# 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/

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### How can I prove monotonicity of slope MLE in EIV regression model?

I'm trying to figure out Casella and Berger Exercise 12.4(c), regarding monotonicity of the maximum likelihood estimator of the slope of an errors-in-variables regression model. The goal is to show ...
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### Question Intuition behind mathematics of activation function in a neural network.

Does this intuition behind why an activation function is used in a neural network make sense mathematically : For this example lets consider a fully connected (NOT CONVOLUTIONAL) network that ...
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### Simple matrix calculus but I am struggling to understand [duplicate]

Here is my problem: We have $\mathbf{D} \in \Re^{m n}$, $\mathbf{W} \in \Re^{m q}$, and $\mathbf{X} \in \Re^{q n}$. Furthermore, $\mathbf{D} = \mathbf{W}\mathbf{X}$. (NOT an element wise ...
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### Theory and mathematical background of active contour and segmentation models

I am looking for reference books/online material for self-learning the mathematical background in active contours and segmentation models (e.g., snakes, level set, geodesic). Can someone help me with ...
59 views

### Calculating derivative for the final layer of a neural network

I'm first learning about backpropagation in neural networks. We're doing stochastic gradient descent. The lecture provides incomplete detail on computing the derivatives for the final layer. We have ...
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### Solving integrals using incomplete gamma function (upper gamma rule)

I am attempting to integrate this function, ∫15x^(0.28) * e^(-0.21x) dx and am struggling with what techniques to apply. The lower boundary is 0 and the upper boundary is infinity. From research, I ...
105 views

### What is the derivative of gamma variates with respect to the shape parameter? [closed]

Given a gamma distribution with unit scale and shape $\theta$, and given an arbitrary variate $x$, what is the derivative of the variate $x$ with respect to $\theta$? In other words, I would like to ...
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### Calculus versus matrix representation in OLS

In the Wikipedia article Ordinary Linear Squares there is an example for finding the estimators $\beta_i$ for a linear model of the sort: $$y_i = \beta_0 + x_1\beta_1 + x_2\beta_2 + \ldots$$ In the ...
1 vote
19 views

### Changing Bounds and Multiply by -1 [closed]

Sorry my calculus knowledge is extremely rusty - what is the reason that we can flip the bounds from $-\infty\to 0$ to $0\to\infty$ and then also flip the $x$ value to $-x$?
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### I am not able to understand how did the elementwise multiplication came into the picture of backpropagation in neural networks

I have understood the backpropagation algorithm along with the chain rule well enough that I can derive it on my own, but I don't understand where the elementwise multiplication came from and how does ...
1 vote
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### When will $\mathbb{E}[g(S_n/n)]$ exist given $\mathbb{E}[g(X_1)]$ exists?

Suppose $X_1, X_2,..., X_n$ are i.i.d. random variables with distribution $\pi$ on some probability space. Let $g$ be a measurable function such that $\mathbb E_\pi[g(X_1)]<\infty$. I am curious ...
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### Forecasting Peak/Global Maximum from Raw Data

I'm trying to see what methods there are to predict when the data will peak based on raw values, along with how to accomplish it in R. Here's what you can assume... The data has a start and end point....
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### Pattern Recognition and ML Exercise 1.4

I am studying "Pattern Recognition and Machine Learning" by Christopher Bishop and I'm trying to understand his solution in the solution manual to exercise 1.4. The problem statement for ...
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### Approximate / Standardize value in certain range

I have table with numeric values like ...
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1 vote
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### Backpropogation Derivatives

I've been working on trying to understand the backpropogation algorithm and the calculus behind it, and in my work I have stumbled across a sort of odd situation. I am just practicing on a 1 input, 1 ...
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1 vote
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### What is the mean average of $y=kg^t$ from $t=a$ to $t=b$ [closed]

Mean average of $y$ in $y=kg^t$ from $t=a$ to $t=b$. $g$ is a constant, $t$ varies. I have looked this up in textbooks and online and all I can find is the mean average of a function where $t$ is a ...
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### Is there a smart algorithm of finding the maximum of $X^{\top}a$ with $X$ and $a$ both belong to some compact convex set? [closed]
Suppose $X\in\mathcal{X}\subset R^k$ and $a\in\mathcal{A}\subset R^k$, where $\mathcal{X}$ and $\mathcal{A}$ are both compact convex set. Is there a systematic way of finding the maximum of $X^{\top}a$...