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publications
Power weighted shortest paths for clustering Euclidean data
Published in Foundations of Data Science, 2019
We study the use of power weighted shortest path distance functions for clustering high dimensional Euclidean data, under the assumption that the data is drawn from a collection of disjoint low dimensional manifolds. We argue, theoretically and experimentally, that this leads to higher clustering accuracy. We also present a fast algorithm for computing these distances
Recommended citation: McKenzie, Daniel and Damelin, Steven. (2019). "Power weighted shortest paths for clustering Euclidean data. " Foundations of Data Science. 1(3). https://arxiv.org/abs/1905.13345
Compressive sensing for cut improvement and local clustering
Published in SIMODS, 2020
We apply tools from compressive sensing to the problem of finding clusters in graphs.
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Who killed Lilly Kane? A case study in applying knowledge graphs to crime fiction.
Published in GTA3 workshop at IEEE Big Data, 2020
We construct and analyze a knowledge graph for season one of the TV show Veronica Mars.
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Zeroth Order Regularized Optimization (ZORO): Approximately sparse gradients and adaptive sampling.
Published in SIOPT (to appear) , 2021
We propose a new zeroth-order optimization algorithm that uses compressive sensing to approximate gradients.
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A zeroth-order block coordinate descent algorithm for huge-scale black-box optimization.
Published in ICML , 2021
We propose a new algorithm for ultra-high dimensional black-box optimization (over 1 million variables).
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Learn to predict equilibria via Fixed Point Networks.
Published in (under review), 2021
We apply the FPN technology developed in an earlier work to the problem of predicting Nash equilibria in parametrized games.
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Curvature-Aware Derivative-Free Optimization.
Published in (under review), 2021
We propose a line search algorithm for zeroth-order optimization with low query complexity, both in theory and in practice.
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Adapting zeroth order algorithms for comparison-based optimization.
Published in (Submitted to SIURO), 2021
We provide a criterion for converting ZO algorithms to the comparison-based setting.
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Balancing geometry and density: Path distances on high dimensional data.
Published in SIMODS (to appear) , 2021
We further explore the use of shortest path metrics on high dimensional data.
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From the simplex to the sphere: Faster constrained optimization using the Hadamard parametrization.
Published in submitted , 2021
We show how to convert the problem of minimizing a convex function over the standard probability simplex to that of minimizing a nonconvex function over the unit sphere..
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JFB: Jacobian-Free Backpropagation for Implicit Networks.
Published in AAAI , 2022
We propose a new, much faster, kind of backprop for implicit-depth neural networks.
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A one-bit, comparison-based gradient estimator.
Published in ACHA , 2022
We use tools from one-bit compressed sensing to construct a new algorithm for comparison-based optimization.
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talks
Cut Improvement and Clustering using Compressive Sensing.
Published:
Based on this paper. Here are the slides. This talk has been given virtually and in person at several other venues.
Learning to predict Nash equilibria from data.
Published:
Based on this and this paper. Here are the slides. Similar versions of this talk were/ will be given at the ZiF Mathematics of Machine Learning conference and in the Mean-field games and optimal transport seminar.
A zeroth-order block coordinate descent algorithm for huge-scale black-box optimization.
Published:
Based on this paper. Here are the slides. This short ICML talk was actually presented by Yuchen Lou.
teaching
Precalculus
Undergraduate course, University of Georgia, 2014
( 2014–2019 ) While a graduate student at UGA I taught Math1113, a one semester precalculus course, six times. The textbook we used was Precalculus by Julie Miller and Donna Gerkin. For some sections we used the ALEKS homework system. You can find a sample syllabus here and a copy of my first day of class slides here.
Calculus 1
Undergraduate course, University of Georgia, 2015
( 2014–2019 ) While a graduate student at UGA I taught Math2250, a one semester Calculus 1 course, three times. We used the textbook University Calculus, Early Transcendentals by Hass, Weir and Thomas. We used the WebWork homework system. I experimented with a variety of teaching modalities but one thing I found to be effective was creating a worksheet for every lesson which we would start in class and students would finish at home. You can find an example of such a worksheet here. You can find a copy of the syllabus here.
Calculus 3
Undergraduate course, University of California, Los Angeles, 2019
Math 32A is a large (~200 students), one-quarter course on multivariable calculus. Teaching Math 32A was an interesting experience as it involved giving auditorium-style lectures as well as managing a grader and three TA’s who met with the students in smaller groups. You can find a copy of the syllabus here. The reviews were mostly favorable.
Mathematics of Data Theory
Undergraduate course, University of California, Los Angeles, 2020
( 2019–2021 ) At UCLA I co-developed and then taught (three times) Math 118, an introduction to the mathematics of data science. I try to emphasize both theory and practice, so some lectures are slide-based presentations while others are more interactive and use Jupyter notebooks to play around with algorithms. I am happy to share my complete set of lecture slides, but not yet willing to make them completely public, so email me if you would like access.
Introduction to Statistics
Undergraduate course, University of California, Los Angeles, 2020
Math 170S is a mathematically rigorous introduction to statistics, using Hogg, Tanis and Zimmerman’s Probability and Statistical Inference . This was the first course I taught entirely over Zoom.
Honors Applied Numerical Methods
Undergraduate course, University of California, Los Angeles, 2021
At UCLA I co-developed Math151AH and Math151BH, honors versions of the pre-existing applied numerical methods classes. This two course sequence examines the theory and implementation of algorithms to solve fundamental problems in numerical analysis, for example least squares and SVD decompositions. We used this textbook. Here are the syllabi for Math151AH and Math151BH, and here is a sample lecture on one of my favorite algorithms, the power method.
Linear Algebra
Undergraduate course, Colorado School of Mines, 2022
40 person section of Linear Algebra.
Computational Linear Algebra
Graduate course, Colorado School of Mines, 2023
A graduate course on numerical linear algebra. We will focus on three fundamental problems; solving linear systems, solving least squares problems, and finding eigenvalues/eigenvectors. We’ll present multiple computational approaches for each. If you are a Mines student enrolled in this course you can find additional details on the canvas page.
Linear Algebra
Undergraduate course, Colorado School of Mines, 2023
40 person section of Linear Algebra. If you are enrolled in this class, please see our canvas page for further information.