Commit 4cfdf644 authored by Ying-Qiu Zheng's avatar Ying-Qiu Zheng
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Update 2021JUL01.md

parent 5d1db82b
......@@ -88,12 +88,12 @@ When $`d >> n`$, Lasso appears superior to the others.
### Panel B - with structured ARD priors (in progress).
#### On the high quality data
Instead of using ARD priors $`\mathbf{w}\sim\mathcal{N}(0, \text{diag}(\alpha_1,...\alpha_d))`$, we assume the hyperparamters have a underlying structure, e.g., $`\mathbf{w}\sim\mathcal{N}(0, \text{diag}(\exp(\mathbf{u}))`$, where $`\mathbf{u}`$ is a Gaussian Process $`\mathbf{u}\sim\mathcal{N}(\mathbf{0}, \mathbf{C}_{\Theta})`$ such that neighbouring features (i.e., adjoining/co-activating voxels) share similar sparsity. [ref](https://proceedings.neurips.cc/paper/2014/file/f9a40a4780f5e1306c46f1c8daecee3b-Paper.pdf)
Instead of using ARD priors $`\mathbf{w}\sim\mathcal{N}(0, \text{diag}(\alpha_1,...\alpha_d))`$, we assume the hyperparamters have a underlying structure, e.g., $`\mathbf{w}\sim\mathcal{N}(0, \text{diag}(\exp(\mathbf{u}))`$, where $`\mathbf{u}`$ is a Gaussian Process $`\mathbf{u}\sim\mathcal{N}(\mathbf{0}, \mathbf{C}_{\Theta})`$ such that neighbouring features (i.e., adjoining/co-activating voxels) share similar sparsity. [(Ref)](https://proceedings.neurips.cc/paper/2014/file/f9a40a4780f5e1306c46f1c8daecee3b-Paper.pdf)
#### On the low quality data
The low-quality coefficients have similar structured ARD priors (exp of a Gaussian Process) that may not share the same hyperparameters with the high-quality coefficients' priors. We seek to solve the hyperparameters for the low-quality classification model, marginalising over the posteriors of the high-quality model.
### Panel C - with structured spike-and-slab priors (in progress).
#### On the high quality data
Similarly, instead of using ARD priors, we assume the coefficients have spike-and-slab priors with latent variables $`\gamma_i^{H}, i=1,2,...d`$, where $`\gamma_i\sim\text{Bernoulli}(\sigma(\theta))`$. The hyperparameter $`\theta`$ can be a Gaussian Process. [ref](https://ohbm.sparklespace.net/srh-2591/)
Similarly, instead of using ARD priors, we assume the coefficients have spike-and-slab priors with latent variables $`\gamma_i^{H}, i=1,2,...d`$, where $`\gamma_i\sim\text{Bernoulli}(\sigma(\theta))`$. The hyperparameter $`\theta`$ can be a Gaussian Process. [(ref)](https://ohbm.sparklespace.net/srh-2591/)
#### On the low quality data
The low quality coefficients have similar priors to enforce sparsity.
The low quality coefficients have similar spike-and-slab priors to enforce sparsity.
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