# TenIPS: Inverse Propensity Sampling for Tensor Completion

arXiv: https://arxiv.org/abs/2101.00323 · HTML: https://mlsanity.com/paper/2101.00323/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 36 references that are in the map.
- First posted on arXiv 1 Jan 2021.

## Builds on (most cited first, 16 of 16)

- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [Square Deal: Lower Bounds and Improved Relaxations for Tensor Recovery](https://mlsanity.com/paper/1307.5870/) (2013)
- [Generalized Canonical Polyadic Tensor Decomposition](https://mlsanity.com/paper/1808.07452/) (2018)
- [Provable Tensor Factorization with Missing Data](https://mlsanity.com/paper/1406.2784/) (2014)
- [Missing Not at Random in Matrix Completion: The Effectiveness of Estimating Missingness Probabilities Under a Low Nuclear Norm Assumption](https://mlsanity.com/paper/1910.12774/) (2019)
- [A Max-Norm Constrained Minimization Approach to 1-Bit Matrix Completion](https://mlsanity.com/paper/1309.6013/) (2013)
- [Statistically Optimal and Computationally Efficient Low Rank Tensor Completion from Noisy Entries](https://mlsanity.com/paper/1711.04934/) (2017)
- [Low-Rank Matrix and Tensor Completion via Adaptive Sampling](https://mlsanity.com/paper/1304.4672/) (2013)
- [Missing Slice Recovery for Tensors Using a Low-rank Model in Embedded Space](https://mlsanity.com/paper/1804.01736/) (2018)
- [Low-Rank Tucker Approximation of a Tensor From Streaming Data](https://mlsanity.com/paper/1904.10951/) (2019)
- [Tensor Completion Made Practical](https://mlsanity.com/paper/2006.03134/) (2020)
- [Learning tensors from partial binary measurements](https://mlsanity.com/paper/1804.00108/) (2018)
- [Cross: Efficient Low-rank Tensor Completion](https://mlsanity.com/paper/1611.01129/) (2016)
- [Tensor Completion by Alternating Minimization under the Tensor Train (TT) Model](https://mlsanity.com/paper/1609.05587/) (2016)
- [Fundamental Conditions for Low-CP-Rank Tensor Completion](https://mlsanity.com/paper/1703.10740/) (2017)
- [Proximal-Proximal-Gradient Method](https://mlsanity.com/paper/1708.06908/) (2017)

## Built on by (most cited first, 7 of 7)

- [Causal Matrix Completion](https://mlsanity.com/paper/2109.15154/) (2021)
- [Covariate-assisted Sparse Tensor Completion](https://mlsanity.com/paper/2103.06428/) (2021)
- [Symmetric Matrix Completion with ReLU Sampling](https://mlsanity.com/paper/2406.05822/) (2024)
- [Exploiting Observation Bias to Improve Matrix Completion](https://mlsanity.com/paper/2306.04775/) (2023)
- [Two-Sided Nearest Neighbors: An adaptive and minimax optimal procedure for matrix completion](https://mlsanity.com/paper/2411.12965/) (2024)
- [Truncated Matrix Completion - An Empirical Study](https://mlsanity.com/paper/2504.09873/) (2025)
- [Causal Matrix Completion under Multiple Treatments via Mixed Synthetic Nearest Neighbors](https://mlsanity.com/paper/2603.11942/) (2026)

## Abstract (arXiv)

Tensors are widely used to represent multiway arrays of data. The recovery of missing entries in a tensor has been extensively studied, generally under the assumption that entries are missing completely at random (MCAR). However, in most practical settings, observations are missing not at random (MNAR): the probability that a given entry is observed (also called the propensity) may depend on other entries in the tensor or even on the value of the missing entry. In this paper, we study the problem of completing a partially observed tensor with MNAR observations, without prior information about the propensities. To complete the tensor, we assume that both the original tensor and the tensor of propensities have low multilinear rank. The algorithm first estimates the propensities using a convex relaxation and then predicts missing values using a higher-order SVD approach, reweighting the observed tensor by the inverse propensities. We provide finite-sample error bounds on the resulting complete tensor. Numerical experiments demonstrate the effectiveness of our approach.