Episode #125 of the Stack Overflow podcast is here. We talk Tilde Club and mechanical keyboards. Listen now

Questions tagged [complex-numbers]

A complex number is of the form a + bi, where i is the square root of -1.

Filter by
Sorted by
Tagged with
0
votes
1answer
18 views

Expectation over complex multiplication is multiplication of expectation

Suppose I have $\mathbb{E}\left[{\bf x} {\bf x}^H \right]$, where ${\bf x} \in \mathbb{C}^{N \times 1}$ is a random vector which has a uniform distribution, then can I say, $\mathbb{E}\left[{\bf x} {\...
0
votes
0answers
19 views

Complex Linear Regression - Problem with Multicollinearity and Bayesian approach

I want to test out complex linear regressions with a simple model y = a*x + b. The normal equation is not invertible because of multicollinearity. The first two columns are equal to 1 because the two ...
0
votes
0answers
14 views

MLE standard errors: complex from optimizing negative loglikelihood using fminunc

Does anyone know what goes wrong when fminunc in matlab returns a hessian of which the square root of the diagonal of the inverse hessian provides complex numbers? The complex numbers arise due to ...
1
vote
0answers
15 views

Wald test for complex-valued data

Let $\mathbf{x} = [x_1,\ldots,x_N] \in \mathbb{C}^N$ be a set of complex-valued data and let $p(\mathbf{x};\alpha)$ their joint probability density function parametrized by the unknown complex scalar $...
1
vote
0answers
73 views

Using a surrogate model for the solution space of an optimization problem

I have an optimization problem: Given a complex $n\times n$ covariance matrix $C$ one must find a complex $n$-vector $v_C^\ast$ which (approximately) minimizes an objective $f_C(v)$ over all space. $...
1
vote
0answers
42 views

gam/gamm when response variable is complex

I would like to fit a generalized additive mixed model using mgcv or gamm4, but have a response variable consisting of complex numbers where y=a+1i*b. Is this possible, and if so are there any special ...
6
votes
1answer
391 views

Use of Complex Numbers in Statistics

I was asked recently if complex numbers were used in Statistics by a friend of mine who is an electrical engineer. Besides statistical applications in other fields (e.g. quantum mechanics) and ...
1
vote
0answers
55 views

Using complex number in non-negative matrix factorization (NMF)

In short, I wonder which kind of data can use complex number for NMF. And could an imaginary part possibly be a vector? For detail, as I saw some papers used complex number in NMF (1), I think it ...
0
votes
0answers
95 views

An alternative to seasonal analysis in ARIMA models (SARIMA)?

I recently became aware of a property of time series with which I was previously unfamiliar: that a finite-dimensional autocovariance function is equivalent to an infinite-dimensional power spectrum, ...
0
votes
0answers
11 views

Principled estimate of joint PDF given marginals and first and second-order statistics

(Trying to solve the same underlying problem as this.) Let's say we know the marginal probability density functions $p_i(x)$ of a set of zero-mean random variables $\{X_i\}_{i=1}^N$ as well as the ...
1
vote
1answer
494 views

Soft-thresholding for the LASSO with complex valued data

I'm currently implementing coordinate descent for the LASSO with complex-valued data. For this, one needs a complex version of the soft-thresholding operator, which seems hardly available on the net. ...
4
votes
1answer
97 views

How to find the expectation $\mathbb{E} \left[ \frac{|h|^4}{|h+w|^2} \right]$?

Given the independent and complex Gaussian random variables $h$ and $w$, how does one can find the following expectation? $$\mathbb{E} \left[ \frac{|h|^4}{|h+w|^2} \right] = \int_{\mathbb{C}}\...
4
votes
0answers
137 views

Complex vs. Standard Neural Nets for Complex Data

I've seen some recent papers describing complex valued neural networks like this one. What I'm wondering is, rather than invent a new complex network architecture that takes a complex value as a ...
1
vote
0answers
507 views

AR(2) process- covariance stationary- complex roots

I am trying to check if this process is covariance stationary. I have an AR(2) process given by: $Y_t(1-1.1L+0.8L^{2})=\epsilon_t$ I saw that to check if the process is stationary, instead of ...
2
votes
0answers
231 views

pca on polar coordinates?

I have a dataset composed of 123 rows (time bins) and 20 columns (variables) The question I have is the following. each row,column pair has a radian value and a radius value. If I convert these pairs ...
2
votes
1answer
81 views

How to formally define a probability distributions over complex random variables?

Would that be just a probability over a bivariate real random variable, one representing the real part and another representing the imaginary part? How can I formally take moments of the complex ...
1
vote
0answers
56 views

Complex valued design matrix

In statistics design matrix is fundamental concept. It includes set of explanatory variables, for example in case of MRI data we use dc component, drift,physiological noise and so on. What will ...
31
votes
4answers
14k views

Analysis with complex data, anything different?

Say for example you are doing a linear model, but the data $y$ is complex. $ y = x \beta + \epsilon $ My data set is complex, as in all the numbers in $y$ are of the form $(a + bi)$. Is there ...