{"ID":2865919,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.20993","arxiv_id":"2509.20993","title":"Learning the Inverse Temperature of Ising Models under Hard Constraints using One Sample","abstract":"We consider the problem of estimating inverse temperature parameter $β$ of an $n$-dimensional truncated Ising model using a single sample. Given a graph $G = (V,E)$ with $n$ vertices, a truncated Ising model is a probability distribution over the $n$-dimensional hypercube $\\{-1,1\\}^n$ where each configuration $\\mathbfσ$ is constrained to lie in a truncation set $S \\subseteq \\{-1,1\\}^n$ and has probability $\\Pr(\\mathbfσ) \\propto \\exp(β\\mathbfσ^\\top A\\mathbfσ)$ with $A$ being the adjacency matrix of $G$. We adopt the recent setting of [Galanis et al. SODA'24], where the truncation set $S$ can be expressed as the set of satisfying assignments of a $k$-SAT formula. Given a single sample $\\mathbfσ$ from a truncated Ising model, with inverse parameter $β^*$, underlying graph $G$ of bounded degree $Δ$ and $S$ being expressed as the set of satisfying assignments of a $k$-SAT formula, we design in nearly $O(n)$ time an estimator $\\hatβ$ that is $O(Δ^3/\\sqrt{n})$-consistent with the true parameter $β^*$ for $k \\gtrsim \\log(d^2k)Δ^3.$ Our estimator is based on the maximization of the pseudolikelihood, a notion that has received extensive analysis for various probabilistic models without [Chatterjee, Annals of Statistics '07] or with truncation [Galanis et al. SODA '24]. Our approach generalizes recent techniques from [Daskalakis et al. STOC '19, Galanis et al. SODA '24], to confront the more challenging setting of the truncated Ising model.","short_abstract":"We consider the problem of estimating inverse temperature parameter $β$ of an $n$-dimensional truncated Ising model using a single sample. Given a graph $G = (V,E)$ with $n$ vertices, a truncated Ising model is a probability distribution over the $n$-dimensional hypercube $\\{-1,1\\}^n$ where each configuration $\\mathbfσ...","url_abs":"https://arxiv.org/abs/2509.20993","url_pdf":"https://arxiv.org/pdf/2509.20993v2","authors":"[\"Rohan Chauhan\",\"Ioannis Panageas\"]","published":"2025-09-25T10:42:19Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.DS\",\"stat.ML\"]","methods":"[]","has_code":false}