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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6 views

Optimally stratifying training, validation and testing samples using simulated targets

I'm fitting a large-scale (both in size of sample and input vector) single hidden-layer feedforward neural network on simulated targets, $\tilde{t}_{\tilde{n}} \in \{\tilde{t}_1,\cdots,\tilde{t}_\...
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Anisotropic noise in gaussain process prediction

In GP regression we predict using $\mu^* = ... (K(X,X)+\sigma^2I)^{-1}...$ This is fine when the noise $\sigma$ is a scalar, but I am confused about what happens when $\sigma$ is anisotropic. $K(X,X) \...
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Bias in estimation of a latent / hidden variable drawn from a skewed distribution: what is it called?

I observe a bias effect in my measurement system that I can explain and correct using a simple latent or hidden variable model. I am sure this kind of effect has been described earlier in other fields ...
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Remove subtractive noise

I have a dataset that I'd like to remove noise from. All the noise is subtractive, so the ideal value would always be greater than or equal to the measured value. The following chart shows the raw ...
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Noise in regression problems and ways to reduce it

In the theory of bias-variance decomposition for regression problems (this page is a very nice reference on this theory) noise is defined as $$\mathrm{Noise} = \mathrm{E}_{X,Y}[(Y - \mathrm{E}[Y|X])^2]...
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37 views

Autoregressive model with observable noise

The classical autoregressive model is a linear model for the dynamic variable $x$, where the added noise $\epsilon$ is directly affecting the dynamics of the model $$x_{t} = \sum_i \alpha_i x_{t-i} + \...
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How to extract noise parameters from $y = kx$ data, with multiparameter noise components

I'm interested in extracting noise parameters from (x, y) data, where x are known input values and y are the corresponding signals. There is strict linear relationship between y and x; in the absence ...
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25 views

How to remove the covariance of two measurement methods in order to separately estimate the variance of each

I wish to compare two different methods of measuring an underlying property, and wish to extract the variance of each method of measurement, independent of the other. The problem is how to correctly ...
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48 views

Are colored noises correlated / uncorrelated?

Let, x be a random variable (r.v) that is white Gaussian, has a flat power spectrum. y can be any colored noise. I think another ...
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52 views

Coordinates from noisy distance matrix?

I have a black box in which I know there is a 1D line and points along this line, and as output from this box I can get out a distance matrix for the points, but I know there is noise in the estimate ...
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What is the meaning of noise in a dataset with no dependant variable?

My understanding of noise & signal comes from the context of bias-variance tradeoff in supervised methods. But given a dataset with no dependant variable, how do you define noise? & how do you ...
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best hypothesis for data with zero mean noise is the one which assumes no noise at all?

In an ml-class, they introduced overfitting with an example: Say, we have $x$ picked from $Uniform(0,1)$ $v$ random noise, picked indepidently of $x$ from $Uniform(-0.3,0.3)$ and $\mathbb{E}[v] = 0$ $...
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Seeking recommended literature search terms for a solution to a specific kind of data structure?

Hopefully this isn't considered too off-topic. I'm working in industry these days and came up with a solution to an analysis problem we'd been facing. I'd like to get a sense as to whether said ...
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What is statistical difference?

In the paper "Calibrating Noise to Sensitivity in Private Data Analysis" by Dwork et al., the term "statistical difference" is used as following (in page 280): Finally, if a $1 − \...
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30 views

What is the name of this data denoising method

I've been working on extracting data from an extremely noisy signal. The signal itself is the 1st derivative of raw mean squared (RMS) of an audio that may contain segments with some single low ...
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45 views

Separating signal from noise: noise models in standard deep learning

In a regression setting, one wants to identify some model of a process of interest, based on noisy measurements. The model usually goes like this: $$ y_i = f(x_i, \theta_1) + \varepsilon_i.$$ Here, $...
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Relationship between overfitting and robustness to outliers

What's the relationship between overfitting and sensitivity to outliers? For example: Does robustness to outliers make necessarily models less prone to overfitting? What about the other way around? ...
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53 views

Can RMSE be greater than standard deviation of noise

I am working on model selection problem for noisy data sets. I am having non-parametric models like SVR, regression splines etc. which have can overfit if the hyperparameters are not tuned properly. I ...
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How to calculate the similarity of data with noise?

I'm stuck on calculating similarity. Please tell me in which direction to move. There are three files of different lengths that need to be compared for similarity. It is supposed to use the cosine ...
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288 views

Linear Regression for Noisy Data

I have noisy dataset collected from a source and I am planning to fit a regression to this dataset. The dataset has Y and X1 variables (both continuous between (-1, 1)) and I plotted a scatter plot to ...
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10 views

Beta adjustment for added noise

Let's say we have a model that takes the following form: $$r_t = \sum_{i=1}^N (w_i \times \beta_i \times f_{t,i})$$ Now I'd like to add a noise term $z_i$ distributed normally with $(0,\sigma)$: $$r_{...
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Bayesian optimization with offline stochastic function and sticky decisions

Is there a bayesian optimization (BO) framework which allows: 1. Warm start with offline data 2. Stochastic function f(x) is noisy 3. Every iteration is n samples controlled by agent and there are ...
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why model perform slighty worst after removing co-related features

I have a classification problem on which I am testing the main classification models like Logistic Regression, SVM, KNN and deep neural networks. I have a feature set of 40. And around 5-6 are ...
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How does a probability distribution change when adding Gaussian noise?

Instance Noise is a trick for stabilising Generative Adversarial Network (GAN) training. In this paper, the authors say that (page 14, fig. 6) Instance Noise broadens the support of both ...
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Calibration of correlation

Let's say there are two random variables (for example, two time series data of S&P500 and a stock) and their correlation is 0.95. What is the best way to reduce the correlation between these two ...
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Fourier transforms for noise reduction

Given a signal, which is regularly sampled over time and is noisy. The standard method is with a Fourier transform to reduce the noise and minimise the change to the signal. ...
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22 views

PCA to reduce Noise on usps data set, problem with the eigen values

I am currently working on PCA. My main task is to apply Gaussian noise to the usps data set and then denoise it by using PCA. The concept is pretty clear, but I am struggling with the eigenvalues plot....
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ICA for Noise Reduction over a Dataset

Suppose my dataset consists of $N$ example vectors $\mathbf{x}_{1}, \ldots, \mathbf{x}_{N}$ where $\mathbf{x}_{n} \in \mathbb{R}^{p}$ $\forall n$. I assume that each vector $\mathbf{x}_{n}$ is ...
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38 views

Can a random variable be expressed as a sum of deterministic and random variable?

Say we have a sequence of random variables $\{X_t:t\geq 0\}$ following an unknown stochastic process with distribution $X_t\sim N(\mu_X,\sigma_X^2)$. This idea came to me from the additive noise model....
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Extreme Image Noise Removal

I've been trying to solve a noise removal (from images) problem using deep learning and I've tried a lot of the newer architectures for noise removal including FFDNet, NLRN and MWCNN. The problem is, ...
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How can i compute noise (1 sigma error) given a signal

I have a signal organized as an image, i.e. a matrix. Each "pixel" has an error $\sigma_{i,j}$. Simplifying, let's assume that the error is the same for all the involved "pixels". How can I compute ...
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How to estimate the fluctuations in a data?

The question is more about an method of extracting relevant "universal" information from multiple experimental data. Let say, for every $\alpha$, we have a function of the form $$f_\alpha(t) = g_\...
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40 views

Simulation from generalized linear model with specific signal to noise ratio

I am trying to simulate from a generalized linear model (GLM) in a specific signal to noise ratio (SNR) setting, but run in to problems if I try to define a reasonable SNR for non-Gaussian data. In ...
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1answer
50 views

Adding a vector of values to encoder output in autoencoder (keras)

I am experimenting with autoencoders for a very specific application, but cannot unfortunately go into the specific details of what I am doing yet (fingers crossed I can do so after I make some ...
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14 views

Procedure to Smooth Noise for Threshold Values

Suppose I am looking at an estimate $\hat\beta$ in a clinical trial data. With $a=.05$, a patient with $\hat\beta>1$ is considered to have some medical condition. A daily example could be a 24-hr ...
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Research on neural networks mimicking behavior

My question is regarding neural networks mimicking noise specifically. The idea. I have clinically clean image generated by a ray tracer and a neural network (type does not matter) that is mimicking ...
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1answer
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What is Massart Noise?

One of best papers during NeurIPS 2019 - Distribution-Independent PAC Learning of Halfspaces with Massart Noise mentions Massart Noise in the title. What is this type of noise? How is it different ...
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NaiveBayes: Adding a new predictor which is random noise

In the NaiveBayes method, can adding a random noise vector where each element is sampled from, e.g., a standard normal distribution, help? In what cases this may be a 'clever' approach? I imagine ...
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Ornstein-Uhlenbeck process inside boundaries

I have some simulation of the Ornstein-Uhlenbeck process: ...
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24 views

Learning from “similar” data points

Suppose we have predictor variables $x_{i,1}, x_{i,2}, ..., x_{i,m}$ and a response $y_i$ for $i = 1, ..., 1000$. However, $y_i$ is inherently stochastic in nature, and needs to be represented by ...
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27 views

Math for Gaussian noise on top of another Gaussian noise

I have worked on this project for a while and I have some results. However, I want to communicate in my paper the mathematics involved. When an image is introduced with 11 standard deviations, this ...
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Adding noise to existing noise

I have been working on a little project for myself. It involves adding the following noise types to images: Gaussian blur, Salt and Pepper, and Speckle. I know that there exists some fancy formula for ...
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39 views

Laplacian noise applications

I would like to know whether Laplacian distribution can be used to model a Poisson noise. I have met this case while checking this book and here what it says (see the picture below) As far as I ...
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45 views

Median or mode for measurements with erroneous outliers

Background: I am working with real measurements that likely contain two sources of error, (1) measurements that were performed incorrectly, and (2) natural variability of the measured quantity and ...
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60 views

Log of cost function converges to 0 and is extremely “noisy”

I'm writing my very first NN algorithm to solve a regression problem. I have a signal I would like to use a NN to find its correlation with eight other signals (along the line as f = f(x1, x2,..., x8))...
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60 views

Maximum level of label noise for binary classification so that dataset is “Learnable”?

Assume we have an imbalanced dataset (minority label frequency 1-20%), where subset of samples have their labels randomly flipped. Now, of all samples with positive label (the minority class) in this ...
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Addings noise to emperical distribution

Say I have the following samples from a joint distribution (note I only have access to the samples and not the functional form of the distribution it self) ...
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1answer
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Is there a good measure of “paternless-ness” in a set of data?

This may be a slightly open-ended question, or even a bad one, but are there any measures of looking at a set of data and seeing whether there is any kind of pattern or not? For some context my ...
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Timing Jitter of Counter Query … verify hypothesis / noise reduction

I am measuring traffic on an interface every 5 minutes, but the data platform is having an issue with the SNMP data. I think it is caused by timing jitter ... where the data platform queries the ...

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