Name
Abstract | ||
|---|---|---|
A new successive encoding scheme is proposed to effectively generate a random vector with prescribed joint density that induces a latent Gaussian tree structure. We prove the accuracy of such encoding scheme in terms of vanishing total variation distance between the synthesized and desired statistics. The encoding algorithm relies on the learned structure of tree to use minimal number of common random variables to synthesize the desired density, with compact modeling complexity. We characterize the achievable rate region for the rate tuples of multi-layer latent Gaussian tree, through which the number of bits needed to simulate such Gaussian joint density are determined. The random sources used in our algorithm are the latent variables at the top layer of tree along with Bernoulli sign inputs, which capture the correlation signs between the variables. In latent Gaussian trees the pairwise correlation signs between the variables are intrinsically unrecoverable. Such information is vital since it completely determines the direction in which two variables are associated. Given the derived achievable rate region for synthesis of latent Gaussian trees, we also quantify the amount of information loss due to unrecoverable sign information. It is shown that maximizing the achievable rate-region is equivalent to finding the worst case density for Bernoulli sign inputs where maximum amount of sign information is lost. |
Year | Venue | Field |
|---|---|---|
2016 | arXiv: Information Theory | Total variation,Discrete mathematics,Random variable,Gaussian random field,Latent variable,Gaussian,Multivariate random variable,Tree structure,Mathematics,Bernoulli's principle |
DocType | Volume | Citations |
Journal | abs/1608.04484 | 0 |
PageRank | References | Authors |
0.34 | 4 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ali Moharrer | 1 | 7 | 4.56 |
| Shuangqing Wei | 2 | 409 | 57.82 |
| George Amariucai | 3 | 65 | 12.06 |
| Jing Deng | 4 | 3887 | 221.06 |