We in this paper theoretically go over a rate-distortion based sparse dictionary learning problem. We show that the Degrees-of-Freedom (DoF) interested to be calculated $-$ satnding for the minimal set that guarantees our rate-distortion trade-off $-$ are basically accessible through a Langevin equation. We indeed explore that the relative time evolution of DoF, i.e., the transition jumps is the essential issue for a relaxation over the relative optimisation problem. We subsequently prove the aforementioned relaxation through the \textit{Graphon} principle w.r.t. a stochastic Chordal Schramm-Loewner evolution etc via a minimisation over a distortion between the relative realisation times of two given graphs $\mathscr{G}_1$ and $\mathscr{G}_2$ as $ \mathop{{\rm \mathbb{M}in}}\limits_{ \mathscr{G}_1, \mathscr{G}_2} {\rm \; } \mathcal{D} \Big( t\big( \mathscr{G}_1 , \mathscr{G} \big) , t\big( \mathscr{G}_2 , \mathscr{G} \big) \Big)$. We also extend our scenario to the eavesdropping case. We finally prove the efficiency of our proposed scheme via simulations.
翻译:我们在本文中从理论上将基于比例扭曲的稀有字典学习问题放在一个基于比例扭曲的字典中。 我们显示, 想要为保证我们的成本扭曲交易的美元基本可以通过 Langevin 方程式获取。 我们确实探索了 DoF 的相对时间演变, 即过渡跳跃是缓解相对优化问题的基本问题 。 我们随后通过\ textit{ graphon} 原则 w.r. 来证明上述的放松 。 通过最小化的 Chordalal Schramm- Loewner 进化, 通过最小化两种特定图形的相对实现时间之间的扭曲, $\ mathcr{G} 1 和 $\ mathcr{G} 2 的相对时间演变, 也就是 mathr} gr\ cr=cr=cr=cr=s proupations (math{gr{ gr2} lax gg\\\ crus mas\ mass pas pas. gr% gr\\\ case sals pas pas pas.