REVIEW 5 cited by
Generic and lifted probabilistic comparisons -- max replaces minmax
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original abstract
In this paper we introduce a collection of powerful statistical comparison results. We first present the results that we obtained while developing a general comparison concept. After that we introduce a separate lifting procedure that is a comparison concept on its own. We then show how in certain scenarios the lifting procedure basically represents a substantial upgrade over the general strategy. We complement the introduced results with a fairly large collection of numerical experiments that are in an overwhelming agreement with what the theory predicts. We also show how many well known comparison results (e.g. Slepian's max and Gordon's minmax principle) can be obtained as special cases. Moreover, it turns out that the minmax principle can be viewed as a single max principle as well. The range of applications is enormous. It starts with revisiting many of the results we created in recent years in various mathematical fields and recognizing that they are fully self-contained as their starting blocks are specialized variants of the concepts introduced here. Further upgrades relate to core comparison extensions on the one side and more practically oriented modifications on the other. Those that we deem the most important we discuss in several separate companion papers to ensure preserving the introductory elegance and simplicity of what is presented here.
Forward citations
Cited by 5 Pith papers
-
Precise sample covariance spectral norm error -- an RDT view
For Gaussian data in the proportional limit, the spectral-norm error of the sample covariance converges to γ̂√φ1/(√φ1−√α), with γ̂ solving an equation in the covariance spectrum.
-
An RDT based approach to large deviations of Wishart and Wigner matrices spectral edges
Develops an RDT-based LDP framework for spectral edges of Wishart and Wigner matrices matching prior Coulomb gas results.
-
Deep ReLU networks -- injectivity capacity upper bounds
For deep ReLU networks with random Gaussian weights, the paper gives upper bounds on the layer expansion needed for injectivity and finds the expansion need saturates by four layers.
-
A CLuP algorithm to practically achieve $\sim 0.76$ SK--model ground state free energy
The authors propose a CLuP-SK barrier-descent algorithm and report it achieves approximately 0.76 of the SK ground state free energy for n around 2000 to 8000, approaching the theoretical Parisi limit of about 0.763.
- Optimal spectral initializers impact on phase retrieval phase transitions -- an RDT view
Discussion (0). Continue with ORCID to comment.