Difference between revisions of "Stochastic"
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* [https://www.semanticscholar.org/paper/Markovian-Representation-of-Stochastic-Processes-by-Akaike/3aa40fd8bf6d61357b74c915dc3547bde87e5897 Markovian Representation of Stochastic Processes by Canonical Variables] | * [https://www.semanticscholar.org/paper/Markovian-Representation-of-Stochastic-Processes-by-Akaike/3aa40fd8bf6d61357b74c915dc3547bde87e5897 Markovian Representation of Stochastic Processes by Canonical Variables] | ||
has played an important role in simulating stochastic processes by means of mathematical models. The aim of canonical representation is to display a complex stochastic process using the sum of elementary stochastic functions, such as Brownian motion and White noise. | has played an important role in simulating stochastic processes by means of mathematical models. The aim of canonical representation is to display a complex stochastic process using the sum of elementary stochastic functions, such as Brownian motion and White noise. | ||
| + | |||
| + | == Brownian Motion == | ||
| + | * [https://en.wikipedia.org/wiki/Brownian_noise Brownian noise] | ||
| + | * [https://math.stackexchange.com/questions/1639320/what-is-white-noise-and-how-is-it-related-to-the-brownian-motion What is "white noise" and how is it related to the Brownian motion?] | ||
| + | * [https://pubmed.ncbi.nlm.nih.gov/3154801 White-noise analysis in visual neuroscience | PubMed] | ||
| + | * [https://www.math.lsu.edu/grad/kuo Brief Introduction to White Noise Analysis | LSU Math] | ||
| + | <b>Brownian Motion</b>, also called a Wiener process, is obtained as the integral of a white noise signal. It is named after Robert Brown, who documented the erratic motion for multiple types of inanimate particles in water. White noise is a type of signal noise produced by a random process with a flat power spectral density. This means that it has equal power at all frequencies. | ||
Revision as of 07:12, 23 May 2023
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- Stochastic | Wikipedia
- Stochastic - AI Acceleration Platform
- What Does Stochastic Mean in Machine Learning?
Stochastic refers to a variable process where the outcome involves some randomness and has some uncertainty. It is a mathematical term and is closely related to “randomness” and “probabilistic” and can be contrasted to the idea of “deterministic”. In artificial intelligence, stochastic programs work by using probabilistic methods to solve problems, as in simulated annealing, stochastic neural networks, stochastic optimization, genetic algorithms, and genetic programming.
Stochastic Neural Network (SNN)
Stochastic neural networks are a type of artificial neural network built by introducing random variations into the network, either by giving the network’s artificial neurons stochastic transfer functions, or by giving them stochastic weights.
Stochastic neural networks are used to simulate internal stochastic properties of natural and biological systems. Developing a suitable mathematical model for SNNs is based on the canonical representation of stochastic processes by means of Karhunen-Loève Theorem. There are many research projects that aim to build the next generation of deep learning models which are more data-efficient and can enable machines to learn more efficiently and eventually to be truly creative.
Canonical representation of stochastic processes
- Canonical processes of a stochastic process
- Markovian Representation of Stochastic Processes by Canonical Variables
has played an important role in simulating stochastic processes by means of mathematical models. The aim of canonical representation is to display a complex stochastic process using the sum of elementary stochastic functions, such as Brownian motion and White noise.
Brownian Motion
- Brownian noise
- What is "white noise" and how is it related to the Brownian motion?
- White-noise analysis in visual neuroscience | PubMed
- Brief Introduction to White Noise Analysis | LSU Math
Brownian Motion, also called a Wiener process, is obtained as the integral of a white noise signal. It is named after Robert Brown, who documented the erratic motion for multiple types of inanimate particles in water. White noise is a type of signal noise produced by a random process with a flat power spectral density. This means that it has equal power at all frequencies.
