BME 6780: Data Science for Bioengineers
- For postdoctoral, graduate, and advanced undergraduate students in Engineering, Sciences, and Medicine, and professionals in industry.
- Fall 2025, Mondays and Wednesdays 11:50am–1:10pm, LCB 115; office hours upon request or Wednesdays 11:00am, WEB 3803.
Prerequisites: Some experience programming and instructor approval.
100% grade = 40% labs and quizzes, 30% class project, 20% presentation, 10% class participation; late assignments are not accepted; class attendance is required.
This project-oriented data science and fundamentals of machine learning and artificial intelligence (AI/ML) course covers:
- Databases: From, e.g., the Genomic Data Commons (GDC), to, e.g., the Surveillance, Epidemiology, and End Results (SEER) Database.
- Data Types: From large-scale molecular biological data, e.g., genomics, transcriptomics, and proteomics, to biosignals, e.g., electrocardiograms (ECGs/EKGs) and
electroencephalograms (EEGs), and from imaging, e.g., magnetic resonance images (MRIs) and pathology tissue slides, to electronic health records and epidemiological data.
- Algorithms and Models: From the singular value decomposition (SVD) and principal component analysis (PCA) to tensor decompositions, the perceptron and the Hopfield network.
- Predictors and Applications: From a better understanding of the principles of nature, e.g., the Luria–Delbrück experiment, to a better patient care, e.g., via personalized/precision medicine.
Objective/Outcome:
The design and realization of a data science project by each student.
Skills:
- Proving mathematical theorems and coding symbolic computations.
- Designing algorithms and programming numerical computations.
- Working with biomedical databases.
- Modeling biomedical data.
Activities:
- In-class presentations of, e.g., scientific journal articles and patents.
- Participation in guest lectures and seminars on campus and discussions of professional conference reports.
- End-of-class celebration and discussion of future directions.
Readings on the SVD and deep learning:
- The syllabus is subject to change at the discretion of the instructor.
- Fall 2025 Calendar
- University Policies
- Health, Wellness, and Counseling
August 18:
August 20:
Lab 1:
Code the SVD or the tensor SVD of synthetic data and its visualization. Test and debug your code.
August 25, 11:50am–1:10pm, SMBB 2650:
Bioengineering Elevated Lecture Celebrating 50 Years of Biomedical Engineering at the University of Utah
February 29:
Matrix Computations, Golub and Van Loan (1996).
August 27:
Numerical Linear Algebra, Trefethen and Bau, III (1997).
Notebook 1: Computation and Visualization of the SVD
September 1:
September 4:
Composition and decomposition of synthetic data:
Testing and debugging your SVD code:
Notebook 2: The SVD of Synthetic Data
September 8:
September 10:
September 15:
In-Class Quiz 1: Testing and Debugging Your SVD Code
Modeling nonlinear phenomena with linear algebra
September 17:
September 22:
The SVD is used for the stable computation of PCA:
PCA identifies patterns across the columns separately from patterns across the rows; the SVD simultaneously computes the corresponding sets of patterns across the
rows and columns, ensuring consistent data interpretation:
Paper 8: Correspondence Analysis Applied to Microarray Data, Fellenberg et al., Proceedings of the National Academy of Sciences (PNAS) USA (2001).
September 24:
Lab 2:
Compute and visualize the SVD or the tensor SVD of your data. Interpret your data based upon its SVD or its tensor SVD. Use at least two different approaches each for preprocessing and sorting your data and for assessing the statistical significance of your interpretation.
September 29:
Notebook 3: The Hypergeometric Probability Distribution and P-Value
October 1:
Example of the hypergeometric probability distribution in manufacturing:
Technical Report 1: Single Sampling and Double Sampling Inspection Tables, Dodge and Romig, The Bell System Technical Journal (1941).
October 6:
October 8:
October 13:
October 15:
Mathematical variations on the SVD and PCA for blind source separation (BSS):
October 20:
More mathematical variations on the SVD and PCA for BSS
The cocktail party problem and BSS
October 22:
Mathematics of a tensor SVD, the higher-order SVD (HOSVD):
Examples of the HOSVD of measured data:
Paper 27: A Tensor Higher-Order Singular Value Decomposition for Integrative Analysis of DNA Microarray Data from Different Studies, Omberg et al., Proceedings of the National Academy of Sciences (PNAS) USA (2007).
Paper 28: Characterizing the Evolution of Genetic Variance Using Genetic Covariance Tensors, Hines et al., Philosophical Transactions of the Royal Society B Biological Sciences (2009).
Paper 29: Integrative Analysis of Many Weighted Co-Expression Networks Using Tensor Computation, Li et al., Public Library of Science (PLoS) Computational Biology (2011).
Paper 30: MultiFacTV: Module Detection from Higher-Order Time Series Biological Data, Li et al., BMC Genomics (2013).
Paper 31: Subgraph Augmented Nonnegative Tensor Factorization (SANTF) for Modeling Clinical Narrative Text, Luo et al., Journal of the American Medical Informatics Association (2015).
October 27:
Computation of the HOSVD:
Notebook 4: The tensor SVD of Synthetic Data
October 29:
In-Class Quiz 2: The Hypergeometric Probability Distribution and P-Value
November 3:
November 5:
November 10:
PCA assumes preprocessing of the data, which limits the data interpretation (e.g., the SVD of a dataset can identify the probability distribution function that is sampled by the dataset with no a-priori assumptions; PCA cannot):
Slides 4: The SVD as a Transform
November 12:
Notebook 5: The tensor SVD of Measured Data
November 17:
Verification and validation
November 19:
November 24:
The "perceptron," i.e., single-layer neural network, as a mathematical variation on the SVD:
November 26:
From the perceptron to deep learning:
On convergence, completeness, and overfitting
November 27:
December 1:
"State of the project" presentations
December 3:
"State of the project" presentations
End-of-class celebration!
Happy Winter Break!
