All Questions
Tagged with complex-numbers regression
6 questions
5
votes
1
answer
84
views
Interpreting complex roots of $R^2$
This is a common way to define $R^2$ in a regression problem.
$$
R^2=1-\left(\dfrac{
\overset{N}{\underset{i=1}{\sum}}\left(
y_i-\hat y_i
\right)^2
}{
\overset{N}{\underset{i=1}{\sum}}\left(
y_i-\bar ...
- 67.2k
3
votes
0
answers
83
views
Putting a constraint on the output of the neural network
I am using a neural network to input some complex numbers and to obtain complex numbers. I converted the input complex numbers into real values by stacking the real part and imaginary parts as a ...
0
votes
0
answers
25
views
Sum of squares for datasets valued in $\mathbb{R}^{m \times m}$ or $\mathbb{C}^{m\times m}$
Let us assume we have $k \times k$ matrix valued data and assume this is organized (possibly as time series):
$$ M_1, M_2, \ldots, M_n $$
Now, assume we are interested in writing down an error ...
- 81
1
vote
0
answers
1k
views
Maximum likelihood estimation for the complex multivariate Gaussian
Background
Consider a multivariate Gaussian dataset $\mathbf{Y}$ with observations on $k$ individuals (rows) over $m$ variables (columns). The variables have covariance $\boldsymbol{\Sigma}$ (an $m\...
- 435
2
votes
0
answers
90
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 ...
- 615
46
votes
5
answers
23k
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 ...
- 2,861