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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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What is the difference between “random noise” and “statistical noise”?

According to English wikipedia, there are Statistical noise and Random noise (e.g., white noise). However, I've never seen definitions of what statistical noise is. So, what is the difference if any? ...
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5 views

power spectrum density (V**2/Hz) for nonuniform logarithmic array?

I have nonuniform logarithmic time data array which have 1000pts/decade. that means sampling rate is changing in each intervals or decade. How can I calculate and plot power spectrum density (V**2/Hz)...
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530 views

Influence of noisy training data on neural network

I want to count instances of an object in an image. I can generate as many images as desired in an automated fashion. However I can not yet guarantee that one instance will not completely cover ...
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3answers
880 views

Training a RNN on time series: How to cope with different sequence origins?

I am wondering if I should apply a recurrent neural network on my data. Data is EEG from sleep, and thus there is much information hidden in the temporal domain. Ergo, RNNs make sense. Intro: I have ...
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9 views

RNN outputs noisy predictions

I have an RNN that I've trained and I'm now using to generate new sequences. These sequences are basically discrete state time courses for K different states. The ...
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36 views

Techniques to apply Discrete Wavelet Transform (DWT) to denoise and predict time series

I just started playing with wavelets and have been using this library (https://github.com/rafat/wavelib) to further my understanding and see if 'denoising' the series at all possible levels is ...
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72 views

What is known about 2nd order estimation biases due to correlated noise between response variables?

I have recently run into a statistical bias in a type of analysis that I believe is somewhat common in my field, and not typically corrected for. I would like to know if this is more well-known in ...
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1answer
2k views

What is the Fourier Transform of a brownian motion?

I looked into this article http://en.wikipedia.org/wiki/Brownian_noise and it says that: If we have a brownian motion $W(t) = \int _{0}^{t} dW(s)$, then given that the spectral density of white noise ...
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1answer
5k views

Comparison of distribution mean or median

I am working with very noisy biological data for which I will compare two experimental settings. For each setting I will get a set of measure with a huge variance, sometimes with a skewed distribution,...
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1answer
38 views

differentially private release of histograms (non-negative valued queries)

Two practical questions arise when releasing differentially private histograms/counts via addition of Laplace/Gaussian noise: 1) Is the result of noise addition truncated/rounded (since we know that ...
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15 views

What is the effect of noisy labels in distant-supervision?

I am just learning about distant supervision. I read the paper of Mintz et al. and trying to get some intuition of how the noise influences the classification. My general assumption is, that having ...
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18 views

Bayesian vs Frequentist inference in the presence of noisy data

I'm wondering how Bayesian inference and Classical/Frequentist inference fair towards noisy data. I can't seem to find too much literature addressing this issue and it seems the conclusion is usually ...
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1answer
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Recovering a distribution after Gaussian noise is added

I have a large dataset (400k rows) in which I suspect the data has been obfuscated by the addition of a Gaussian distribution. My guess is that some of the data had categorical variables (based on the ...
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1answer
218 views

Mathematical approach for finding baseline shifts in data

I have a raw signal from a sensor which is attached in this question . The x-axis is time, and the y-axis is the signal response. As you can see from the data, the baseline of the noisy signal shifts ...
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2answers
49 views

Sensitivity of regression parameters to noise

How sensitive are the parameters obtained from OLS, logistic or other regression methods to noise ? By noise, I mean minor changes. For e.g. adding a small noise $-1<\Delta<1$ to $\beta_1$ in $...
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1answer
861 views

How to detect noisy datasets (bias and variance trade-off)

Studying the bias-variance trade-off: expected loss = bias + variance + noise I understand that we minimize this quantity by finding the "best" balance between ...
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46 views

Signal processing techniques for unevenly spaced and repeated measures series

I am considering using signal processing techniques to find the minimum on a noisy 1D response line. More specifically I have a simulation that requires one parameter, but also includes randomness, ...
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158 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 ...
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1answer
57 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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18 views

How to perform feature scaling on noise removel process?

i'm working on dataset contain machinery sensor data. each column(feature) represent different sensor data(pressure, temperature, speed, etc) of the machine part. here task is to predict normal ...
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0answers
32 views

Noise reduction with known noise distribution

I have a time signal with a known noise distribution parameters (gaussian, sd is known). I would like to estimate the true value statistically and in the best case obtain a confidence interval. As I ...
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29 views

Prediction of noisy target variable

The target variable for my regression problem has a very high noise, so measurement error is very high and trends can only be seen in longer time periods. What are good approaches to address this ...
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2answers
144 views

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
259 views

How to specify K cluster in Hierarchical clustering with noisy data?

I'm new in Mining and Clustering and I wonder how to cut off the hierarchical clustering Dendrogram to obtain a specific number of clusters. The problem is here that the data is noisy and the ...
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1answer
34 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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1answer
123 views

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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1answer
144 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
59 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 ...
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27 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

Total Variation Denoising help

I am trying to work through the "Mathematical exposition for 1D digital signals" in the wikipedia entry for Total Variation Denoising (TVD). I am familiar with Lagrange multipliers. However, I cant ...
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1answer
146 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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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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0answers
31 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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0answers
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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2answers
53 views

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
34 views

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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2answers
29 views

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
535 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 (...
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0answers
14 views

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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489 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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0answers
76 views

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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1answer
33 views

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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0answers
26 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 ...
3
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1answer
37 views

Regression with review scores containing excess zeroes

Here is an imaginary problem, representing something I am dealing with right now. We have a set of movies with averages scores ranging from 0 to 10, such that the target is a continuous variable. By ...
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0answers
43 views

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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0answers
10 views

($L_2$) 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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0answers
69 views

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: ...