`

Timezone: »

 
Poster
The Generalized Lasso with Nonlinear Observations and Generative Priors
Zhaoqiang Liu · Jonathan Scarlett

Mon Dec 07 09:00 PM -- 11:00 PM (PST) @ Poster Session 0 #67
In this paper, we study the problem of signal estimation from noisy non-linear measurements when the unknown $n$-dimensional signal is in the range of an $L$-Lipschitz continuous generative model with bounded $k$-dimensional inputs. We make the assumption of sub-Gaussian measurements, which is satisfied by a wide range of measurement models, such as linear, logistic, 1-bit, and other quantized models. In addition, we consider the impact of adversarial corruptions on these measurements. Our analysis is based on a generalized Lasso approach (Plan and Vershynin, 2016). We first provide a non-uniform recovery guarantee, which states that under i.i.d.~Gaussian measurements, roughly $O\left(\frac{k}{\epsilon^2}\log L\right)$ samples suffice for recovery with an $\ell_2$-error of $\epsilon$, and that this scheme is robust to adversarial noise. Then, we apply this result to neural network generative models, and discuss various extensions to other models and non-i.i.d.~measurements. Moreover, we show that our result can be extended to the uniform recovery guarantee under the assumption of a so-called local embedding property, which is satisfied by the 1-bit and censored Tobit models.

Author Information

Zhaoqiang Liu (National University of Singapore)
Jonathan Scarlett (National University of Singapore)

More from the Same Authors

  • 2021 Poster: Towards Sample-Optimal Compressive Phase Retrieval with Sparse and Generative Priors »
    Zhaoqiang Liu · Subhroshekhar Ghosh · Jonathan Scarlett
  • 2019 : Poster Session »
    Jonathan Scarlett · Piotr Indyk · Ali Vakilian · Adrian Weller · Partha P Mitra · Benjamin Aubin · Bruno Loureiro · Florent Krzakala · Lenka Zdeborová · Kristina Monakhova · Joshua Yurtsever · Laura Waller · Hendrik Sommerhoff · Michael Moeller · Rushil Anirudh · Shuang Qiu · Xiaohan Wei · Zhuoran Yang · Jayaraman Thiagarajan · Salman Asif · Michael Gillhofer · Johannes Brandstetter · Sepp Hochreiter · Felix Petersen · Dhruv Patel · Assad Oberai · Akshay Kamath · Sushrut Karmalkar · Eric Price · Ali Ahmed · Zahra Kadkhodaie · Sreyas Mohan · Eero Simoncelli · Carlos Fernandez-Granda · Oscar Leong · Wesam Sakla · Rebecca Willett · Stephan Hoyer · Jascha Sohl-Dickstein · Samuel Greydanus · Gauri Jagatap · Chinmay Hegde · Michael Kellman · Jonathan Tamir · Nouamane Laanait · Ousmane Dia · Mirco Ravanelli · Jonathan Binas · Negar Rostamzadeh · Shirin Jalali · Tiantian Fang · Alex Schwing · SĂ©bastien Lachapelle · Philippe Brouillard · Tristan Deleu · Simon Lacoste-Julien · Stella Yu · Arya Mazumdar · Ankit Singh Rawat · Yue Zhao · Jianshu Chen · Xiaoyang Li · Hubert Ramsauer · Gabrio Rizzuti · Nikolaos Mitsakos · Dingzhou Cao · Thomas Strohmer · Yang Li · Pei Peng · Gregory Ongie
  • 2019 Poster: Learning Erdos-Renyi Random Graphs via Edge Detecting Queries »
    Zihan Li · Matthias Fresacher · Jonathan Scarlett
  • 2018 Poster: Adversarially Robust Optimization with Gaussian Processes »
    Ilija Bogunovic · Jonathan Scarlett · Stefanie Jegelka · Volkan Cevher
  • 2018 Spotlight: Adversarially Robust Optimization with Gaussian Processes »
    Ilija Bogunovic · Jonathan Scarlett · Stefanie Jegelka · Volkan Cevher