User nullgeppetto

16 votes

1 answer

1k views

How to Prove the Semi-parametric Representer Theorem

hilbert-spaces

asked Jul 3, 2014 at 20:14

11 votes

2 answers

605 views

On the evaluation of the integral $\int_{-\frac{b}{a}}^{\frac{1-b}{a}}\log\left(ax+b\right)\exp\left(-\frac{1}{2}x^2\right)\mathrm{d}x$.

asked Oct 28, 2016 at 17:22

8 votes

2 answers

375 views

On visualizing the spaces $\Bbb{S}_{++}^n$ and $\Bbb{R}^n\times\Bbb{S}_{++}^n$ for $n=1,2,\ldots$

metric-spaces visualization

asked May 24, 2015 at 15:54

8 votes

2 answers

2k views

Optimization problem using Reproducing Kernel Hilbert Spaces

hilbert-spaces convex-optimization calculus-of-variations

asked Jun 19, 2014 at 19:37

8 votes

2 answers

12k views

Minimize the Frobenius norm of the difference of two matrices with respect to matrix: $\underset{B} {\mathrm{argmin}} \left\| A- B \right\|_F$

linear-algebra matrices optimization

asked Sep 26, 2014 at 12:41

8 votes

2 answers

4k views

Gaussian integrals over a half-space

integration

asked Nov 8, 2013 at 15:36

6 votes

0 answers

1k views

Rotating an $n$-dimensional hyperplane

rotations

asked Nov 11, 2013 at 11:40

6 votes

1 answer

317 views

On integrating a "gaussian-like" integral

integration

asked Nov 15, 2013 at 22:57

6 votes

1 answer

1k views

Expressing a quadratic form, $\mathbf{x}^TA\mathbf{x}$ in terms of $\lVert\mathbf{x}\rVert^2$, $A$

linear-algebra quadratic-forms matrix-decomposition

asked Jul 11, 2014 at 9:01

6 votes

3 answers

803 views

Optimal approximation of quadratic form

linear-algebra optimization eigenvalues-eigenvectors

asked Jun 29, 2015 at 12:26

6 votes

2 answers

173 views

Find $\lim_{x\to0}\frac{\sin\left(1-\frac{\sin(x)}{x}\right)}{x^2}$. Is my approach correct?

limits trigonometry

asked Dec 7, 2015 at 20:47

6 votes

2 answers

1k views

If $x\sim\mathcal{N}(\mu, \sigma^2)$, what is $E\left(\frac{\exp(x)}{a+\exp(x)}\right)$ for $a>0$?

probability random-variables normal-distribution expected-value

asked Sep 11, 2017 at 15:49

5 votes

2 answers

683 views

Volume of intersection of the $n$-ball with a hyperplane

euclidean-geometry volume

asked May 29, 2016 at 19:07

5 votes

1 answer

1k views

Reproducing Kernel Hilbert Space (RKHS) constructed by the summation of positive-definite kernels.

functional-analysis hilbert-spaces normed-spaces

asked Jul 30, 2014 at 18:30

5 votes

0 answers

172 views

Applying PCA on covariance matrix in order to generate a new random variable.

random-variables transformation covariance

asked Oct 23, 2014 at 15:13

5 votes

4 answers

3k views

Expected distance between two vectors that belong to two different Gaussian distributions

probability random-variables normal-distribution

asked Sep 2, 2014 at 17:56

5 votes

1 answer

90 views

Number of antipodal pairs of $n$-sphere points mapped to discrete points in $\mathbb{R}^n$

algebraic-topology

asked Jul 19, 2020 at 14:15

5 votes

0 answers

183 views

Find point of $n$-sphere after moving on geodesic by given angle

differential-geometry riemannian-geometry geodesic arc-length

asked Oct 18, 2020 at 3:14

4 votes

0 answers

103 views

Can a curve on $n$-sphere be uniquely defined by a "direction" vector?

soft-question manifolds riemannian-geometry noneuclidean-geometry

asked Oct 16, 2020 at 23:09

4 votes

1 answer

111 views

Diffeomorphism from $n$-cone to $\mathbb{R}^{n+1}$ -- parametric equation of geodesic?

differential-geometry geodesic diffeomorphism

asked Nov 11, 2020 at 20:05

4 votes

2 answers

159 views

On the convexity of a particular form of integrals

integration functional-analysis convex-analysis locally-convex-spaces

asked Apr 14, 2014 at 12:58

4 votes

2 answers

2k views

Expected value of the sign of a normal random variable

probability normal-distribution expectation

asked Nov 12, 2017 at 12:15

4 votes

1 answer

733 views

Estimation of the expected value of a function of a random variable

normal-distribution estimation sampling descriptive-statistics

asked Jan 19, 2017 at 11:11

4 votes

1 answer

3k views

Malalanobis distance between two multivariate Gaussian distributions

probability-distributions mahalanobis-distance

asked Jul 12, 2015 at 18:13

4 votes

1 answer

156 views

Help on the following indefinite integral: $\int\big(\sqrt{1-t^2}\big)^{n-1}\mathrm{d}t$

integration indefinite-integrals

asked Feb 3, 2015 at 12:55

3 votes

0 answers

295 views

Prove or disprove that the Bhattacharyya distance is a true distance function

probability-distributions metric-spaces normal-distribution

asked Jun 12, 2015 at 9:24

3 votes

1 answer

702 views

Integration over the intersection of the $n$-ball and a hyperplane

real-analysis integration multivariable-calculus

asked Feb 2, 2015 at 12:17

3 votes

4 answers

191 views

Prove that $\cos\left(\frac{2\pi}{n}\right)+\cos\left(\frac{4\pi}{n}\right)+\ldots+\cos\left(\frac{2(n-1)\pi}{n}\right)=-1$

induction roots-of-unity

asked Dec 10, 2015 at 14:28

3 votes

0 answers

154 views

Is $h(\mathbf{a},b)=\int_\Omega f(\mathbf{x})e^{-g(\mathbf{x})}\mathrm{d}\mathbf{x}$ differentiable?

real-analysis integration multivariable-calculus derivatives

asked Dec 12, 2015 at 18:02

3 votes

2 answers

4k views

Find the marginal distributions (PDFs) of a multivariate normal distribution

probability normal-distribution density-function

asked Nov 19, 2017 at 21:28

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87 Questions

How to Prove the Semi-parametric Representer Theorem

On the evaluation of the integral $\int_{-\frac{b}{a}}^{\frac{1-b}{a}}\log\left(ax+b\right)\exp\left(-\frac{1}{2}x^2\right)\mathrm{d}x$.

On visualizing the spaces $\Bbb{S}_{++}^n$ and $\Bbb{R}^n\times\Bbb{S}_{++}^n$ for $n=1,2,\ldots$

Optimization problem using Reproducing Kernel Hilbert Spaces

Minimize the Frobenius norm of the difference of two matrices with respect to matrix: $\underset{B} {\mathrm{argmin}} \left\| A- B \right\|_F$

Gaussian integrals over a half-space

Rotating an $n$-dimensional hyperplane

On integrating a "gaussian-like" integral

Expressing a quadratic form, $\mathbf{x}^TA\mathbf{x}$ in terms of $\lVert\mathbf{x}\rVert^2$, $A$

Optimal approximation of quadratic form

Find $\lim_{x\to0}\frac{\sin\left(1-\frac{\sin(x)}{x}\right)}{x^2}$. Is my approach correct?

If $x\sim\mathcal{N}(\mu, \sigma^2)$, what is $E\left(\frac{\exp(x)}{a+\exp(x)}\right)$ for $a>0$?

Volume of intersection of the $n$-ball with a hyperplane

Reproducing Kernel Hilbert Space (RKHS) constructed by the summation of positive-definite kernels.

Applying PCA on covariance matrix in order to generate a new random variable.

Expected distance between two vectors that belong to two different Gaussian distributions

Number of antipodal pairs of $n$-sphere points mapped to discrete points in $\mathbb{R}^n$

Find point of $n$-sphere after moving on geodesic by given angle

Can a curve on $n$-sphere be uniquely defined by a "direction" vector?

Diffeomorphism from $n$-cone to $\mathbb{R}^{n+1}$ -- parametric equation of geodesic?

On the convexity of a particular form of integrals

Expected value of the sign of a normal random variable

Estimation of the expected value of a function of a random variable

Malalanobis distance between two multivariate Gaussian distributions

Help on the following indefinite integral: $\int\big(\sqrt{1-t^2}\big)^{n-1}\mathrm{d}t$

Prove or disprove that the Bhattacharyya distance is a true distance function

Integration over the intersection of the $n$-ball and a hyperplane

Prove that $\cos\left(\frac{2\pi}{n}\right)+\cos\left(\frac{4\pi}{n}\right)+\ldots+\cos\left(\frac{2(n-1)\pi}{n}\right)=-1$

Is $h(\mathbf{a},b)=\int_\Omega f(\mathbf{x})e^{-g(\mathbf{x})}\mathrm{d}\mathbf{x}$ differentiable?

Find the marginal distributions (PDFs) of a multivariate normal distribution