Unsupervised Learning: Difference between revisions
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====Model==== | ====Model==== | ||
Our model for how the data is generated is as follows: | Our model for how the data is generated is as follows: | ||
* Generate latent variables <math>z^{(1)},...,z^{(m)} \in \mathbb{R}^r<math> iid where dimension r is less than n. | * Generate latent variables <math>z^{(1)},...,z^{(m)} \in \mathbb{R}^r</math> iid where dimension r is less than n. | ||
** We assume <math>Z^{(i)} \sim N(\mathbf{0},\mathbf{I})</math> | ** We assume <math>Z^{(i)} \sim N(\mathbf{0},\mathbf{I})</math> | ||
* Generate <math>x^{(i)}</math> where <math>X^{(i)} \vert Z^{(i)} \sin N(g_{\theta}(z), \sigma^2 \mathbf{I})</math> | * Generate <math>x^{(i)}</math> where <math>X^{(i)} \vert Z^{(i)} \sin N(g_{\theta}(z), \sigma^2 \mathbf{I})</math> | ||