Energy-based Model
Energy-based model like Boltzmann machine is a special type of neural networks
Diffusion Models for Forecasting
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Category: { Energy-based Model }
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Summary: Objective In a denoising diffusion model, given
an input $\mathbf x^0$ drawn from a complicated and unknown distribution $q(\mathbf x^0)$, we find
a latent space with a simple and manageable distribution, e.g., normal distribution, and the transformations from $\mathbf x^0$ to $\mathbf x^n$, as well as the transformations from $\mathbf x^n$ to $\mathbf x^0$. An Example For example, with $N=5$, the forward process is
flowchart LR x0 --> x1 --> x2 --> x3 --> x4 --> x5 and the reverse process is
flowchart LR x5 --> x4 --> x3 --> x2 --> x1 --> x0 The joint distribution we are searching for is
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4 Restricted Boltzmann Machine
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Category: { Energy-based Model }
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References:
- Mehta P, Bukov M, Wang C-HH, Day AGRR, Richardson C, Fisher CK, et al. A high-bias, low-variance introduction to Machine Learning for physicists. Phys Rep. 2018;810: 122. doi:10.1016/j.physrep.2019.03.001
- Hubbard J. Calculation of Partition Functions. Physical Review Letters. 1959. pp. 77–78. doi:10.1103/physrevlett.3.77
- Contributors to Wikimedia projects. Cumulant. In: Wikipedia [Internet]. 7 May 2021 [cited 18 Jun 2021]. Available: https://en.wikipedia.org/wiki/Cumulant
Summary: Introducing latent variables to Boltzmann machine and restrict the connections within groups.
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3 Boltzmann Machine
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Category: { Energy-based Model }
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References:
- Mehta P, Bukov M, Wang C-HH, Day AGRR, Richardson C, Fisher CK, et al. A high-bias, low-variance introduction to Machine Learning for physicists. Phys Rep. 2018;810: 122. doi:10.1016/j.physrep.2019.03.001
- Hinton GE. Boltzmann Machines. 2007.
Summary: Boltzmann machine is much like a spin glass model in physics. In short words, Boltzmann machine is a machine that has nodes that can take values, and the nodes are connected through some weight. It is just like any other neual nets but with complications and theoretical implications.
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1 MaxEnt Model
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Summary: Maximum Entropy models makes least assumption about the data
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