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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11
votes
2answers
6k views

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 ...
6
votes
2answers
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 ...
10
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1answer
7k views

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 ...
1
vote
1answer
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 (...
1
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0answers
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 ...
2
votes
1answer
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. ...
1
vote
0answers
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 ...
1
vote
1answer
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 ...
0
votes
1answer
2k views

How to detect noisy entries in the data set

I have a data set (entries described by the list of features X1-X7). This data set contains a small percentage of noise. How can I detect those entries that are subject to noise and exclude them from ...
0
votes
3answers
66 views

How can I understand the concept of a noise in machine learning?

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 ...