Difference between revisions of "Stochastic"
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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 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. | ||
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| + | = 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. | ||
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| + | 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. | ||
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| + | = Canonical representation of stochastic processes = | ||
| + | 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. | ||
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| + | Source: Conversation with Bing, 5/23/2023 | ||
| + | (1) Stochastic Neural Networks for Modelling Random Processes from Observed .... https://link.springer.com/chapter/10.1007/978-3-319-28495-8_5. | ||
| + | (2) Canonical processes of a stochastic process. https://math.stackexchange.com/questions/308581/canonical-processes-of-a-stochastic-process. | ||
| + | (3) Kolmogorov extension theorem - Wikipedia. https://en.wikipedia.org/wiki/Kolmogorov_extension_theorem. | ||
| + | (4) Markovian Representation of Stochastic Processes by Canonical Variables .... https://epubs.siam.org/doi/10.1137/0313010. | ||
| + | (5) Markovian Representation of Stochastic Processes by Canonical Variables .... https://www.semanticscholar.org/paper/Markovian-Representation-of-Stochastic-Processes-by-Akaike/3aa40fd8bf6d61357b74c915dc3547bde87e5897. | ||
Revision as of 07:01, 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
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.
Source: Conversation with Bing, 5/23/2023 (1) Stochastic Neural Networks for Modelling Random Processes from Observed .... https://link.springer.com/chapter/10.1007/978-3-319-28495-8_5. (2) Canonical processes of a stochastic process. https://math.stackexchange.com/questions/308581/canonical-processes-of-a-stochastic-process. (3) Kolmogorov extension theorem - Wikipedia. https://en.wikipedia.org/wiki/Kolmogorov_extension_theorem. (4) Markovian Representation of Stochastic Processes by Canonical Variables .... https://epubs.siam.org/doi/10.1137/0313010. (5) Markovian Representation of Stochastic Processes by Canonical Variables .... https://www.semanticscholar.org/paper/Markovian-Representation-of-Stochastic-Processes-by-Akaike/3aa40fd8bf6d61357b74c915dc3547bde87e5897.
