User dohmatob

1 vote

Prove / disprove: If $1 \le n < N$ and $A$ is an $N \times n$ matrix with iid from $\mathcal N(0,1)$, then $s_\min(A) \ge c\sqrt{N}$ w.p $1-2e^{-N}$

answered Sep 19, 2020 at 23:22

1 vote

Bounds for the extreme singular-values of random matrix with thresholded entries

answered Feb 23, 2021 at 3:31

1 vote

Limiting eigenvalue distribution of $YY^\top$ where $Y_{ij} = X_{ij} + a$ and $X$ has iid rows from an isotropic log-concave distribution

answered Mar 9, 2021 at 21:05

1 vote

Accepted

Simple non-asymptotic upper-bound for packing number of a hamming cube

answered Mar 22, 2021 at 12:50

1 vote

Almost independence of $x^\top a$ and $x^\top b$ for $x$ uniform on the sphere in $\mathbb R^d$ and $a,b \in \mathbb R^d$ with $a^\top b = 0$

answered Apr 14, 2021 at 17:27

1 vote

Use statistical physics ideas ("replica trick") to compute asymptotic value of $\inf_{\|w\| \le r} (1/n)\|Xw-y\|^2$ for random $X$ and $y$

answered Jun 2, 2021 at 23:16

1 vote

Express Dirichlet energy $E_\mu(f) := \int \|\nabla f(x)\|^2 d\mu(x)$ in terms of Fourier information alone

answered Jun 25, 2021 at 14:55

1 vote

Accepted

Relationship between volume and area

answered Jun 17, 2020 at 18:46

1 vote

Anti-concentration of Gaussian quadratic form

answered Aug 16, 2020 at 7:54

1 vote

Accepted

How to sample a path between 2 states in a Markov chain

answered Aug 17, 2017 at 12:10

1 vote

Accepted

Non-asymptotic tail bounds for $D_{\text{Hellinger}}(P\|\hat{P}_N)$

answered Nov 25, 2018 at 20:12

1 vote

Practical bounds for the Wasserstein distance in 2 dimensions

answered Dec 5, 2018 at 0:10

1 vote

Accepted

Anti-concentration: upper bound for $P(\sup_{a \in \mathbb S_{n-1}}\sum_{i=1}^na_i^2Z_i^2 \ge \epsilon)$

answered Jan 7, 2019 at 1:42

1 vote

Use covering number to get uniform concentration from pointwise concentration

answered Feb 1, 2019 at 6:54

1 vote

Isoperimetry on $[0, 1]^n$ w.r.t $\ell_p$ distance, with $p \in [1,\infty]$

answered May 28, 2019 at 6:13

1 vote

Estimating the shift in the $\lambda_{\max}$ of a matrix under a diagonal perturbation

answered Aug 30, 2015 at 11:23

1 vote

Accepted

Upper bound for $\mathbb P(|f(A+XX^T)-f(A)| > \epsilon)$, where $A$ is a fixed pd matrix and $X$ has random iid entries

answered Jun 10, 2020 at 17:24

1 vote

Mathematics of doodling and the winding number

answered Jun 12, 2020 at 17:04

0 votes

Lower bound for sum of binomial coefficients?

answered Aug 31, 2020 at 12:24

0 votes

How to prove that a Brownian bridge $\mathbb{P}(M[0, 1/2]\geq s)\leq 2\mathbb{P}(B(1/2)\geq s/2)?$

answered Jun 13, 2020 at 11:20

0 votes

Sum of Square of the Eigenvalues of Wishart Matrix

answered Jun 29, 2021 at 12:31

0 votes

Wasserstein distance between $N(0,1/d)$ and the marginal distribution of $x_1$ when $x=(x_1,\ldots,x_d)$ is uniform on the unit-sphere in $R^d$

answered Aug 12, 2021 at 11:12

0 votes

Concentration inequality for norm of solution to nonlinear least-squares problem

answered Jan 13, 2021 at 15:51

0 votes

Approximate the singular values of a certain random dot-product kernel matrix (in the sense of El Karoui, Cheng-Singer, etc.)

answered Oct 8, 2021 at 18:20

0 votes

Integral of product of Hermite polynomials w.r.t marginal distribution of first two-coordinate of random vector on unit-sphere

answered Oct 11, 2021 at 12:04

0 votes

Lower-bound on zero-crossing probability of the nonstationary gaussian process $X(t) = tU+(1-t^2)^{1/2}V$, with $(U,V) \sim N(0,I_2)$

answered Oct 24, 2021 at 7:16

0 votes

Given iid $w_1,\ldots,w_N \sim N(0,1/d)$ iid, find a simple matrix $A$ s.t $\|aa^T-A\|_{op} \to 0$, where $a_i := E_{G \sim N(0,1)}[f(\|w_i\| G)]$

answered Nov 26, 2021 at 15:01

0 votes

High-probability lower bound for norm of least squares solution when both design matrix $X$ and response vector $y$ are random (and independent)

answered Mar 7, 2021 at 14:44

0 votes

VC dimension of a certain derived class of binary functions

answered Apr 16, 2022 at 12:29

0 votes

Rademacher complexity of function class $\{(x,y) \mapsto 1[|yf(x)-\alpha| \ge \beta]$ in terms of $\alpha$, $\beta$, and Rademacher complexity of $F$

answered Apr 16, 2022 at 13:34

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68 Answers

Prove / disprove: If $1 \le n < N$ and $A$ is an $N \times n$ matrix with iid from $\mathcal N(0,1)$, then $s_\min(A) \ge c\sqrt{N}$ w.p $1-2e^{-N}$

Bounds for the extreme singular-values of random matrix with thresholded entries

Limiting eigenvalue distribution of $YY^\top$ where $Y_{ij} = X_{ij} + a$ and $X$ has iid rows from an isotropic log-concave distribution

Simple non-asymptotic upper-bound for packing number of a hamming cube

Almost independence of $x^\top a$ and $x^\top b$ for $x$ uniform on the sphere in $\mathbb R^d$ and $a,b \in \mathbb R^d$ with $a^\top b = 0$

Use statistical physics ideas ("replica trick") to compute asymptotic value of $\inf_{\|w\| \le r} (1/n)\|Xw-y\|^2$ for random $X$ and $y$

Express Dirichlet energy $E_\mu(f) := \int \|\nabla f(x)\|^2 d\mu(x)$ in terms of Fourier information alone

Relationship between volume and area

Anti-concentration of Gaussian quadratic form

How to sample a path between 2 states in a Markov chain

Non-asymptotic tail bounds for $D_{\text{Hellinger}}(P\|\hat{P}_N)$

Practical bounds for the Wasserstein distance in 2 dimensions

Anti-concentration: upper bound for $P(\sup_{a \in \mathbb S_{n-1}}\sum_{i=1}^na_i^2Z_i^2 \ge \epsilon)$

Use covering number to get uniform concentration from pointwise concentration

Isoperimetry on $[0, 1]^n$ w.r.t $\ell_p$ distance, with $p \in [1,\infty]$

Estimating the shift in the $\lambda_{\max}$ of a matrix under a diagonal perturbation

Upper bound for $\mathbb P(|f(A+XX^T)-f(A)| > \epsilon)$, where $A$ is a fixed pd matrix and $X$ has random iid entries

Mathematics of doodling and the winding number

Lower bound for sum of binomial coefficients?

How to prove that a Brownian bridge $\mathbb{P}(M[0, 1/2]\geq s)\leq 2\mathbb{P}(B(1/2)\geq s/2)?$

Sum of Square of the Eigenvalues of Wishart Matrix

Wasserstein distance between $N(0,1/d)$ and the marginal distribution of $x_1$ when $x=(x_1,\ldots,x_d)$ is uniform on the unit-sphere in $R^d$

Concentration inequality for norm of solution to nonlinear least-squares problem

Approximate the singular values of a certain random dot-product kernel matrix (in the sense of El Karoui, Cheng-Singer, etc.)

Integral of product of Hermite polynomials w.r.t marginal distribution of first two-coordinate of random vector on unit-sphere

Lower-bound on zero-crossing probability of the nonstationary gaussian process $X(t) = tU+(1-t^2)^{1/2}V$, with $(U,V) \sim N(0,I_2)$

Given iid $w_1,\ldots,w_N \sim N(0,1/d)$ iid, find a simple matrix $A$ s.t $\|aa^T-A\|_{op} \to 0$, where $a_i := E_{G \sim N(0,1)}[f(\|w_i\| G)]$

High-probability lower bound for norm of least squares solution when both design matrix $X$ and response vector $y$ are random (and independent)

VC dimension of a certain derived class of binary functions

Rademacher complexity of function class $\{(x,y) \mapsto 1[|yf(x)-\alpha| \ge \beta]$ in terms of $\alpha$, $\beta$, and Rademacher complexity of $F$