This paper is concerned with estimation of functionals of a latent weight function that satisfies possibly high‐dimensional multiplicative moment conditions. Main examples are functionals of stochastic discount factors in asset pricing, missing data problems, and treatment effects. We propose to estimate the latent weight function by an information theoretic approach combined with the ℓ₁‐penalization technique to deal with high‐dimensional moment conditions under sparsity. We study asymptotic properties of the proposed method and illustrate it by a theoretical example on treatment effect analysis and empirical example on estimation of stochastic discount factors.