All Questions
10
questions
1
vote
1
answer
47
views
How to find an expression for an MGF
The MGF, $M_x(t)$ is a function of $t$. It has the property that $\lim_{t\to 0} M_x(t)=1$. It can be shown that:
$\lim_{t\to 0}\frac{d}{dt} \log[M_x(t)]=E[X^1]=E[X]$
Find an expression for
$\lim_{t\to ...
- 31
1
vote
1
answer
140
views
CDF as a result of a Cauchy problem: how to solve it?
I'm studying a particular class of random variables.
In order to find the CDF $F(x)$ of my variable, I should solve the following Cauchy problem:
$$
\begin{cases}
F(x)=e^{-\lambda F'(x)} \\
F(0)=0
\...
- 97
1
vote
0
answers
19
views
How to obtain the parameter update for the multiclass classification (general loss and activation function)?
Consider the feature space $\mathcal{X}=\mathbb R^{d}$ and $\mathcal{Y}=\{1,...,c\}$ such that $c > 2$. We consider some activation function $\alpha: \mathbb R^{c} \to \mathbb R^{c}$ and out weight ...
- 998
0
votes
1
answer
312
views
Write down the backward equations for $P_{12}$ and $P_{21}$ and use the symmetry of Q to solve these equations.
Hint: Whenever confronted with an ordinary differential equation of the form x′(t) = ax(t)+b(t), it might be beneficial to consider the function y(t) = $e^{−at}x(t)$.
$$Q = \left[ \begin{matrix}
...
- 253
0
votes
0
answers
94
views
Validity of Coronavirus Curves - Are we using the correct baseline?
For most analysis (models), are we inaccurately assuming that the newly reported cases are the number of actual new cases? Could this exponentially growing number just be a function of the way testing ...
- 17
1
vote
0
answers
79
views
Epidemic threshold on activity driven network
I am trying to understand the equations used in a paper
(https://www.nature.com/articles/srep00469.pdf)
Mainly I'm trying to understand how the epidemic thershold was calculated using the ...
- 111
3
votes
1
answer
318
views
Geodesics of Fisher-Rao metric on the open interior of the finite-dimensional simplex.
I am curious about the explicit form of the geodesics of the Fisher-Rao metric tensor on the open interior of the n-dimensional simplex.
In the 2-dimensional case (only 1 parameter on the 2-simplex), ...
- 1,322
0
votes
2
answers
351
views
Is jump intensity inaccurate in describing random process?
In https://en.wikipedia.org/wiki/It%C3%B4's_lemma
Under the section of Poisson jump processes, it is said that
We may also define functions on discontinuous stochastic processes.
Let h be the jump ...
- 948
1
vote
0
answers
158
views
Stable distribution law related to the Dickman function
It is known that if $U$ is a random variable with uniform distribution on the interval $(0,1]$, then the random variable defined as
$$
X\stackrel{d}{=} U^{1/\alpha}(1+X)
$$
where $\alpha>0$ ...
- 765
1
vote
1
answer
121
views
Trick in integration with Taylor expansion
I am struggling with the expression of the LHS of the following equation.
The RHS is just the Taylor expansion of the first function around point y and the differentiation wrp to the argument y.
How ...
- 145