The Discrete Fourier Transform (DFT) is one of the most important operators in computational mathematics.The DFT operator acts on the n-dimenional Hilbert Space of complex valued functions on the group of integers modulo-n. It becames very useful in the last century due to the Cooley–Tukey algorithm that computes this transform …
Given the proliferation of wireless communication devices, the need for increased power and bandwidth efficiencyin emerging technologies is getting ever more pronounced. Two echnological trends offer new opportunities for addressing these challenges: mm-wave systems (60-100GHz) that afford large bandwidths, and multi-antenna (MIMO) transceivers that exploit the spatial dimension. In particular, …
Phase retrieval is the recovery of signals from Fourier transform magnitude with wide applications in crystallography, microscopy, optics, and astronomy. Although a unique solution almost always exists for two or higher dimensional signals, there is no known algorithm with guaranteed recovery. An iterative algorithm for recovering nonnegative real signals, based …
For functions acquired through point evaluations, is there an optimal way to estimate a quantity of interest or even to approximate the functions in full? We give an affirmative answer to this question under the novel assumption that the functions belong to a model set defined by approximation capabilities. In …
Pregnancy loss is a primary limit on human reproduction and a key driver of population dynamics. It is also very difficult to study. 85% of pregnancy loss happens prior to clinical interaction. We use information from over a million users of a fertility tracking application to construct estimates of pregnancy …
Entity matching (EM) finds data instances that refer to the same real-world entity. In 2015, we started the Magellan project at UW-Madison to build EM systems. Most current EM systems are stand-alone monoliths. In contrast, Magellan borrows ideas from the field of data science (DS), to build a novel kind …
Given a data set $\mathcal{X}=\{x_1, \dots, x_n\}$ and a weighted graph structure $\Gamma= (\mathcal{X},W)$ on $\mathcal{X}$, graph based methods for learning use analytical notions like graph Laplacians, graph cuts, and Sobolev semi-norms to formulate optimization problems whose solutions serve as sensible approaches to machine learning tasks. When the data set …
In this talk, we present recent progress towards developing learning-based control strategies for the design of safe and robust autonomous systems. Our approach is to recognize that machine learning algorithms produce inherently uncertain estimates or predictions, and that this uncertainty must be explicitly quantified (e.g., using non-asymptotic guarantees of contemporary …
The bulk of research in psychology and neuroscience has focused on studying processes within single individuals. However, outside of the laboratory people rarely operate independently but rather in the context of a complex constellation of social relationships. Social interactions form a critical aspect of the human experience from romantic relationships, …
In many limited budget experimental settings, such as A/B testing or Protein design, there is a need for adaptive sampling to guide the discovery of as many true positives as possible subject to a low rate of false discoveries (i.e. false alarms). Like active learning for binary classification, this experimental …