Monday, February 5, 2018 - 22:10 , Location: skiles 005 , Riccardo Montalto , University of Zurich , Organizer: Livia Corsi
In this talk I will present some results concerning the existence and the stability of quasi-periodic solutions for quasi-linear and fully nonlinear PDEs. In particular, I will focus on the Water waves equation. The proof is based on a Nash-moser iterative scheme and on the reduction to constant coefficients of the linearized PDE at any approximate solution. Due to the non-local nature of the water waves equation, such a reduction procedure is achieved by using techniques from Harmonic Analysis and microlocal analysis, like Fourier integral operators and Pseudo differential operators.
Monday, February 5, 2018 - 11:15 , Location: Skiles 005 , Renato Iturriaga , CIMAT , Organizer: Livia Corsi
Series: ACO Student Seminar
Physical sensors (thermal, light, motion, etc.) are becoming ubiquitous and offer important benefits to society. However, allowing sensors into our private spaces has resulted in considerable privacy concerns. Differential privacy has been developed to help alleviate these privacy concerns. In this talk, we’ll develop and define a framework for releasing physical data that preserves both utility and provides privacy. Our notion of closeness of physical data will be defined via the Earth Mover Distance and we’ll discuss the implications of this choice. Physical data, such as temperature distributions, are often only accessible to us via a linear transformation of the data. We’ll analyse the implications of our privacy definition for linear inverse problems, focusing on those that are traditionally considered to be "ill-conditioned”. We’ll then instantiate our framework with the heat kernel on graphs and discuss how the privacy parameter relates to the connectivity of the graph. Our work indicates that it is possible to produce locally private sensor measurements that both keep the exact locations of the heat sources private and permit recovery of the ``general geographic vicinity'' of the sources. Joint work with Anna C. Gilbert.
Series: Job Candidate Talk
The mean field variational inference is widely used in statistics and machine learning to approximate posterior distributions. Despite its popularity, there exist remarkably little fundamental theoretical justifications. The success of variational inference mainly lies in its iterative algorithm, which, to the best of our knowledge, has never been investigated for any high-dimensional or complex model. In this talk, we establish computational and statistical guarantees of mean field variational inference. Using community detection problem as a test case, we show that its iterative algorithm has a linear convergence to the optimal statistical accuracy within log n iterations. We are optimistic to go beyond community detection and to understand mean field under a general class of latent variable models. In addition, the technique we develop can be extended to analyzing Expectation-maximization and Gibbs sampler.
Wednesday, January 31, 2018 - 13:55 , Location: Skiles 005 , Amalia Culiuc , Georgia Tech , firstname.lastname@example.org , Organizer: Galyna Livshyts
An overarching problem in matrix weighted theory is the so-called A2 conjecture, namely the question of whether the norm of a Calderón-Zygmund operator acting on a matrix weighted L2 space depends linearly on the A2 characteristic of the weight. In this talk, I will discuss the history of this problem and provide a survey of recent results with an emphasis on the challenges that arise within the setup.