User dohmatob

30 votes

1 answer

1k views

Functional-analytic proof of the existence of non-symmetric random variables with vanishing odd moments

asked Feb 9, 2021 at 15:52

15 votes

2 answers

2k views

Categorification of probability theory: what does a "probability sheaf" tell us (if anything) about probability theory?

asked Jun 7, 2020 at 19:10

14 votes

1 answer

918 views

So after all, what is this thing about topos theory and non-binary truth?

asked Mar 12, 2021 at 14:37

13 votes

1 answer

2k views

Minimize sum of $\ell_2$ norm and linear combination, on simplex

asked Dec 5, 2015 at 21:12

12 votes

0 answers

650 views

Understanding a certain algebraic set arising in Deep Learning

asked Nov 6, 2018 at 19:53

12 votes

1 answer

1k views

Making sense of "every non-commutative algebra has its own internal time evolution (aka a one-parameter group)"?

asked Mar 14, 2021 at 19:17

12 votes

5 answers

1k views

Examples of metric spaces with measurable midpoints

asked Jun 22, 2020 at 8:52

11 votes

2 answers

1k views

Low-degree polynomial approximation of the piecewise-linear function $x \mapsto \max(x, 0)$ on an interval $x \in [-R,R]$

asked Jul 8, 2019 at 19:55

9 votes

2 answers

891 views

When is a mapping the proximity operator of some convex function?

asked May 17, 2016 at 21:21

8 votes

2 answers

1k views

VC dimension, fat-shattering dimension, and other complexity measures, of a class BV functions

asked Jul 30, 2018 at 17:37

8 votes

2 answers

941 views

Approximation of Wasserstein distance between $p_\theta$ and $p_{\theta + d\theta}$

asked Aug 9, 2018 at 14:06

7 votes

1 answer

384 views

Transportation-cost inequality for pushforward measure

asked Sep 3, 2018 at 0:00

7 votes

4 answers

455 views

What does $\mathbb E_V \max_{x \in V,\,\|x\|=1} x^T Ax$ evaluate to when $V$ is random $k$-dim suspace of $\mathbb R^n$ and $A$ is fixed psd matrix?

asked Dec 21, 2021 at 20:05

6 votes

0 answers

338 views

Atiyah–Singer Index theorem for the pedestrian / layperson

asked Jan 8, 2022 at 22:08

6 votes

3 answers

417 views

Isoperimetric inequality for $\epsilon$-expansion of a set only along a certain subspace

asked Dec 1, 2021 at 23:42

6 votes

1 answer

198 views

Good upper-bound for $\mathbb E[|X-np|^r]$ where $X \sim \text{Binomial}(n,p)$ and $r \ge 1$

asked May 27, 2019 at 10:29

5 votes

3 answers

5k views

Distribution of the individual coordinates of a uniform random vector on a high-dimensional sphere

asked Nov 13, 2018 at 11:58

5 votes

1 answer

837 views

Hausdorff distance is a lower (or upper bound) for what probability metric?

asked Sep 8, 2018 at 19:41

5 votes

1 answer

230 views

General distributions with the "transportation-cost inequality" property to piece log-concave distributions

asked Aug 29, 2018 at 14:29

5 votes

2 answers

715 views

Factorization of a Markov chain as the product of smaller chains

asked Mar 13, 2017 at 16:01

5 votes

0 answers

249 views

Eigenvalues of a certain product of matrices with special structure

asked Oct 5, 2015 at 7:43

5 votes

1 answer

520 views

Conditions for the support function of ellipsoid to define a norm

asked May 29, 2017 at 11:59

5 votes

3 answers

605 views

What quantities are conserved under a general gradient-flow $\dot X(t) = -\nabla L(X(t))$?

asked Oct 30, 2020 at 18:55

5 votes

0 answers

128 views

What kinds of gradient-flows on $\mathbb R^d$ preserve the log-concavity of the distribution $\mu_0$ of starting point $x_0$

asked Nov 29, 2020 at 17:24

4 votes

0 answers

207 views

Fréchet subdifferentiation on riemannian manifolds

asked Nov 17, 2020 at 2:11

4 votes

3 answers

625 views

Quick derivation of classical probability theory from von Neumann algebraic framework

asked Feb 22, 2021 at 10:15

4 votes

2 answers

167 views

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 $a^\top b = 0$

asked Apr 14, 2021 at 8:51

4 votes

1 answer

147 views

When does a gaussian quadratic form converge (in probability) to a constant?

asked Sep 22, 2020 at 11:49

4 votes

0 answers

105 views

Upper bound $\tau_C := \int_{\|x\| \le 1}(vol(C \cap (x + C))/vol(C))dx$ for a convex body $C \subseteq \mathbb R^n$, by reducing to a ball

asked May 26, 2020 at 23:14

4 votes

0 answers

550 views

Optimal transport between two distributions in a Markov chain

asked Aug 21, 2017 at 19:16

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250 Questions

Functional-analytic proof of the existence of non-symmetric random variables with vanishing odd moments

Categorification of probability theory: what does a "probability sheaf" tell us (if anything) about probability theory?

So after all, what is this thing about topos theory and non-binary truth?

Minimize sum of $\ell_2$ norm and linear combination, on simplex

Understanding a certain algebraic set arising in Deep Learning

Making sense of "every non-commutative algebra has its own internal time evolution (aka a one-parameter group)"?

Examples of metric spaces with measurable midpoints

Low-degree polynomial approximation of the piecewise-linear function $x \mapsto \max(x, 0)$ on an interval $x \in [-R,R]$

When is a mapping the proximity operator of some convex function?

VC dimension, fat-shattering dimension, and other complexity measures, of a class BV functions

Approximation of Wasserstein distance between $p_\theta$ and $p_{\theta + d\theta}$

Transportation-cost inequality for pushforward measure

What does $\mathbb E_V \max_{x \in V,\,\|x\|=1} x^T Ax$ evaluate to when $V$ is random $k$-dim suspace of $\mathbb R^n$ and $A$ is fixed psd matrix?

Atiyah–Singer Index theorem for the pedestrian / layperson

Isoperimetric inequality for $\epsilon$-expansion of a set only along a certain subspace

Good upper-bound for $\mathbb E[|X-np|^r]$ where $X \sim \text{Binomial}(n,p)$ and $r \ge 1$

Distribution of the individual coordinates of a uniform random vector on a high-dimensional sphere

Hausdorff distance is a lower (or upper bound) for what probability metric?

General distributions with the "transportation-cost inequality" property to piece log-concave distributions

Factorization of a Markov chain as the product of smaller chains

Eigenvalues of a certain product of matrices with special structure

Conditions for the support function of ellipsoid to define a norm

What quantities are conserved under a general gradient-flow $\dot X(t) = -\nabla L(X(t))$?

What kinds of gradient-flows on $\mathbb R^d$ preserve the log-concavity of the distribution $\mu_0$ of starting point $x_0$

Fréchet subdifferentiation on riemannian manifolds

Quick derivation of classical probability theory from von Neumann algebraic framework

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 $a^\top b = 0$

When does a gaussian quadratic form converge (in probability) to a constant?

Upper bound $\tau_C := \int_{\|x\| \le 1}(vol(C \cap (x + C))/vol(C))dx$ for a convex body $C \subseteq \mathbb R^n$, by reducing to a ball

Optimal transport between two distributions in a Markov chain