Near-Efficient and Non-Asymptotic Multiway Inference

Technical Report · Sat Nov 01 04:00:00 EDT 2025

DOI:https://doi.org/10.2172/3002981· OSTI ID:3002981

López, Oscar F. ^[1]; Prasadan, Arvind ^[2]; Llosa, Carlos ^[3]; Lehoucq, Richard B. ^[3]; Dunlavy, Daniel Michael ^[3]

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1. Florida Atlantic Univ., Boca Raton, FL (United States)
2. Sandia National Laboratories (SNL-CA), Livermore, CA (United States)
3. Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

We establish non-asymptotic efficiency guarantees for tensor decomposition–based inference in count data models. Under a Poisson framework, we consider two related goals: (i) parametric inference, the estimation of the full distributional parameter tensor, and (ii) multiway analysis, the recovery of its canonical polyadic (CP) decomposition factors. Our main result shows that in the rank-one setting, a rank-constrained maximum-likelihood estimator achieves multiway analysis with variance matching the Cramér–Rao Lower Bound (CRLB) up to absolute constants and logarithmic factors. This provides a general framework for studying “near-efficient” multiway estimators in finite-sample settings. For higher ranks, we illustrate that our multiway estimator may not attain the CRLB; nevertheless, CP-based parametric inference remains nearly minimax optimal, with error bounds that improve on prior work by offering more favorable dependence on the CP rank. Numerical experiments corroborate near-efficiency in the rank-one case and highlight the efficiency gap in higher-rank scenarios.

• Research Organization: Sandia National Laboratories (SNL-CA), Livermore, CA (United States)
• Sponsoring Organization: USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)
• DOE Contract Number: NA0003525
• OSTI ID: 3002981
• Report Number(s): SAND--2025-14006R; 1793733
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING