Tootfinder

Cokernels of random matrix products and flag Cohen--Lenstra heuristic
Yifeng Huang
https://arxiv.org/abs/2403.09909 https://arxiv.org…

Cokernels of random matrix products and flag Cohen--Lenstra heuristic
In [NVP22], Nguyen and Van Peski raised the question of whether the surjective flag of $\mathbb Z_p$-modules modeled by $\mathrm{cok}(M_1\cdots M_k)\twoheadrightarrow \dots\twoheadrightarrow \mathrm{cok}(M_1)$ for independent random matrices $M_1,\dots,M_k\in \mathrm{Mat}_n(\mathbb Z_p)$ satisfies the Cohen--Lenstra heuristic. We answer the question affirmatively when $M_1,\dots,M_k$ follow the Haar measure, and our proof demonstrates how classical ideas in Cohen--Lenstra heuristic adapt natura…

Does anyone have any ideas or hypothesis why Shortcuts show up only sometimes in the iPhone searches?
There are times when Shortcuts show up. There are times when they do not. It is completely random. Not showing up is the more frequent result though.
(I'd appreciate any ideas or reposting to get answers. Thank you)

This https://arxiv.org/abs/2312.10881 has been replaced.
link: https://scholar.google.com/scholar?q=a

Dirac walks on regular trees
The study of matter fields on an ensemble of random geometries is a difficult problem still in need of new methods and ideas. We will follow a point of view inspired by probability theory techniques that relies on an expansion of the two point function as a sum over random walks. An analogous expansion for Fermions on non-Euclidean geometries is still lacking. Casiday et al. [\textit{Laplace and Dirac operators on graphs}, Linear and Multilinear Algebra (2022) 1] proposed a classical "Dirac wal…

Hunter's positivity theorem and random vector norms
Ludovick Bouthat, \'Angel Ch\'avez, Stephan Ramon Garcia
https://arxiv.org/abs/2403.10314 h…

Hunter's positivity theorem and random vector norms
A theorem of Hunter ensures that the complete homogeneous symmetric polynomials of even degree are positive definite functions. A probabilistic interpretation of Hunter's theorem suggests a broad generalization: the construction of so-called random vector norms on square complex matrices. This paper surveys these ideas, starting from the fundamental notions and developing the theory to its present state. We study numerous examples and present a host of open problems.

This https://arxiv.org/abs/2206.13090 has been replaced.
link: https://scholar.google.com/scholar?q=a

Variance Reduced Random Relaxed Projection Method for Constrained Finite-sum Minimization Problems
For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to efficiently solve this problem. Compared with existing RPMs, our proposed algorithm features two useful algorithmic ideas. First, at each iteration, instead of projecting onto the subset defined by one of the constraints, our algorithm only requires projecti…

Probabilistic Easy Variational Causal Effect
Usef Faghihi, Amir Saki
https://arxiv.org/abs/2403.07745 https://arxiv.org/pdf/2403.0774…

Probabilistic Easy Variational Causal Effect
Let $X$ and $Z$ be random vectors, and $Y=g(X,Z)$. In this paper, on the one hand, for the case that $X$ and $Z$ are continuous, by using the ideas from the total variation and the flux of $g$, we develop a point of view in causal inference capable of dealing with a broad domain of causal problems. Indeed, we focus on a function, called Probabilistic Easy Variational Causal Effect (PEACE), which can measure the direct causal effect of $X$ on $Y$ with respect to continuously and interventionally…

This https://arxiv.org/abs/2312.11428 has been replaced.
link: https://scholar.google.com/scholar?q=a

Random surfaces with large systoles
We present two constructions, both inspired by ideas from graph theory, of sequences random surfaces of growing area, whose systoles grow logarithmically as a function of their area. This also allows us to prove a new lower bound on the maximal systole of a closed orientable hyperbolic surface of a given genus.

This https://arxiv.org/abs/2210.03859 has been replaced.
link: https://scholar.google.com/scholar?q=a

Spectrally-Corrected and Regularized Linear Discriminant Analysis for Spiked Covariance Model
This paper proposes an improved linear discriminant analysis called spectrally-corrected and regularized LDA (SRLDA). This method integrates the design ideas of the sample spectrally-corrected covariance matrix and the regularized discriminant analysis. With the support of a large-dimensional random matrix analysis framework, it is proved that SRLDA has a linear classification global optimal solution under the spiked model assumption. According to simulation data analysis, the SRLDA classifier …

Provably Stable Feature Rankings with SHAP and LIME
Jeremy Goldwasser, Giles Hooker
https://arXiv.org/abs/2401.15800 https://arXiv.or…

Provably Stable Feature Rankings with SHAP and LIME
Feature attributions are ubiquitous tools for understanding the predictions of machine learning models. However, popular methods for scoring input variables such as SHAP and LIME suffer from high instability due to random sampling. Leveraging ideas from multiple hypothesis testing, we devise attribution methods that correctly rank the most important features with high probability. Our algorithm RankSHAP guarantees that the $K$ highest Shapley values have the proper ordering with probability exc…