no code implementations • 27 Feb 2024 • Michael Celentano, William S. DeWitt, Sebastian Prillo, Yun S. Song
Consequently, the computational cost is determined not by the size of the final simulated tree, but by the size of the population tree in which it is embedded.
no code implementations • 14 Nov 2023 • Michael Celentano, Zhou Fan, Licong Lin, Song Mei
In settings where it is conjectured that no efficient algorithm can find this local neighborhood, we prove analogous geometric properties for a local minimizer of the TAP free energy reachable by AMP, and show that posterior inference based on this minimizer remains correctly calibrated.
no code implementations • 5 Sep 2023 • Seunghoon Paik, Michael Celentano, Alden Green, Ryan J. Tibshirani
Maximum mean discrepancy (MMD) refers to a general class of nonparametric two-sample tests that are based on maximizing the mean difference over samples from one distribution $P$ versus another $Q$, over all choices of data transformations $f$ living in some function space $\mathcal{F}$.
no code implementations • 19 Aug 2022 • Michael Celentano
As an example of its use, we provide a new, and arguably simpler, proof of some of the results of Celentano et al. (2021), which establishes that the so-called TAP free energy in the $\mathbb{Z}_2$-synchronization problem is locally convex in the region to which AMP converges.
no code implementations • 21 Jun 2021 • Michael Celentano, Zhou Fan, Song Mei
This provides a rigorous foundation for variational inference in high dimensions via minimization of the TAP free energy.
no code implementations • 30 Mar 2021 • Michael Celentano, Theodor Misiakiewicz, Andrea Montanari
We study random features approximations to these norms and show that, for $p>1$, the number of random features required to approximate the original learning problem is upper bounded by a polynomial in the sample size.
no code implementations • 27 Jul 2020 • Michael Celentano, Andrea Montanari, Yuting Wei
On the other hand, the Lasso estimator can be precisely characterized in the regime in which both $n$ and $p$ are large and $n/p$ is of order one.
no code implementations • 28 Feb 2020 • Michael Celentano, Andrea Montanari, Yuchen Wu
These lower bounds are optimal in the sense that there exist algorithms whose estimation error matches the lower bounds up to asymptotically negligible terms.