White Noise (Statistics)

What is White Noise (Statistics)?

White Noise is a random signal with equal intensities at every frequency and is often defined in statistics as a signal whose samples are a sequence of unrelated, random variables with no mean and limited variance. In some cases, it may be required that the samples are independent and have identical probabilities. Furthermore, when each sample has a normal distribution with no mean, the signal is labelled as additive white Gaussian noise. While in this context, white noise refers to a statistical signal, the concept of white noise extends to other technical disciplines such as physics, audio engineering, and telecommunications.

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How does White Noise work?

White Noise, by definition, works by defining parameters in which data is ensured to be random, unrelated, and have zero mean. White Noise can even be produced within the context of binary variables. For example, a sequence of 0's and 1's would be white if the sequence is statistically uncorrelated. Additionally, any continuous distribution of variables, like a normal distribution, can also be white.

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White Noise and Machine Learning

As mentioned above, White Noise is a concept that extends beyond strictly mathematics, and into other technical disciplines, including computer science. Neural networks can incorporate the principles of white noise in their models. For example, a data scientist may intentionally add noise to their neural network as it not only can improve the training performance, but also the overall accuracy of the model. There are a few methods of incorporating the principles of noise into one's model. One popular method of using noise is through a technique called dropout regularization. In this method, some of the units in the network are randomly zeroed out, forcing the network to train and learn under limited bandwidth.