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Teaching & Mentoring

Methods as a craft — derivation, code, and a worked example.

I teach mathematical and statistical methods so students meet each one from at least three directions, and learn to be honest about what a method assumes and where it fails.

Philosophy

Students meet each method from at least three directions — a derivation, working code, and a worked example on data they care about. In clinical and biomedical settings I treat calibration, subgroup performance, and uncertainty as part of the modeling task itself, not as caveats appended at the end. Many of my undergraduate students at WVU came from rural Appalachian backgrounds and were first-generation college students, which shaped a layered assignment structure — a required core, optional technical extensions, and short interpretation prompts — that lets students contribute from their strengths while building new skills.

Courses Taught

  • Algebra with Applications (MATH 124)Instructor · Fall 2021
  • Multivariable CalculusAssistant · Spring 2021
  • Applied Linear AlgebraAssistant · Spring 2020
  • Numerical Analysis (MATH 521)Assistant · Spring 2019
  • Advanced Linear AlgebraAssistant · Fall 2018
  • Engineers' Calculus (MATH 155E)Recitation · Fall 2018
  • Advanced Engineering MathematicsInstructor · Shiraz, Spring 2009
  • Differential EquationsAssistant · Shiraz, Fall 2008

As Teaching Instructor for Algebra with Applications I designed the problem sets and exams and built a grading pipeline that re-ran student notebooks to flag silent failures — so students learned to defend the correctness of a result, not its appearance.

Proposed Graduate Courses

Five courses I am prepared to develop.

Drawn directly from my research program in causal inference, uncertainty-aware clinical machine learning, Bayesian biomedical networks, and optimal transport. Each pairs methods with public clinical datasets and a reproducible final artifact. Expand any course for a full graduate syllabus.

Catalog description
A hands-on introduction to statistical learning for students entering data science from outside mathematics, taught entirely through health data. Every method is met three ways — a derivation, working code, and a worked analysis on a public clinical dataset.
Why it matters
Health data science needs practitioners who can not only fit a model but defend it. The course builds that judgment from the first week, treating calibration, subgroup performance, and label noise as part of the modeling task rather than caveats.
Target audience
First-year graduate students and advanced undergraduates in data science, biomedical informatics, statistics, or clinical fields entering quantitative work.
Prerequisites
One course each in probability/statistics and programming (Python); linear algebra recommended.
Learning objectives
  • Fit and evaluate supervised models on clinical data and reason about bias–variance and regularization.
  • Test conditional independence and perform principled feature selection.
  • Analyze censored outcomes with survival models.
  • Produce a reproducible analysis another student can rerun.
Module schedule
  1. Reproducible workflows — notebooks, environments, data manifests.
  2. Regression & loss functions.
  3. Penalized regression — ridge, lasso, elastic net.
  4. Classification, logistic regression & calibration.
  5. Resampling, cross-validation & leakage.
  6. Tree ensembles — random forests, gradient boosting.
  7. Conditional-independence testing & feature selection.
  8. Survival analysis — Kaplan–Meier, Cox models.
  9. Evaluation for health — AUC pitfalls, subgroup metrics.
  10. Missing data & interpretability (permutation importance, PDP).
Assignments
Weekly labs, each on a public clinical dataset; a mid-term "why is this AUC misleading?" critique.
Grading
45% weekly labs · 15% critique · 30% final project · 10% participation.
Final project
Choose a public clinical dataset, define a prediction task, fit at least two model families, evaluate with calibration and subgroup analysis, and submit a reproducible notebook with a short written report.
Datasets
MIMIC-IV derived tables, a public sepsis cohort, UCI clinical datasets, SEER (for survival).
Tools
Python, scikit-learn, lifelines, pandas, Jupyter, Git.
Readings
James et al., ISLR; Hastie, Tibshirani & Friedman, ESL (selected); selected clinical-ML method papers.
Program fit
The entry point to my teaching sequence; it feeds the causal-inference and uncertainty-aware courses below.
Catalog description
Methods for estimating causal effects from observational health records, taught alongside the data-generating realities that make naive estimates fail.
Why it matters
Clinical decisions need causal answers — for which patients does this intervention help? — but EHR data are confounded and messy. The course builds principled estimation paired with honest sensitivity analysis.
Target audience
Master's and doctoral students in data science, biostatistics, and biomedical informatics; clinical fellows with quantitative training.
Prerequisites
Regression and probability; a prior ML or statistics course; Python.
Learning objectives
  • Formalize causal questions with potential outcomes and DAGs.
  • Estimate effects with IPW, doubly-robust methods, TMLE, and instrumental variables.
  • Conduct sensitivity analysis for unmeasured confounding.
  • Diagnose EHR-specific biases and interpret treatment-effect heterogeneity.
Module schedule
  1. Causal questions & potential outcomes.
  2. DAGs & identification.
  3. Confounding, adjustment & propensity scores.
  4. IPW & doubly-robust estimation.
  5. Targeted maximum likelihood (TMLE).
  6. Instrumental variables.
  7. Time-varying treatments & g-methods.
  8. Heterogeneous treatment effects.
  9. EHR realities — missingness, irregular sampling, label leakage.
  10. Sensitivity analysis (E-values); governance, fairness & transportability.
Assignments
Problem sets on identification and estimation; an EHR "bias audit" of a published observational claim.
Grading
40% problem sets · 20% bias audit · 30% final project · 10% participation.
Final project
Pose a causal question on a public EHR cohort, justify identification, estimate with a doubly-robust method, run a sensitivity analysis, and report with clinical interpretation.
Datasets
MIMIC-IV, eICU, public claims subsets.
Tools
Python, DoWhy, EconML, scikit-learn; R optional.
Readings
Hernán & Robins, Causal Inference: What If; Pearl, Causality (selected); Peters, Janzing & Schölkopf (selected); TMLE method papers.
Program fit
The methodological core of my D2 direction — causal phenotyping and treatment-effect estimation for perioperative recovery.
Catalog description
A doctoral course on building and auditing clinical machine learning that reports what it does not know, organized around calibration, distribution shift, and subgroup performance.
Why it matters
Models that are accurate on average fail at the edges that matter most — induction, decompensation, weaning, recovery. Trustworthy deployment requires uncertainty-aware evaluation, not just higher average accuracy.
Target audience
Doctoral students in data science, statistics, biomedical informatics, and computer science; postdocs; clinical fellows in research electives.
Prerequisites
A machine-learning course; probability/statistics; Python. Causal inference helpful.
Learning objectives
  • Calibrate and evaluate probabilistic predictions with proper scoring rules.
  • Apply conformal prediction and quantify uncertainty.
  • Detect and quantify distribution shift across time and sites.
  • Audit subgroup performance, fairness, and instance-level harm.
  • Combine supervised prediction, phenotyping, representation learning, and causal inference on multimodal clinical data.
Module schedule
Unit I — Calibration.
  1. Probabilistic prediction & proper scoring.
  2. Calibration methods & reliability diagrams.
  3. Conformal prediction.
  4. Uncertainty quantification.
Unit II — Distribution shift.
  1. Covariate & label shift.
  2. Shift detection & monitoring.
  3. Domain adaptation & optimal transport.
  4. Temporal & multi-site shift.
Unit III — Subgroup auditing.
  1. Subgroup metrics & fairness.
  2. Instance-level error & harm scoring.
  3. Governance & reproducibility.
Assignments
Labs on calibration, conformal sets, shift detection, and subgroup audits; a paper-replication assignment (reproduce one figure from a clinical-AI paper).
Grading
40% labs · 30% final project · 20% paper replication & critique · 10% participation.
Final project
Define a cohort (justify inclusion/exclusion), construct features, train and evaluate a model, and write a report combining quantitative results with clinical interpretation. Submit reproducible code and a data manifest another student can rerun end-to-end on a SLURM cluster or containerized workstation.
Datasets
MIMIC-IV and MIMIC-CXR (PhysioNet-credentialed), eICU; physiologic-waveform subsets.
Tools
Python, PyTorch, scikit-learn, MAPIE (conformal), Docker, SLURM/HPC.
Readings
Guo et al. (calibration); Angelopoulos & Bates (conformal prediction); clinical distribution-shift literature; subgroup/fairness auditing papers.
Program fit
The flagship of my teaching program — the course expression of D1 and D2, directly aligned with my MIT reliability work and Duke postdoctoral research.
Catalog description
A research seminar on Bayesian network inference for biomedical systems, drawing on ensemble structure learning and stability analysis.
Why it matters
Biomedical discovery needs reproducible causal structure with honest uncertainty — not brittle graphs from a single algorithm run once.
Target audience
Doctoral students in data science, statistics, and computational biology; methodologically oriented postdocs.
Prerequisites
Probability and a graphical-models or ML course; Python; some Bayesian statistics.
Learning objectives
  • Represent and score Bayesian networks.
  • Run constraint- and score-based structure learning.
  • Explore graph posteriors with MCMC.
  • Assess edge stability via bootstrapping and report calibrated uncertainty.
Module schedule
  1. Graphical models & d-separation.
  2. Conditional-independence testing with multiple-hypothesis correction.
  3. Score-based search.
  4. Constraint-based algorithms.
  5. Ensemble / hybrid structure learning.
  6. MCMC over graph spaces.
  7. Bootstrap stability & edge uncertainty.
  8. Deconvolution & network-immunology case study.
  9. Evaluation & benchmarks.
  10. Project presentations.
Assignments
Implement and apply a structure-learning pipeline; lead a seminar critique of a published network-inference paper.
Grading
35% implementation · 25% critiques & seminar leadership · 30% project · 10% participation.
Final project
Infer a network from a real biomedical dataset with calibrated edge stability, and report the structure together with its uncertainty.
Datasets
Public gene-expression (TCGA subsets); immunology / cytometry references.
Tools
Python, bnlearn, PyMC, causalnex, TETRAD, NetworkX.
Readings
Koller & Friedman (selected); Latifizadeh et al., BaMANI (arXiv, 2025); Klinke et al., Nature Communications (2022).
Program fit
The seminar form of my causal-discovery methodology (BaMANI); feeds the D2 causal-phenotyping direction.
Catalog description
A seminar on optimal transport for aligning biomedical distributions across instruments, sites, and species, emphasizing unbalanced and relaxed-marginal methods.
Why it matters
Models fail across sites and platforms. Principled distribution alignment — with honest reporting of unmatched mass — is a precondition for transferable biomedical AI.
Target audience
Doctoral students in data science, statistics, computational biology, and computer science.
Prerequisites
Linear algebra, probability, and optimization basics; Python.
Learning objectives
  • Formulate optimal transport (Monge and Kantorovich).
  • Compute entropic OT with the Sinkhorn algorithm.
  • Apply unbalanced and relaxed-marginal OT.
  • Use Wasserstein distances in machine-learning pipelines for alignment.
Module schedule
  1. OT foundations.
  2. Kantorovich duality.
  3. Entropic regularization & Sinkhorn.
  4. Wasserstein distances & barycenters.
  5. Unbalanced OT.
  6. Relaxed-marginal formulations & unmatched mass.
  7. OT for domain adaptation.
  8. Gaussian-mixture embeddings & graph clustering.
  9. Cross-species / cross-site case study.
  10. Project presentations.
Assignments
Implement Sinkhorn; apply unbalanced OT to an alignment task; lead a critique of an OT-in-biology paper.
Grading
35% implementation · 25% critiques & seminar leadership · 30% project · 10% participation.
Final project
Align two real biomedical datasets with (unbalanced) optimal transport, reporting transfer performance and unmatched mass.
Datasets
Flow-cytometry references; multi-site expression subsets.
Tools
Python, POT (Python Optimal Transport), scikit-learn, scanpy, Leiden/igraph.
Readings
Peyré & Cuturi, Computational Optimal Transport; Cuturi (Sinkhorn); Chizat et al. (unbalanced OT); Latifizadeh et al., OT-RMC (in preparation).
Program fit
The seminar form of my cross-dataset harmonization work (OT-RMC); supports multi-site perioperative phenotyping.

Mentoring

I have mentored across levels and settings: as Trainee Mentor and Hackathon Co-Organizer for the NIH-funded MISM Center of Excellence Summer Trainee Program at Duke (2026); as External Graduate Student Panelist for the NSF REU on Discrete and Continuous Analysis in Appalachia at Fairmont State University (2022); and as Invited Graduate Judge for the WVU Undergraduate Research Symposia (2022, 2023). Earlier, I mentored three M.Sc. students through thesis research at Shiraz University of Technology (2010–2014).

I also founded and led the WVU SIAM Student Chapter (2022–2024), a student-led seminar bridging applied mathematics and data-driven research.