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Questions tagged [complex-numbers]

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

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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 ...
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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 $...
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63 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. $...
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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 ...
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158 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 ...
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39 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 ...
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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, ...
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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 ...
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362 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. ...
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95 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}}\...
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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 ...
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465 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 ...
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179 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 ...
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1answer
69 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 ...
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52 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 ...