# Tag Info

### Principal Component Analysis Eliminate Noise In The Data

Principal Component Analysis (PCA) is used to a) denoise and to b) reduce dimensionality. It does not eliminate noise, but it can reduce noise. Basically an orthogonal linear transformation is used ...
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### Comparison of distribution mean or median

The two experiments are mostly unpaired, so the answer applies to that situation. The information regarding outliers defined as >5 IQR is not given. Regarding outliers, when you have nonsense ...
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### Correcting Kullback-Leibler divergence for size of datasets

The fundamental issue is that the KL divergence between the true underlying distributions is zero, as they are the same in your code ($U(0,1)$,) but sampling variation (almost) ensures that in finite ...
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### Sum of Bernoulli random variables with Gaussian noise

Here I simply show the results of a sum of Bernoulli random variables where there is noise added to the probability parameter that follows a truncated Gaussian distribution, restricted to valid values ...

### Calibration of correlation

Given the intended application, you might be interested in creating realistic modifications of the series of data. Overview This is easier to do than you might think. (See the three-line function <...
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### Are colored noises correlated / uncorrelated?

Question1: If the power spectrum is not flat, then does that mean the colored noises are correlated? One way to construct the power spectral density is to take the Fourier transform of the ...
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### Does Gaussian Noise tend to move the Pearson Correlation to zero?

Pearson correlation is, a bit loosely speaking (but not that loosely), measuring how well the points fit a diagonal line. When the points are far from the line, as the noisy setting will show, they ...

### What might be the simplest (least flexible, least expressive) model to avoid over-fit?

Use ridge regression. The ridge parameter is a control on the complexity of the model class. Ridge regression is equivalent to fitting a regression model with a constraint on the norm of the weight ...
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### Calculating the noise on data fitting an exponential decay

The usual measure of the size of noise about a nonlinear least squares regression fit is the standard error of the residuals, which is the square root of the variance estimate s^2=\hat{\sigma}^2=\...

### Drawing independent Random Variables out of a Probability Distribution

Drawing a random variable $X$ with realisation $x$ is like picking a point $\omega$ in a certain space $\Omega$ (this can be formalised as being equivalent). On that space $\Omega$, a collection of ...
Noise (n) is the component of a signal (s) that is not information (i). $s = i + n$ Any signal has one or more sources. Typically, each of these sources can theoretically be approximated by some ...