## Seminar Categories

This page lists seminar series that have events scheduled between two months ago and twelve months from now and have speaker information available.

## Current Series

Mon Mar 29 |
## Applied and Computational Mathematics Seminar3:35pm - via ZoomTheoretical guarantees of machine learning methods for statistical sampling and PDEs in high dimensions Yulong Lu, University of Massachusetts, Amherst Neural network-based machine learning methods, including the most In this talk, I will demonstrate the power of neural network methods |

Mon Apr 12 |
## Applied and Computational Mathematics Seminar3:35pm - via ZoomGraph-based Bayesian semi-supervised learning: prior design and posterior contraction. Daniel Sanz-Alonso, University of Chicago In this talk I will introduce graphical representations of stochastic partial differential equations that allow to approximate Matern Gaussian fields on manifolds and generalize the Matern model to abstract point clouds. Under a manifold assumption, approximation error guarantees will be established building on the theory of spectral convergence of graph Laplacians. Graph-based Matern prior models facilitate computationally efficient inference and sampling exploiting sparsity of the precision matrix. Moreover, we will show that they are natural priors for Bayesian semi-supervised learning and can give optimal posterior contraction. This is joint work with Ruiyi Yang. |

Mon Apr 26 |
## Applied and Computational Mathematics Seminar3:35pm - via ZoomApplied math colloquium Prof. Anne Gelb, Dartmouth College TBD |

Mon May 03 |
## Applied and Computational Mathematics Seminar3:35pm - Via ZoomGeneralization Bounds for Sparse Random Feature Expansions Hayden Schaeffer, Carnegie Mellon University "Random feature methods have been successful in various machine learning tasks, are easy to compute, and come with theoretical accuracy bounds. They serve as an alternative approach to standard neural networks since they can represent similar function spaces without a costly training phase. However, for accuracy, random feature methods require more measurements than trainable parameters, limiting their use for data-scarce applications or problems in scientific machine learning. This paper introduces the sparse random feature expansion via sparse features which promotes parsimonious random feature expansions. The sparse random feature expansion uses random features with $\ell^1$ optimization to generate approximations with theoretical guarantees. In particular, we provide uniform bounds on the approximation error and generalization bounds for functions in a certain class depending on the number of samples and the distribution of features. The error bounds improve with additional structural conditions, such as coordinate sparsity, compact clusters of the spectrum, or rapid spectral decay. In particular, by introducing sparse features, i.e. features with random sparse weights, we provide improved bounds for low order functions. We show that the sparse random feature expansions outperforms shallow networks in several scientific machine learning tasks." |