# Questions tagged [jacobian]

For statistical questions involving the Jacobian matrix (or determinant) of first partial derivatives. For purely mathematical questions about the Jacobian it is better to ask at math SE https://math.stackexchange.com/.

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### shape of the Jacobian tensor of the output of the layer w.r.t. the input 𝑿

Suppose we have a linear (i.e. fully-connected) layer, defined with in_features=1024 and out_features=2048. We apply this layer to an input tensor 𝑿 containing a batch of N=128 samples. What would ...
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### Vector Jacobian product in automatic differentiation

my questions is related to this post Higher Order of Vectorization in Backpropagation in Neural Network @shimao I don't really get the following claim (I know how the chain rule works and what is the ...
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### Jacobian for transformation of discrete random variables (intuition)

I am reading Blitzstein's introduction to probability. He states that, while a transformation of continuous r.v.s needs a Jacobian (or derivative), a transformation of discrete r.v.s does not. Is ...
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### Transformation of random normal variable $x/y^2$

If $x \sim N(\mu_x, \sigma_y)$ and $y \sim N(\mu_y, \sigma_y)$ what is the distribution of $x/y^2$ using Jacobian method?
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### Reason for absolute value of Jacobian determinant in change-of-variable formula?

When we have a random variable $x$ with a probability density $p(x)$, and a function $y = f(x)$ that is differentiable and can be solved for $x = g(y)$, the change of variable formula leads us to a ...
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### Transformation of random variables and Jacobian

When transforming 2+ continuous random variables, you use a Jacobian matrix and compute the determinant. Do you also compute the Jacobian for discrete random variables?
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### Change of variables: 4-dimensional PDF to 2-dimensional PDF

I have a 4-dimensional joint-PDF between variables $X_1,X_2,X_3,X_4$ which are all Gaussian. I want to transform this into a 2-dimensional joint-PDF between new variables $Y_1=Y_1(X_1,X_2,X_3,X_4)$ ...
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### Wrong vector calculus in lecture note 5 of cs224n, Stanford

I am studying NLP via cs224n from Stanford. I am reading this lecture note now. When you refer to the 5th page, they want to derive the gradient with respect to W for RNN, to show the mathematical ...
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### Shouldn't it be Jacobian Descent?

Whenever we have a multiclass prediction the classifier generates a vector output. Per the definition of a Jacobian we are actually taking Jacobian steps towards a local minimum - so should it ...
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### Prediction Interval for Regression Models with Weights

Courtesy Prediction Interval for Neural Net With Hessian :: nnet in R I would like to understand how to manually derive a point-wise prediction confidence interval applicable to neural models. ...
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### Weighted Least Squares weights not changing Jacobian matrix

I currently have 4 data points and the following Jacobian matrix $A$ and cost vector $b$ \$ A = \begin{bmatrix} -0.7867 & 0.0464& -0.6155 & 1.0000 \\ -0.3751 & 0.4299 &...
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### What is the jacobian for a neural network

I know that a Jacobian is a matrix holding all of the first-order derivatives for a vector-valued-function. What is the Jacobian of a neural network, though? What are the inputs and what are the ...