I am a Senior Research Scientist in the
Center for Computational Mathematics (CCM)
at the
Flatiron Institute.
I joined CCM in July 2022 as a group leader in machine learning.
My current research focuses on high dimensional data analysis, latent variable modeling,
and deep learning; other interests include variational inference, optimization, and kernel methods. Before joining Flatiron, I was a research scientist at
AT&T Labs
and a faculty member at UPenn and
UC San Diego.
I also served previously as EditorinChief of JMLR and as program chair for
NeurIPS.
I obtained my PhD in Physics from MIT, with a thesis on exact computational methods in
the statistical mechanics of disordered systems.
Research
High dimensional data analysis
How can we discover low dimensional structure in high dimensional data?
How does this question change (if at all) when the data is sparse?
These are fascinating problems that lie at the intersection of statistics, geometry,
and computation.
Manifold learning
If high dimensional data lives on (or near) a low dimensional manifold,
then we can attempt to learn a similaritypreserving embedding. Recent
work on this problem has revealed surprising connections to models of
unsupervised learning in ReLU neural networks.
Deep learning
Deep neural networks provide stateoftheart performance in many tasks,
but the representations they learn are largely inscrutable.
To learn more interpretable representations, we may need to reexamine
the mathematical foundations of deep learning, particularly the
types of nonlinearities and loss functions that are commonly used for training.
Latent variable modeling
Many types of structure in high dimensional data can be modeled via a smaller
number of latent variables. An ongoing project is to discover new and richer latent
variable models in which exact probabilistic inference remains
tractable.
Recent papers

L. K. Saul (2022).
A nonlinear matrix decomposition for mining the zeros of sparse data.
SIAM Journal of Mathematics of Data Science 4(2):431463.
PDF

L. K. Saul (2021). An online passiveaggressive algorithm for differenceofsquares classification.
In M. A. Ranzato, A. Beygelzimer, Y. N. Dauphin, P. Liang, and J. W. Vaughan (eds.),
Advances in Neural Information Processing Systems 34,
pages 2142621439.
PDF

L. K. Saul (2021). An EM algorithm for capsule regression. Neural Computation 33(1):194226
PDF

L. K. Saul (2020). A tractable latent variable model for nonlinear dimensionality reduction.
Proceedings of the National Academy of Sciences USA 117(27):1540315408.
PDF
Older (representative) papers

D.K. Kim, G. Voelker, L. K. Saul (2013).
A variational approximation for topic modeling of hierarchical corpora.
Proceedings of the 30th International Conference on Machine Learning (ICML13),
pages 5563.
PDF

Y. Cho and L. K. Saul (2009).
Kernel methods for deep learning.
In Y. Bengio, D. Schuurmans, J. Lafferty, C. Williams, and A. Culotta (eds.),
Advances in Neural Information Processing Systems 22, pages 342350.
PDF

K. Q. Weinberger and L. K. Saul (2009).
Distance metric learning for large margin nearest neighbor classification.
Journal of Machine Learning Research 10:207244.
PDF

F. Sha, Y. Lin, L. K. Saul, and D. D. Lee (2007).
Multiplicative updates for nonnegative quadratic programming.
Neural Computation 19(8):20042031.
PDF

K. Q. Weinberger and L. K. Saul (2006).
Unsupervised learning of image manifolds by semidefinite programming.
International Journal of Computer Vision 70(1):7790.
PDF
 S. T. Roweis and L. K. Saul (2000).
Nonlinear dimensionality reduction by locally linear embedding.
Science 290:23232326.
PDF
 M. I. Jordan and Z. Ghahramani and T. S. Jaakkola and L. K. Saul (1999).
An introduction to variational methods for graphical models.
Machine Learning 37:183233.
PDF
All papers