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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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Regression algorithm on [0,1] with lots of mislabeled data

I have a training set mapping some Likert-scale variables (integers between 1 and 7, rescaled to real numbers between 0 and 1) to predict a continuous variable between 0 and 1. The data set is ...
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1answer
23 views

Apply 3 sigma formula in gamma distribution?

Let say i have some data that follows gamma distribution, and i calculated the Mean and Standard deviation of the gamma distribution. I also know that there are some outliers(Noise) in the data i ...
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Noise and Outliers in DBSCAN

Why are noise and outliers treated as the same concept in DBSCAN (density-based spatial clustering of applications with noise)?
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21 views

How to perform signal denoising from corrupted data

In sensors, the data collected is always noisy. I want to denoise the data using machine learning methods. As per my understanding, the output of the trained algorithm should be the clean signal and ...
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1answer
32 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. ...
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3answers
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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 ...
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25 views

How sensitive are Neural Networks to weight changes?

Let's consider the space of feedforward neural networks with a given structure: $L$ layers, $m$ neurones per layer, ReLu activation, input dimension $d$, output dimension $k$. Which means I'm ...
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1answer
58 views

Calculate threshold value for Poisson distributed noise

I need to calculate a threshold value to get rid of Poisson distributed noise in an image to perform a cluster analysis on the image. The image is the representation of a signal, whose datapoints ...
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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 ...
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25 views

Using a neural network for a regression problem, where the model to be learned suffers from awgn

I have currently a neural network to learn a (relatively non complex) system model (vector regression). Its problem is that the outputs of the system suffer from arbitry additional white gaussian ...
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1answer
36 views

Incorporating noise into machine learning models?

Usually, in machine learning textbooks the $X$ dataset and the target $y$ are defined with exact values. How about the case if the values of both $X$ and $y$ have noises: for instance, we only know ...
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21 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 ...
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What is the probability that sample variance decreases by adding random Gaussian noise to the variable?

If we assume WLOG that our variable X has mean zero (mean-centered), then this can be stated $Pr \bigg(\sum x^2 > \sum (x-n)^2 \bigg)$ for some random variable $n$ distributed under $N \sim N(0, \...
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1answer
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How to remove cofounding effect on a variable?

I'm working in a team that is collecting data by bicycle : We have biometric t-shirts that measure our ventilation rate. The problem is that during the last data collection, participants used masks to ...
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1answer
11 views

Supervised learning with error-range in labels?

I am working in a problem where labels have an error range (we know the range). For instance, a label can be expressed as $y_i \pm e_i$ with $e_i$ is the error range for the label of the instance $i^{...
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What determines whether relative or absolute Gaussian noise should be added to data?

Suppose I have some data vector, $\mathbf{d}$ with length $N$. I want to add "Gaussian noise" to the data. My understanding is that there are two ways to do this. 1) Relative noise percentage $$\...
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226 views

“Add White Gaussian Noise with SNR” vs. “Add 5% Gaussian Noise”

I have a noise-free dataset which is a vector of numbers, $\mathbf{d}$, with length $N$. I want to "add noise" to this data. My understanding is that there are two ways to do this. 1) Add some ...
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2answers
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Formula to detect non uniformity noise

I have this line profile, how is the best way to detect this kind of non uniformity? I must detect a sudden change, as opposed to the last section that decreases slowly.. But the sudden difference ...
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1answer
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Why adding noisy predictors improves my random Forest prediction?

I am doing some tests with randomForest and I cannot understand the following results : ...
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25 views

Optimization of a noisy function with binary output

What frameworks exist to optimize the following problem: $\theta^\ast = \operatorname*{argmin}\limits_{\theta \in \Theta} f(\theta)$ with the characteristic that $f$ is noisy and has a binary output ...
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How do you use the predictive distribution with noise in Bayesian Optimization?

I have been reading a paper on Bayesian Optimization, and I was reading the section on adding Gaussian noise to your Gaussian process. The article is: Brochu, Cora and de Freitas (2010). A Tutorial ...
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($L_2$) distance for noisy data

I'm given a subspace $V$ and a set of $n$ corrupted observations $\tilde{x}_1 = x_1 +\epsilon_1,...,\tilde{x}_n = x_n + \epsilon_n \in \mathbb{R}^D$. Assume $D$ is large and that $\epsilon_i \sim N(0, ...
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What is the difference between Noise, error and residuals?

I was reading about Kalman filter. http://web.mit.edu/kirtley/kirtley/binlustuff/literature/control/Kalman%20filter.pdf They talk about additive noise and error. I need to understand difference ...
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MIxture model in R to generate noise in data

I have a bit of code in R that adds noise to an harmonic series according to a normal distribution: ...
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27 views

How does Noise affect the results of Transfer Entropy?

I was reading about Transfer Entropy and came across this package: https://cran.r-project.org/web/packages/TransferEntropy/TransferEntropy.pdf The code in the package: ...
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Awful performance of LSTM on noisy time series after stationarisation

Note. The post is quite long because I added some thought process for the sake of seeing the big picture. So grab a coffee and indulge yourself. For tldr the actual question on the bottom. I put my ...
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1answer
57 views

Ridge Regression as Robust Optimization

We were told to assume in class that the below optimization formulations are equivalent- $$\min_w\max_{\delta:||\delta||_F\leq\epsilon}||(X+\delta)w-y||_2^2$$ $$\min_{w}||Xw-y||_2^2+\lambda||w||_2^2 ...
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1answer
58 views

Can redundant/irrelevant features be called a Noise?

Let's say we want to predict job applicant' salary. We have a dataset with following features: {Age, Experience, Education, Astrological_Sign, Weather_Today} 5 features in total. In this set, ...
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31 views

How to add noise to obfuscate patterns in data

I have a program that generates output data depending on the inputs it is given. Lets say the data generated is a list of n items where each item is a natural number between 1 and k. I need to release ...
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2answers
526 views

Generate uniform noise from a p-norm ball ($||x||_p \leq r$)

I am trying to write a function which generates uniformly distributed noise which comes from a p-norm ball of $n$ dimensions: \begin{equation} ||x||_p \leq r \end{equation} I found possible ...
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0answers
44 views

Get noise model from true and distorted data

I have been given two data sets: Set A: a small data set containing data randomly drawn form an underlying distribution Set B: a very large data set containing data randomly drawn from the same ...
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2answers
867 views

Noise in regression data

How can I compare which distribution has more noise than the other. If for example I generate some data, how do I know that it has a large percentage of noise? Here I have a small sample code that ...
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Correcting for noise in gene expression data

I have a training set of RT-qPCR gene expression data (not run in triplicate) for a batch of samples with two phenotypes $A$ and $B$ on which I've trained a logistic regression classifier. I also ...
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2answers
79 views

ARMA models and residual series

Assuming that model is correct, why does the residual series of an ARMA model resemble a white noise process?
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31 views

Time series clustering/segmentation based on pattern

I'm currently working with a database which contains several large PPG (pulse oximetry) and ECG time series. These series, however, contain segments within them which are highly contaminated by noise, ...
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2answers
348 views

Removing gaussian noise from a time-series data

I have a noisy time-series data (Figure 1). As you can see the variance in this data set is very high and the "Gaussian noise" needs to be removed for me to analyze this signal. Normally we apply a ...
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13 views

Error of solution ranking

I am exploring subset selection of multi-armed bandits and I am curious about an error measure of a selection. So in the scenario of a multi-armed bandit, a set of arms are present and we aim to ...
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1answer
56 views

Why does “sticky noise” defy averaging attack?

I have read an interesting paper (pdf) describing how a privacy preserving technique might be breached, but I am having trouble understanding the following paragraph describing one of several layers ...
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1answer
54 views

Deal with noise data

The following picture represents a graph with price over time. I am a mathematical student, but also a trader. I want to create a function which could localize the good entry and exit points for sale ...
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33 views

How to test for differential privacy on multiple choice data?

I apologize I am new to statistics so I do not know all terms and concepts. My current algorithm for adding noise to multiple-choice favorite color data is this: ...
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Expressing Confidence in Conclusions from Noisy Data

I’m working on improving the robustness of a software engineering process that measures performance of programming language compiler and standard library, a.k.a. benchmarks — in the computing sense of ...
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Evaluation of Jacobian for Extended Kalman Filter

For the non-additive noise case, \begin{equation} x_k = f(x_{k-1}, u_{k-1}, \xi_{k-1}) \\ y_k = h(x_k, \nu_k) \end{equation} the EKF takes into account the jacobian wrt to the noise terms $ L_{k-1} =...
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1answer
47 views

Covariance of 2 dimensional bivariate normal distribution

I'm forgetting my basics, so I must be being a silly sausage, but consider $$X\sim N(0,1)$$ $$Y\sim N(0,1)$$ if $f(x,y)$ is the join probability of these 2 variables, then the 3D plot looks like ...
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166 views

Create Gaussian noise for artificial dataset with different noise levels

I am creating an artificial dataset corresponding to different noise levels. This is to simulate results of a recognition software (e.g. face recognition). For example, for $noise_{level} = 0.1$, the ...
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85 views

Estimating signal-to-noise ratio after smoothing data and covariance estimates

I have data for two variables, let's say $A$ and $B$, which have distributions that are roughly centered at 0. I am computing a value, let's say $C = \sqrt{A^2 + B^2}$, from this data. I also have a ...
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1answer
40 views

what is the meaning of deriving two new set by adding noise features?

I was reading Constrained Clustering with Minkowski Weighted K-Means paper. In this paper, they are using 4 datasets and deriving 2 new datasets from each of the 4. So, total 12 datasets. The ...
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Error on a ratio of two measured values each with just a poisson noise estimate

I am trying to estimate the error on some discrete data. I have a total of N counts of which x have the desired characteristic. So x/N is the fraction of the sample I want to plot. I am assuming ...
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37 views

Noise Robustness For MLP

I am learning neural network using the book "Deep Learning" by Ian Goodfellow, Yoshua Bengio, and Aaron Courville. In section 7.5, the authors explain how adding noise to weight works with an example ...
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Estimate the variance of Gaussian distribution from noisy sample

I have measured a large data sample from an underlying Gaussian distribution and want to estimate the variance and its error. However, the measured values are noisy with some Gaussian noise with a ...