# Questions tagged [calculus]

For statistical questions involving calculus. Please use also a more statistical tag. For purely mathemathical questions about the calculus, it is better to ask at math SE https://math.stackexchange.com/

40 questions
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### Finding the slope at different points in a sigmoid curve

This is my data. x <- c(0.5,3.0,22.2,46.0,77.3,97.0,98.9,100.0) plot(x, pch = 19) I want to fit a curve through these points and then calculate the slope at ...
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### Deriving linear regression gradient with MSE

So I've been tinkering around with the backpropagation algorithm and to try to get a better understanding of how it works and my calculus is quite rusty. I've derived the gradient for linear ...
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### How do you obtain the standard error for a slope at a given data point, for curvilinear regression?

A distribution looks like this: modeled by an equation $y=1.0333x^2 - .5382x + 1.6905.$ Find the rate of change (i.e. the slope at that point of the regression equation) at point 6 (the x axis value)...
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### Why does Judea Pearl call his causal graphs Markovian?

In his texts on causality, Judea Pearl always refers to the simplest graphs he uses, i.e. the acyclic graphs with independent confounders, as Markovian. I don't see why these graphs contain anything ...
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### Why is optimisation solved with gradient descent rather than with an analytical solution? [duplicate]

I'm trying to understand why, when trying to minimise an objective function, gradient descent is often used, rather than setting the gradient of the error to zero, and solving it analytically. In ...
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### What is the second derivative of a B-spline?

A B-spline of degree $j$ is defined at knots $\vec k$ by the Cox-de Boor recursion formula \begin{align} B_{i,1}(x) &= \left\{ \begin{matrix} 1 & \mathrm{if} \quad ...
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### Simple Appplication of Law of Iterated Expectation

Consider a randomized experiment (AB test), where $n$ units are randomized into the treatment group $T_i=1$ and control group $T_i=0$. Let $M_i\in P$ denote the observed value of a continuous variable ...
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### gradient descent momentum vs step size

In the gradient descent method, the learning rate (which is multiplied by the results of the gradient on each weight) identifies the size of the step (steep down) that the algorithm takes in each ...
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### Seeing chi square minimization problem as calculus of variation problem

My question will be less informative because right now I myself don't know where I am heading. Basically I want to know that whether it is possible to think a chi-square minimization problem as a ...
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### Is there local minimums in MSE function?

Here is "mean squared error" function: C = $\frac{1}{2n}$ * $\sum(length(y - a)^2)$ As I understand, this is like paraboloid in multidimensional space. So, I guess, there is only one extremum: global ...
Let $x$ and $z$ be real-valued random vectors, where $x = g(z)$, and $g$ is an invertible, continuous and differentiable transformation of $z$. Then \$p_z(z) = p_x(g(z)) \lvert det(\frac{\partial g(z)}{...