We propose a novel estimator for a specific class of probabilistic models on discrete spaces such as the Boltzmann machine. The proposed estimator is derived from minimization of a convex risk function and can be constructed without calculating the normalization constant, whose computational cost is exponential order. We investigate statistical properties of the proposed estimator such as consistency and asymptotic normality in the framework of the estimating function. Small experiments show that the proposed estimator can attain comparable performance to the maximum likelihood expectation at a much lower computational cost and is applicable to high-dimensional data.

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