Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: One of the main problems in probabilistic grammatical inference consists in inferring a stochastic language, i.e. a probability distribution, in some class of probabilistic models, from a sample of strings independently drawn according to a fixed unknown target distribution  p . Here,  consider the class of  rational stochastic languages  composed of stochastic languages that can be computed by  multiplicity automata , which can be vied as a generalization of probabilistic automata. Rational stochastic languages  p  have a useful algebraic characterization: all the mappings  up :  v  →  p ( uv ) lie in a finite dimensional vector subspace  V p  * of the vector space ℝ 〈〈Σ〉〉 composed of all real-valued functions defined over Σ*. Hence, a first step in the grammatical inference process can consist in identifying the subspace  V p  *. ,  study the possibility of using Principal Component Analysis to achieve this task.  provide an inference algorithm which computes an estimate of this space and then build a multiplicity automaton which computes an estimate of the target distribution.  prove some theoretical properties of this algorithm and  provide results from numerical simulations that confirm the relevance of our approach.
['Raphaël Bailly', 'François Denis', 'Liva Ralaivola']
I am writing a research paper on a idea Grammatical inference as a principal component analysis problem
[{"from": "human", "value": "I am writing a research paper on a idea Grammatical inference as a principal component analysis problem"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: One of the main problems in probabilistic grammatical inference consists in inferring a stochastic language, i.e. a probability distribution, in some class of probabilistic models, from a sample of strings independently drawn according to a fixed unknown target distribution  p . Here,  consider the class of  rational stochastic languages  composed of stochastic languages that can be computed by  multiplicity automata , which can be vied as a generalization of probabilistic automata. Rational stochastic languages  p  have a useful algebraic characterization: all the mappings  up :  v  \u2192  p ( uv ) lie in a finite dimensional vector subspace  V p  * of the vector space \u211d \u2329\u2329\u03a3\u232a\u232a composed of all real-valued functions defined over \u03a3*. Hence, a first step in the grammatical inference process can consist in identifying the subspace  V p  *. ,  study the possibility of using Principal Component Analysis to achieve this task.  provide an inference algorithm which computes an estimate of this space and then build a multiplicity automaton which computes an estimate of the target distribution.  prove some theoretical properties of this algorithm and  provide results from numerical simulations that confirm the relevance of our approach."}]