# 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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15 views

### How to do competing risks regression after IPW?

There are 4 types of treatment in my data. To balance the covariables of different treatment groups, I have used twang::mnps function to perform inverse probability weighting and successfully got the ...
1 vote
11 views

### simultaneous parameter and variance estimation in statistical inverse problem

Background: I'm working on a geophysical inverse problem and interested in regularization parameter selection. Just by way of explanation, we're trying to estimate the friction underneath a flowing ...
10 views

### inverse of canonical correlation

The canonical correlation obtains the most correlative pairs of components across two matrices. However, the inverse is not commonly known but could be useful for obtaining the most different ...
871 views

### 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 ...
1 vote
30 views

### 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 ...
1 vote
23 views

### 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 ...
27 views

1 vote
105 views

### Distribution of population size $n$ given binomial sampled quantity $k$ and selection probability $\pi$

Given a drawn (without replacement) sample size $k$ from a binomial distribution with known probability parameter $\pi$, is there a function which gives distribution of likely population size $n$ from ...
1 vote
120 views

### Existence of least squares and maximum likelihood estimators?

In statistical parameter estimation where there is a deterministic and stochastic component to the observation-generating model, do least squares and maximum likelihood estimators always exist? ...
1 vote
46 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 ...
1 vote
69 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 ...
20 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 ...
133 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 (...
1 vote
80 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 ...
1 vote
77 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 ...
1 vote
105 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 ...
1 vote
685 views

### Is the covariance matrix a diagonal matrix with variances on the diagonals?

I am a geophysicist learning about geophysical inverse problems. In many papers, the authors discuss the "covariance matrix" as it applies to the inverse problem. In most geophysical applications, ...
122 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) ...
35 views

### 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 ...
359 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 (...
114 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 ...
41 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 ...
1 vote
349 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 ...
246 views

### Connection between MCMC and Optimization for Inverse/Parameter-Estmation Problems

I've been considering two approaches to solving inverse/parameter-estimation problems, and I'm curious to the connection and/or difference between the two approaches. Set up: Say we have a forward ...
1 vote