the problem is greatly exacerbated in the context of both online courses or massively open online courses (MOOCs) where potentially thousands of learners have little or no contact with the course instructor. In this work, we propose a novel methodology for collaboration-type identification, which both identifies learners who are likely collaborating and also classifies the type of collaboration employed. Under a fully Bayesian setting, we infer the probability of learners succeeding on a series of test items solely based on graded response data. We then use this information to jointly compute the likelihood that two learners were collaborating and what collaboration model (or type) was used. We demonstrate the efficacy of the proposed methods on both synthetic and real-world educational data; for the latter, the proposed methods find strong evidence of collaboration among learners in two non-collaborative take-home exams.
Below we show a collaboration-type identification result using Bayesian model selection for a collection of homework assignments in an undergraduate signal processing class. The data consists of 38 learners answering 50 homework questions plus 14 midterm exam questions. Grey ellipses designate the assigned homework groups. Dashed green lines denote parasitic collaborations, while solid blue lines denote symbiotic collaborations. Dotted red lines denote the connections found using Wesolowsky’s method, which, in general, finds fewer ground truth connections than the our method.
Rice University-based nonprofit OpenStax, which has already provided free textbooks to hundreds of thousands of college students, has been chosen by the Bill & Melinda Gates Foundation to develop personalized courseware for college students as part of the foundation’s $20 million Next Generation Courseware Challenge. The initiative was announced last week at the 2014 Educause Conference in Orlando.
“The same technology that retailers and online search firms use to deliver personalized choices can be combined with cognitive science models to deliver personalized learning experiences for college students,” said OpenStax founder Richard Baraniuk, Rice’s Victor E. Cameron Professor of Engineering. “Our free textbooks are already making college more accessible for those who couldn’t otherwise afford it, and personalized learning technology will improve student learning outcomes as well.”
In typical applications of machine learning (ML), humans typically enter the process at an early stage, in determining an initial representation of the problem and in preparing the data, and at a late stage, in interpreting and making decisions based on the results. Consequently, the bulk of the ML literature deals with such situations. Much less research has been devoted to ML involving “humans-in-the-loop,” where humans play a more intrinsic role in the process, interacting with the ML system to iterate towards a solution to which both humans and machines have contributed. In these situations, the goal is to optimize some quantity that can be obtained only by evaluating human responses and judgments. Examples of this hybrid, “human-in-the-loop” ML approach include:
- ML-based education, where a scheduling system acquires information about learners with the goal of selecting and recommending optimal lessons;
- Adaptive testing in psychological surveys, educational assessments, and recommender systems, where the system acquires testees’ responses and selects the next item in an adaptive and automated manner;
- Interactive topic modeling, where human interpretations of the topics are used to iteratively refine an estimated model;
- Image classification, where human judgments can be leveraged to improve the quality and information content of image features or classifiers.
In this workshop in December 2014, we focused on the emerging new theories, algorithms, and applications of human-in-the-loop ML algorithms.
Workshop web page with speakers and their slides
More information about the NIPS conference
Rice University-based publisher OpenStax College today announced $9.5 million in philanthropic grants from the Laura and John Arnold Foundation (LJAF), Rice alumni John and Ann Doerr, and the William and Flora Hewlett Foundation to add 10 titles to its catalog of free, high-quality textbooks for the nation’s most-attended college courses by 2017. OpenStax College is creating free books for 25 of the most-attended college courses in the country.
OpenStax College uses philanthropic gifts to produce high-quality, peer-reviewed textbooks that are free online and low-cost in print. Its first seven books have already saved students more than $13 million. The books have been downloaded more than 650,000 times and have been adopted for use in nearly 900 courses at community colleges, four-year colleges, universities and high schools. OpenStax College has four titles in production for next year and plans to expand its library to 21 titles by 2017. The additional funding will allow the nonprofit publisher to develop textbooks for additional high-enrollment courses, including several science and mathematics courses.
“Our books are opening access to higher education for students who couldn’t otherwise afford it,” said Rice Professor Richard Baraniuk, founder and director of OpenStax College. “We’ve already saved students millions of dollars, and thanks to the generosity of our philanthropic partners, we hope to save students more than $500 million by 2020.”