All Questions
Tagged with ordinary-differential-equations statistics
51
questions
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22
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Does probability flow ODE trajectory (in the context of diffusion models) represents a bijective mapping between any distribution to a gaussian? [closed]
I have read several papers about diffusion models in the context of deep learning.
especially this one
As explained in the paper, by learning the score function $(\nabla \log(p_t(x)))$, probability ...
- 113
1
vote
1
answer
30
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Question about Statistical measures
I have recently tried parameter estimation for nonlinear ODE using non-linear fitting techniques. I learned about Statistical measures like p-tests, t-tests, $R^2$ squared, adjusted $R^2$ square, etc. ...
- 31
-1
votes
1
answer
38
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Verify whether it's a Bregman loss function, maybe by solving a differential equation
I have a function $f(x, y;\mu) = \frac{\mu}{x}(x-y)^2$, where $\mu > 0$ is a parameter. I want to see whether it's a Bregman loss function. A Bregman loss function is define as:
$D_\phi(x,y) = \phi(...
- 31
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57
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Time Series Analysis and Recurrence Relations/Differential Equations
I am beginning to watch a video playlist on the subject of time series analysis, and it seems pretty clear both from notation and some of the terminology (such as "characteristic equation") ...
- 1,912
6
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121
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The statistical average of a continuous value: $\overline{O} = \int O(x) \rho(x) dx$, but coordinate invariant
I am trying to solve a Lagrange multiplier problem for the following equation
$$
L= - \int_{-\infty}^\infty \rho(x) \ln \frac{\rho(x)}{q(x)} dx + \alpha \left( 1- \int_{-\infty}^\infty \rho(x) dx \...
- 2,589
1
vote
0
answers
60
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Literature on Principal differential analysis
I'm currently dealing with topics in Functional Data Analysis (FDA), specifically Principal Differential Analysis (PDA). By the corresponding R package description, this is related to estimating a ...
- 61
6
votes
1
answer
110
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Optimal speed for approaching red light to maximize velocity with non-uniform probability
Problem statement
When I cross red lights, my goal is to being going as fast as possible when the light turns green.
I am at distance $D$ from a traffic light when it turns red.
Let the time length of ...
- 327
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31
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Determining correlations of derivatives of a function given only measurements of that function
Cross-posted from statistics stackexchange:
Say we have a permanent-magnet DC motor that roughly obeys the system equation $\ddot{x}(t) = \alpha \dot{x}(t) + \beta u(t) + \gamma$, where $x(t)$ is the ...
- 1,370
1
vote
1
answer
47
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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
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1
answer
23
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Calculate normal distribution from $\frac{1}{f(x)}\frac{d([f(x)])}{dx} = \frac{d-x}{a}$
Calculate normal distribution from $\frac{1}{f(x)}\frac{d([f(x)])}{dx} = \frac{d-x}{a+bx+cx^2}$ when $b=c=0$ then we have $\frac{d-x}{a}$. This is taken from Mathematical Statistics with Applications ...
- 393
0
votes
1
answer
62
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Why does this data not line up with the differential equation that's supposed to model it?
Sorry for the bad title, I wasn't sure how to ask this specific question.
So for a (extra credit) homework assignment, I wrote a python program for my differential equations class that should model ...
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votes
0
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64
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Solving for the $k$, given the survival function for a newborn as: $S(t) = \frac{\left(121 - t\right)^{1/2}}{k},\; t\in\left(0, 121\right]$
I'm doing an assignment and I can't seem to solve the following question:
Given the survival function for a newborn as:
$$S(t) = \frac{\left(121 - t\right)^{1/2}}{k},\; t\in\left(0, 121\right].$$
What ...
- 19
1
vote
1
answer
140
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CDF as a result of a Cauchy problem: how to solve it?
I'm studying a particular class of random variables.
In order to find the CDF $F(x)$ of my variable, I should solve the following Cauchy problem:
$$
\begin{cases}
F(x)=e^{-\lambda F'(x)} \\
F(0)=0
\...
- 97
1
vote
0
answers
19
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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
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1
answer
46
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How to identify linear non-homogenous ODE from data?
I want to fit a model
$$\overset{\cdot} x = Ax + v(t)Bx + Cu(t)$$
to data, where $u(t),v(t)$ are known inputs and $A,B,C$ should be fitted. The data are assumed to be drawn from the above model but ...
- 1,504