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jshe857
jshe857
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I have a random vector $\mathbf{X} \sim \mathcal{N}(\mathbf{m,\Sigma})$ which is transformed by a Gaussian Radial Basis Function into the random variable $\mathbf{Y} = K(\mathbf X)$$\mathbf{Y} = K(\mathbf X) = \exp(-\lambda ||\mathbf X||^2)$ is there an analytic expression for the PDF or atleast the mean and variance of this new variable?

I have a random vector $\mathbf{X} \sim \mathcal{N}(\mathbf{m,\Sigma})$ which is transformed by a Gaussian Radial Basis Function into the random variable $\mathbf{Y} = K(\mathbf X)$ is there an analytic expression for the PDF or atleast the mean and variance of this new variable?

I have a random vector $\mathbf{X} \sim \mathcal{N}(\mathbf{m,\Sigma})$ which is transformed by a Gaussian Radial Basis Function into the random variable $\mathbf{Y} = K(\mathbf X) = \exp(-\lambda ||\mathbf X||^2)$ is there an analytic expression for the PDF or atleast the mean and variance of this new variable?

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jshe857
jshe857
  • 23
  • 4

RBF transformation on a Normally Distributed Random Variable

I have a random vector $\mathbf{X} \sim \mathcal{N}(\mathbf{m,\Sigma})$ which is transformed by a Gaussian Radial Basis Function into the random variable $\mathbf{Y} = K(\mathbf X)$ is there an analytic expression for the PDF or atleast the mean and variance of this new variable?