# 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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### Can we do inverse prediction for data having multi-class response variable after fitting PLS-DA?

I know how to do inverse prediction (predicting one of the input variables when we know what is the output we want) for the case of regression. I know we can do the same for binary classification ...
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### Machine Learning model for optimized recommendation

We need to recommend a set of input variables as a function of a few other input variables so as to maximize an output variable. Its a streaming process (input variables change often and ...
15 views

### What is the inference behind the momentum variable and the Kinetic energy for a weakly non-linear inverse problems in the HMC method?

We generate an auxiliary momentum variable in the HMC method to provide gradient for the propagation of trajectory (m, p) (model or position, momentum) in the phase space. If we look into Newton's ...
61 views

### Probability of Crossing a Threshold as a Function of Time (Forward Model)

I know the state of some object at a given time. Let's assume that the state is temperature. At each time, I also know the mean and variance of that temperature. I would like to obtain a probability ...
29 views

### Finding weight value for smooth constrained least squares that comes closest with a priori solution?

I need to solve a system of $n.k$ equations of form $t_{ij} = a_i + b_j + x_{ij}/v$, with $i = 1, ..., n$ and $j = 1, ..., k$. A least squares approach can be used, as in $d = Gm$. My data is $t_{ij}$...
9 views

### Some Questions on Data Assimilation Methods

I am currently learning about data assimilation methods from this document: https://www.ecmwf.int/sites/default/files/elibrary/2002/16928-data-assimilation-concepts-and-methods.pdf I had a few ...
12 views

### Can we get the input from a multilayer perceptron based on the output of one of its hidden layers?

I was reading a relatively new paper that proposed to split a nerual networks layers into groups and sending each group to different nodes to train them in a distributed manner. In order to not send ...
19 views

### Calibrate multiple regression

I have a df with that looks as following: ...
53 views

### Neural Network Inversion and its consequences

I am currently looking at Federated Learning. Here is a good example from google. The idea is that training happens on multiple devices. This means on one hand that training data never leaves a user (...
14 views

### Most likely domain element in probabalistic forward model

Suppose I have some probablistic forward model $m: T \rightarrow U$, and that the model is then conditioned on observations $u_1, \dots, u_N$ from U. [More specifically, by 'probabalistic model' here,...
56 views

### Population Monte Carlo Algorithm using L2 Distance Measure/ Likelihood Distribution

I am currently struggling with some concepts of the Population Monte Carlo Framework. Initially, I came across this set of algorithms as I am currently trying to infer parameters from a 7D ...
45 views

### How to properly solve for the inverse problem of OLS? [duplicate]

In textbook ordinary least squares we want to find a vector of coefficients $b_{k+1\times n}$ such that the sum of the squared deviations of what's observed ($y_{n\times 1}$) from what's assumed to be ...
79 views

### What is the error of my regression? [closed]

I'm conducting a polynomial of a third degree upon a diode measurement where Amplification was measured against Voltage. It's a very exponential behavior. However, I used the ...
60 views

### Inferring a Markov chain from its invariant measure

Given a probability measure $p$ on $\{1,\dots,n\}$ assumed to be the invariant measure of some irreducible ergodic Markov chain with unknown transition matrix $P$, i.e., $p = pP$, what (if any) ...
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### Approximation of fractional function that has real-power numerator

I have the function $f(x)=\frac{(1+x)^k}{1+ax}$, where $x>0, 0<a<k<1$. The function has only one maximum at $x_0=\frac{a-k}{a(k-1)}$, increases on the left of $x_0$ and decreases on the ...
343 views

### How to select the regularization parameter between two losses?

In deep learning, the total loss commonly consists of a task-specific loss and a weight regularized loss: loss = loss_specific + lambda * reg_loss In my case (...
110 views

### Machine learning/Deep learning to solve inverse tomographic problem

The typical simplifiled representation of a tomographic system is $y = Ax$, where $y$ is the collected data (sinogram in CT), $A$ is the projection matrix, and $x$ is the unknown image. The ...
37 views

### Marginal Posterior Likelihood-Solving inverse Problem

For a university project, we were required to code our own Parallel Tempering Algorithm and use it to solve an Inverse Problem with 4 Parameters. Unfortunately, I'm not sure if I'm too stupid or have ...
341 views

### Solving an inverse problem with machine learning

I am running up against a very tough inverse problem that I suspect might be solvable using machine learning. Here is the problem. Overview I am studying an object $X$ which, internally, is ...