Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Structured high-cardinality data arises in many domains and poses a major challenge for both modeling and inference, which is beyond current graphical model frameworks.  view these data as a stream $(x^{(t)})_{t = 1}^n$ of $n$ observations from an unknown distribution $P$, where $x^{(t)} \in [M]^K$ is a $K$-dimensional vector and $M$ is the cardinality of its entries, which is very large. Suppose that the graphical model $\mathcal{G}$ of $P$ is known, and let $\bar{P}$ be the maximum-likelihood estimate (MLE) of $P$ from $(x^{(t)})_{t = 1}^n$ conditioned on $\mathcal{G}$. In this work,  design and analyze algorithms that approximate $\bar{P}$ with $\hat{P}$, such that $\hat{P}(x) \approx \bar{P}(x)$ for any $x \in [M]^K$ with a high probability, and crucially in the space independent of $M$. The key idea of our approximations is to use the structure of $\mathcal{G}$ and approximately estimate its factors by "sketches". The sketches hash high-cardinality variables using random projections. Our approximations are computationally and space efficient, being independent of $M$. Our error bounds are multiplicative and provably improve upon those of the count-min (CM) sketch, a state-of-the-art approach to estimating the frequency of values in a stream, in a class of naive Bayes models.  evaluate our algorithms on synthetic and real-world problems, and report an order of magnitude improvements over the CM sketch.
['Branislav Kveton', 'Hung Hai Bui', 'Mohammad Ghavamzadeh', 'Georgios Theocharous', 'S. Muthukrishnan', 'Siqi Sun']
I am writing a research paper on a idea Graphical Model Sketch
[{"from": "human", "value": "I am writing a research paper on a idea Graphical Model Sketch"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Structured high-cardinality data arises in many domains and poses a major challenge for both modeling and inference, which is beyond current graphical model frameworks.  view these data as a stream $(x^{(t)})_{t = 1}^n$ of $n$ observations from an unknown distribution $P$, where $x^{(t)} \\in [M]^K$ is a $K$-dimensional vector and $M$ is the cardinality of its entries, which is very large. Suppose that the graphical model $\\mathcal{G}$ of $P$ is known, and let $\\bar{P}$ be the maximum-likelihood estimate (MLE) of $P$ from $(x^{(t)})_{t = 1}^n$ conditioned on $\\mathcal{G}$. In this work,  design and analyze algorithms that approximate $\\bar{P}$ with $\\hat{P}$, such that $\\hat{P}(x) \\approx \\bar{P}(x)$ for any $x \\in [M]^K$ with a high probability, and crucially in the space independent of $M$. The key idea of our approximations is to use the structure of $\\mathcal{G}$ and approximately estimate its factors by \"sketches\". The sketches hash high-cardinality variables using random projections. Our approximations are computationally and space efficient, being independent of $M$. Our error bounds are multiplicative and provably improve upon those of the count-min (CM) sketch, a state-of-the-art approach to estimating the frequency of values in a stream, in a class of naive Bayes models.  evaluate our algorithms on synthetic and real-world problems, and report an order of magnitude improvements over the CM sketch."}]