"Information that is only partially structured (and therefore contains some 'noise' is fuzzy, inconsistent, and indistinct. Such imperfect information may be regarded as having merit only if it represents an intermediate step in structuring the information into a final meaningful form. If the partially Structured information remains in fuzzy form, it will create a state of dissatisfaction in the mind of the originator and certainly in the mind of the recipient. The natural desire is to continue structuring until clarity, simplicity, precision, and definitiveness are obtained." (Cecil H Meyers, "Handbook of Basic Graphs: A modern approach", 1970)
"To understand the need for structuring information, we should examine its opposite - nonstructured information. Nonstructured information may be thought of as exists and can be heard (or sensed with audio devices), but the mind attaches no rational meaning to the sound. In another sense, noise can be equated to writing a group of letters, numbers, and other symbols on a page without any design or key to their meaning. In such a situation, there is nothing the mind can grasp. Nonstructured information can be classified as useless, unless meaning exists somewhere in the jumble and a key can be found to unlock its hidden significance." (Cecil H Meyers, "Handbook of Basic Graphs: A modern approach", 1970)
"Experiments usually are looking for 'signals' of truth, and the search is always ham pered by 'noise' of one kind or another. In judging someone else's experimental results it's important to find out whether they represent a true signal or whether they are just so much noise." (Robert Hooke, "How to Tell the Liars from the Statisticians", 1983)
"Neither noise nor information is predictable." (Ray Kurzweil, "The Age of Spiritual Machines: When Computers Exceed Human Intelligence", 1999)
"Data are collected as a basis for action. Yet before anyone can use data as a basis for action the data have to be interpreted. The proper interpretation of data will require that the data be presented in context, and that the analysis technique used will filter out the noise." (Donald J Wheeler, "Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)
"Data are generally collected as a basis for action. However, unless potential signals are separated from probable noise, the actions taken may be totally inconsistent with the data. Thus, the proper use of data requires that you have simple and effective methods of analysis which will properly separate potential signals from probable noise." (Donald J Wheeler, "Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)
"No matter what the data, and no matter how the values are arranged and presented, you must always use some method of analysis to come up with an interpretation of the data. While every data set contains noise, some data sets may contain signals. Therefore, before you can detect a signal within any given data set, you must first filter out the noise." (Donald J Wheeler," Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)
"We analyze numbers in order to know when a change has occurred in our processes or systems. We want to know about such changes in a timely manner so that we can respond appropriately. While this sounds rather straightforward, there is a complication - the numbers can change even when our process does not. So, in our analysis of numbers, we need to have a way to distinguish those changes in the numbers that represent changes in our process from those that are essentially noise." (Donald J Wheeler, "Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)
"While all data contain noise, some data contain signals. Before you can detect a signal, you must filter out the noise." (Donald J Wheeler, "Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)
"Prediction is rarely perfect. There are usually many unmeasured variables whose effect is referred to as 'noise'. But the extent to which the model box emulates nature's box is a measure of how well our model can reproduce the natural phenomenon producing the data." (Leo Breiman, "Statistical Modeling: The Two Cultures", Statistical Science 16(3), 2001)
"The acquisition of information is a flow from noise to order - a process converting entropy to redundancy. During this process, the amount of information decreases but is compensated by constant re-coding. In the recoding the amount of information per unit increases by means of a new symbol which represents the total amount of the old. The maturing thus implies information condensation. Simultaneously, the redundance decreases, which render the information more difficult to interpret." (Lars Skyttner, "General Systems Theory: Ideas and Applications", 2001)
"In fact, an information theory that leaves out the issue of noise turns out to have no content." (Hans Christian von Baeyer, "Information, The New Language of Science", 2003)
"This phenomenon, common to chaos theory, is also known as sensitive dependence on initial conditions. Just a small change in the initial conditions can drastically change the long-term behavior of a system. Such a small amount of difference in a measurement might be considered experimental noise, background noise, or an inaccuracy of the equipment." (Greg Rae, Chaos Theory: A Brief Introduction, 2006)
"[…] noise is the random variation that results from measurement error or other causes not accounted for. It is always present in a time series to some degree, although we cannot observe it directly." (Galit Shmueli, "Practical Time Series Forecasting: A Hands-On Guide", 2011)
"Some forecasting methods directly model these components by making assumptions about their structure. For example, a popular assumption about trend is that it is linear or exponential over parts, or all, of the given time period. Another common assumption is about the noise structure: many statistical methods assume that the noise follows a normal distribution. The advantage of methods that rely on such assumptions is that when the assumptions are reasonably met, the resulting forecasts will be more robust and the models more understandable." (Galit Shmueli, "Practical Time Series Forecasting: A Hands-On Guide", 2011)
"Overfitting means that the model is not only fitting the systematic component of the data, but also the noise. An over-fitted model is therefore likely to perform poorly on new data." (Galit Shmueli, "Practical Time Series Forecasting: A Hands-On Guide", 2011)
"Data analysis is not generally thought of as being simple or easy, but it can be. The first step is to understand that the purpose of data analysis is to separate any signals that may be contained within the data from the noise in the data. Once you have filtered out the noise, anything left over will be your potential signals. The rest is just details." (Donald J Wheeler," Myths About Data Analysis", International Lean & Six Sigma Conference, 2012)
"Distinguishing the signal from the noise requires both scientific knowledge and self-knowledge." (Nate Silver, "The Signal and the Noise: Why So Many Predictions Fail-but Some Don't", 2012)
"Economists should study financial markets as they actually operate, not as they assume them to operate - observing the way in which information is actually processed, observing the serial correlations, bonanzas, and sudden stops, not assuming these away as noise around the edges of efficient and rational markets." (Adair Turner, "Economics after the Crisis: Objectives and means", 2012)
"Finding patterns is easy in any kind of data-rich environment; that's what mediocre gamblers do. The key is in determining whether the patterns represent signal or noise." (Nate Silver, "The Signal and the Noise: Why So Many Predictions Fail-but Some Don't", 2012)
"The signal is the truth. The noise is what distracts us from the truth." (Nate Silver, "The Signal and the Noise: Why So Many Predictions Fail-but Some Don't", 2012)
"Typically, most outlier detection algorithms use some quantified measure of the outlierness of a data point, such as the sparsity of the underlying region, nearest neighbor based distance, or the fit to the underlying data distribution. Every data point lies on a continuous spectrum from normal data to noise, and finally to anomalies [...] The separation of the different regions of this spectrum is often not precisely defined, and is chosen on an ad-hoc basis according to application-specific criteria. Furthermore, the separation between noise and anomalies is not pure, and many data points created by a noisy generative process may be deviant enough to be interpreted as anomalies on the basis of the outlier score. Thus, anomalies will typically have a much higher outlier score than noise, but this is not a distinguishing factor between the two as a matter of definition. Rather, it is the interest of the analyst, which regulates the distinction between noise and an anomaly." (Charu C Aggarwal, "Outlier Analysis", 2013)
"A complete data analysis will involve the following steps: (i) Finding a good model to fit the signal based on the data. (ii) Finding a good model to fit the noise, based on the residuals from the model. (iii) Adjusting variances, test statistics, confidence intervals, and predictions, based on the model for the noise." (DeWayne R Derryberry, "Basic data analysis for time series with R", 2014)
"The random element in most data analysis is assumed to be white noise - normal errors independent of each other. In a time series, the errors are often linked so that independence cannot be assumed (the last examples). Modeling the nature of this dependence is the key to time series." (DeWayne R Derryberry, "Basic data analysis for time series with R", 2014)
"There are many roads to statistical significance; if data are gathered with no preconceptions at all, statistical significance can obviously be obtained even from pure noise by the simple means of repeatedly performing comparisons, excluding data in different ways, examining different interactions, controlling for different predictors, and so forth. Realistically, though, a researcher will come into a study with strong substantive hypotheses, to the extent that, for any given data set, the appropriate analysis can seem evidently clear. But even if the chosen data analysis is a deterministic function of the observed data, this does not eliminate the problem posed by multiple comparisons." (Andrew Gelman & Eric Loken, "The Statistical Crisis in Science", American Scientist Vol. 102(6), 2014)
"A predictive model overfits the training set when at least some of the predictions it returns are based on spurious patterns present in the training data used to induce the model. Overfitting happens for a number of reasons, including sampling variance and noise in the training set. The problem of overfitting can affect any machine learning algorithm; however, the fact that decision tree induction algorithms work by recursively splitting the training data means that they have a natural tendency to segregate noisy instances and to create leaf nodes around these instances. Consequently, decision trees overfit by splitting the data on irrelevant features that only appear relevant due to noise or sampling variance in the training data. The likelihood of overfitting occurring increases as a tree gets deeper because the resulting predictions are based on smaller and smaller subsets as the dataset is partitioned after each feature test in the path." (John D Kelleher et al, "Fundamentals of Machine Learning for Predictive Data Analytics: Algorithms, Worked Examples, and Case Studies", 2015
"A signal is a useful message that resides in data. Data that isn’t useful is noise. […] When data is expressed visually, noise can exist not only as data that doesn’t inform but also as meaningless non-data elements of the display (e.g. irrelevant attributes, such as a third dimension of depth in bars, color variation that has no significance, and artificial light and shadow effects)." (Stephen Few, "Signal: Understanding What Matters in a World of Noise", 2015)
"Data contain descriptions. Some are true, some are not. Some are useful, most are not. Skillful use of data requires that we learn to pick out the pieces that are true and useful. [...] To find signals in data, we must learn to reduce the noise - not just the noise that resides in the data, but also the noise that resides in us. It is nearly impossible for noisy minds to perceive anything but noise in data." (Stephen Few, "Signal: Understanding What Matters in a World of Noise", 2015)
"When we find data quality issues due to valid data during data exploration, we should note these issues in a data quality plan for potential handling later in the project. The most common issues in this regard are missing values and outliers, which are both examples of noise in the data." (John D Kelleher et al, "Fundamentals of Machine Learning for Predictive Data Analytics: Algorithms, worked examples, and case studies", 2015)
"Information theory leads to the quantification of the information content of the source, as denoted by entropy, the characterization of the information-bearing capacity of the communication channel, as related to its noise characteristics, and consequently the establishment of the relationship between the information content of the source and the capacity of the channel. In short, information theory provides a quantitative measure of the information contained in message signals and help determine the capacity of a communication system to transfer this information from source to sink over a noisy channel in a reliable fashion." (Ali Grami, "Information Theory", 2016)
"High-bias models typically produce simpler models that do not overfit and in those cases the danger is that of underfitting. Models with low-bias are typically more complex and that complexity enables us to represent the training data in a more accurate way. The danger here is that the flexibility provided by higher complexity may end up representing not only a relationship in the data but also the noise. Another way of portraying the bias-variance trade-off is in terms of complexity v simplicity." (Jesús Rogel-Salazar, "Data Science and Analytics with Python", 2017)
"Repeated observations of the same phenomenon do not always produce the same results, due to random noise or error. Sampling errors result when our observations capture unrepresentative circumstances, like measuring rush hour traffic on weekends as well as during the work week. Measurement errors reflect the limits of precision inherent in any sensing device. The notion of signal to noise ratio captures the degree to which a series of observations reflects a quantity of interest as opposed to data variance. As data scientists, we care about changes in the signal instead of the noise, and such variance often makes this problem surprisingly difficult." (Steven S Skiena, "The Data Science Design Manual", 2017)
"The dichotomy of mathematical vs. statistical modeling says more about the culture of modeling and how different disciplines go about thinking about models than about how we should actually model ecological systems. A mathematician is more likely to produce a deterministic, dynamic process model without thinking very much about noise and uncertainty (e.g. the ordinary differential equations that make up the Lotka-Volterra predator prey model). A statistician, on the other hand, is more likely to produce a stochastic but static model, that treats noise and uncertainty carefully but focuses more on static patterns than on the dynamic processes that produce them (e.g. linear regression)." (Ben Bolker, "Ecological Models and Data in R", 2007)
"Using noise (the uncorrelated variables) to fit noise (the residual left from a simple model on the genuinely correlated variables) is asking for trouble." (Steven S Skiena, "The Data Science Design Manual", 2017)
"The high generalization error in a neural network may be caused by several reasons. First, the data itself might have a lot of noise, in which case there is little one can do in order to improve accuracy. Second, neural networks are hard to train, and the large error might be caused by the poor convergence behavior of the algorithm. The error might also be caused by high bias, which is referred to as underfitting. Finally, overfitting (i.e., high variance) may cause a large part of the generalization error. In most cases, the error is a combination of more than one of these different factors." (Charu C Aggarwal, "Neural Networks and Deep Learning: A Textbook", 2018)
"[...] in the statistical world, what we see and measure around us can be considered as the sum of a systematic mathematical idealized form plus some random contribution that cannot yet be explained. This is the classic idea of the signal and the noise." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)
"We thus echo the classical Bayesian literature in concluding that ‘noninformative prior information’ is a contradiction in terms. The flat prior carries information just like any other; it represents the assumption that the effect is likely to be large. This is often not true. Indeed, the signal-to-noise ratios is often very low and then it is necessary to shrink the unbiased estimate. Failure to do so by inappropriately using the flat prior causes overestimation of effects and subsequent failure to replicate them." (Erik van Zwet & Andrew Gelman, "A proposal for informative default priors scaled by the standard error of estimates", The American Statistician 76, 2022)
"Visualizations can remove the background noise from enormous sets of data so that only the most important points stand out to the intended audience. This is particularly important in the era of big data. The more data there is, the more chance for noise and outliers to interfere with the core concepts of the data set." (Kate Strachnyi, "ColorWise: A Data Storyteller’s Guide to the Intentional Use of Color", 2023)
"Overfitting in machine learning is a condition in which a model learns the training data so well that it performs poorly on unseen or test data. The model essentially memorizes the noise or random fluctuations in the training data and fails to generalize its learning to new data. In terms of LLMs, overfitting could occur if the model excessively adjusts to the specifics of the training data, thereby losing its ability to generate sensible responses for unseen prompts. This could lead to the model generating too specific or narrowly tailored responses that do not correctly address the new prompts." (Sinan Ozdemir, "Quick Start Guide to Large Language Models: Strategies and Best Practices for Using ChatGPT and Other LLMs", 2024)
"Besides allowing us to compress a sparse representation into a denser vector, autoencoders are also widely used to process a signal in order to filter out noise and extract only a relevant (characteristic) signal. This can be very useful in many applications, especially when identifying anomalies and outliers." (Aldo Marzullo et al, "Graph Machine Learning" 2nd Ed., 2025)
