Lawrence Saul

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 research focuses on high dimensional data analysis, latent variable modeling, kernel methods, and deep learning. 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 Editor-in-Chief 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.


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.

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.

Deep learning

The distributed representations in deep neural nets are induced by the nonlinearities (e.g., ReLU) at each layer of processing. The effectiveness of these nonlinearities can be studied in layerwise models of unsupervised learning.

Recent Papers

  1. L. K. Saul (2022). A nonlinear matrix decomposition for mining the zeros of sparse data. SIAM Journal of Mathematics of Data Science 4(2):431-463. PDF
  2. L. K. Saul (2021). An online passive-aggressive algorithm for difference-of-squares classification. In M. A. Ranzato, A. Beygelzimer, Y. N. Dauphin, P. Liang, and J. W. Vaughan (eds.), Advances in Neural Information Processing Systems 34: Proceedings of the Conference on Neural Information Processing Systems (NeuRIPS-2021), pages 21426-21439. PDF
  3. L. K. Saul (2021). An EM algorithm for capsule regression. Neural Computation 33(1):194-226 PDF
  4. L. K. Saul (2020). A tractable latent variable model for nonlinear dimensionality reduction. Proceedings of the National Academy of Sciences USA 117(27):15403-15408. PDF

All Papers