# Questions tagged [derivative]

For on-topic questions involving the mathematical concept of a derivative, i.e. $\frac{d}{dx} f(x)$. For purely mathematical questions about the derivative it is better to ask on math SE https://math.stackexchange.com/

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### Covariance of derivative of Gaussian Process Regression

There are a quite a few questions and answers which discuss how to calculate the gradients/derivatives of the posterior of Gaussian Process Regression (see here, here). These include the equations for ...
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### When using OLS on $\ln(y) = \beta_1 \ln(x) + \epsilon$, is $\beta_1$ the elasticity of $E[y\vert x]$, or the $y$ in the data (or both)?

Specifically, suppose we are estimating $$\ln(y)=\beta_1\ln(x) + \epsilon$$ I understand that $\beta_1 = \frac{\partial \ln(y)}{\partial \ln(x)}$ which is the elasticity of $y$ with respect to $x$ ...
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### Back-propagation through cross entropy or logistic loss function

I have neural network which ends with softmax function and I want to minimize cross-entropy cost function which takes output of this network and one-hot labels as arguments. To calculate partial ...
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### Gradient of multivariate normal distribution function?

Let $X\sim\mathcal{N}_J(\mu,\Sigma)$ be a multivariate normal with PDF $f_X$ and CDF $F_X$. Taking derivatives of $f_X$ wrt $X$, $\mu$ and $\Sigma$ is easy as shown here. However, I am interested in ...
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### Relating Two Derivatives (and Elasticities) of a Log-Log Regression

Consider a standard "log-log" linear regression model like this: $\log(y_i) = \log(a_i + b_i)\delta + \epsilon_i$, where $y$ is the dependent variable, $a$ and $b$ are two independent variables, and ...
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### Derivative of Gaussian Process (continued)

This is to extend the discussion of the derivative of the GP. The formulation provided in the previous post describes the gradient of GP as derivative of kernel function as follows with respect to \$(x^...
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### is it a good idea to take the derivative or integral of some features and add them as new features in machine learning?

I'm learning how to do feature Engineering and come across some ideas in my head that's why I want to ask if I had some dataset with some features let's say 2 features and I have a timestamp column ...
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### Why does gradient descent HAVE to find the minimum as oppose to a change in the opposite direction

I have a question about the gradient descent step in neural networks. I fully understand the derivative step and taking the steps required to move in the direction that reduces the loss (finding the ...