# Questions tagged [noise]

noise is a term used for the error term in statistical models and in signal processing. It could be white noise, colored noise or otherwise.

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### Probability distribution for a noisy sine wave

I'm looking to analytically calculate a probability distribution of sampling points from an oscillating function when there is some measurement error. I have already calculated the probability ...
980 views

### Fit exponential distribution with noise

I'm trying to fit an exponential with noise (which in this case is a constant $c$) like this one $$y(x) = \alpha e^{- \alpha x} + c \text{ ,}$$ having $(x_i, y_i)$ values (So $\alpha$ and $c$ are ...
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### Classification with noisy labels?

I'm trying to train a neural network for classification, but the labels I have are rather noisy (around 30% of the labels are wrong). The cross-entropy loss indeed works, but I was wondering are ...
588 views

### Cluster Validation of Incomplete Clustering Algorithms (esp., Density based - DBSCAN, HDBSCAN)

Context -- Unlike, Partitional clustering algorithms like K-Means, Spectral or Hierarchal Methods, Incomplete clustering techniques like DBSCAN, HDBSCAN and many others have the notion of noise (...
193 views

### Adding noise to time series data to increase training data

I am dealing with a weekly time series forecasting problem and I am currently investigating the use of an LSTM to make a multi-step forecast for a univariate time series. I actually have a ...
228 views

### Sum of Bernoulli random variables with Gaussian noise

This relates to a question asked recently where (one of the edits of) the question asked what happens when a sum of Bernoulli random variables has some form of noise on the probability parameter. ...
34 views

### Sum of correlated non-Gaussian random variables with same distribution as individual terms

Let's say there is a sum $s$ of $N$ zero-mean correlated random variables $\{x_i\}$: $$s = x_1 + x_2 + \ldots +x_N,$$ where the correlations $C_{ij} = \mathbb E[ x_i x_j]$ are known. Assume that ...
58 views

### Should PC vectors be of unit length, when used for projection?

I am using principal component analysis (PCA) for noise reduction, i.e. projecting a point from the original space to the reduced space, and then back to the original one. For this sort of usage, is ...
In Bishop's book, one of the first examples is shown here Essentially, the data $x$ are randomly generated, and $t$ are generated by running $x$ through a function $\sin(2\pi x)$, then Gaussian ...