# Near-Efficient and Non-Asymptotic Multiway Inference

arXiv: https://arxiv.org/abs/2511.05368 · HTML: https://mlsanity.com/paper/2511.05368/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 39 references that are in the map.
- First posted on arXiv 7 Nov 2025.

## Builds on (most cited first, 13 of 13)

- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [An Optimal Statistical and Computational Framework for Generalized Tensor Estimation](https://mlsanity.com/paper/2002.11255/) (2020)
- [Spectral algorithms for tensor completion](https://mlsanity.com/paper/1612.07866/) (2016)
- [Learning from Binary Multiway Data: Probabilistic Tensor Decomposition and its Statistical Optimality](https://mlsanity.com/paper/1811.05076/) (2018)
- [Learning tensors from partial binary measurements](https://mlsanity.com/paper/1804.00108/) (2018)
- [Incoherent Tensor Norms and Their Applications in Higher Order Tensor Completion](https://mlsanity.com/paper/1606.03504/) (2016)
- [Cross: Efficient Low-rank Tensor Completion](https://mlsanity.com/paper/1611.01129/) (2016)
- [Poisson Matrix Recovery and Completion](https://mlsanity.com/paper/1504.05229/) (2015)
- [Near-optimal sample complexity for convex tensor completion](https://mlsanity.com/paper/1711.04965/) (2017)
- [Tensor denoising and completion based on ordinal observations](https://mlsanity.com/paper/2002.06524/) (2020)
- [Finite-Sample Maximum Likelihood Estimation of Location](https://mlsanity.com/paper/2206.02348/) (2022)
- [Zero-Truncated Poisson Regression for Sparse Multiway Count Data Corrupted by False Zeros](https://mlsanity.com/paper/2201.10014/) (2022)
- [Spectral gap-based deterministic tensor completion](https://mlsanity.com/paper/2306.06262/) (2023)

## Abstract (arXiv)

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 Cram'er-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.