no code implementations • 27 May 2024 • Ye He, Alireza Mousavi-Hosseini, Krishnakumar Balasubramanian, Murat A. Erdogdu
We study the complexity of heavy-tailed sampling and present a separation result in terms of obtaining high-accuracy versus low-accuracy guarantees i. e., samplers that require only $O(\log(1/\varepsilon))$ versus $\Omega(\text{poly}(1/\varepsilon))$ iterations to output a sample which is $\varepsilon$-close to the target in $\chi^2$-divergence.
no code implementations • 7 Mar 2023 • Alireza Mousavi-Hosseini, Tyler Farghly, Ye He, Krishnakumar Balasubramanian, Murat A. Erdogdu
We do so by establishing upper and lower bounds for Langevin diffusions and LMC under weak Poincar\'e inequalities that are satisfied by a large class of densities including polynomially-decaying heavy-tailed densities (i. e., Cauchy-type).
no code implementations • 29 Sep 2022 • Alireza Mousavi-Hosseini, Sejun Park, Manuela Girotti, Ioannis Mitliagkas, Murat A. Erdogdu
We further demonstrate that, SGD-trained ReLU NNs can learn a single-index target of the form $y=f(\langle\boldsymbol{u},\boldsymbol{x}\rangle) + \epsilon$ by recovering the principal direction, with a sample complexity linear in $d$ (up to log factors), where $f$ is a monotonic function with at most polynomial growth, and $\epsilon$ is the noise.
