# Questions tagged [inverse-problem]

In science an inverse problem is the problem of calculating from a set of observations the causes that produced the observations. Examples are tomography and seismic reconstruction, and many others. Use this tag for statistical methods used with inverse problems.

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### In GD-optimisation, if the gradient of the error function is w.r.t to the weights, isn't the target value dropped since it's a lone constant?

Suppose we have the absolute difference as an error function: $\mathit{loss}(w) = |m_x(w) - t|$ where $m_x$ is simply some model with input $x$ and weight setting $w$, and $t$ is the target value. In ...
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### How to decompose a random walk (array) into its Markov Chain transition matrix?

The algorithm, PageRank, receives a Markov Chain transition matrix (page links from one to another.) Either by random walk, or more efficiently, eigenvectors, the stationary distribution of the Markov ...
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### Does blind source separation (ICA) work if channels of mixture are observed asynchronously?

Does Independent Component Analysis (ICA - fastICA, SOBI, etc.) work reliably when applied to a multidimensional mixture (observation) $X = (X^1, \cdots, X^d)$ if the different channels $X^i$ of the ...
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### Is it possible to recover original normal distributions from observations of sums of normally distributed variables?

I have been trying to solve the following problem for several weeks. I would greatly appreciate it if you help me solve the following problem. Problem description Assume that there are seven iid ...
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### L-curve method for regularization parameter selection

I work on PDE inverse problems and I'm interested in how these can be viewed as problems of statistical inference. I'm looking for some model parameters $m$ which minimize the misfit with some data $d$...
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### Least square regression with L1 regularization and non-negativity constraint

There are two functions associated by the model $a(x) = \int_{k_1}^{k_2} b(k)\exp(-kx)dk$ where $a(x)$ is the experimental data I have, and $b(k)$ is the information I want to get. Or I can write ...
I want to know if there is any literature about the following regression problem: $$Y=X\beta +\epsilon$$ where $Y$ is unknown. But, i know $X$ and the OLS estimator of $\beta$  \hat{\beta}=(X^\top ...