# NOCTA: Non-Greedy Objective Cost-Tradeoff Acquisition for Longitudinal Data

arXiv: https://arxiv.org/abs/2507.12412 · HTML: https://mlsanity.com/paper/2507.12412/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 33 references that are in the map.
- First posted on arXiv 16 Jul 2025.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [EDDI: Efficient Dynamic Discovery of High-Value Information with Partial VAE](https://mlsanity.com/paper/1809.11142/) (2018)
- [Variational Autoencoder with Arbitrary Conditioning](https://mlsanity.com/paper/1806.02382/) (2018)
- [Learning to Maximize Mutual Information for Dynamic Feature Selection](https://mlsanity.com/paper/2301.00557/) (2023)
- [Active Feature Acquisition with Generative Surrogate Models](https://mlsanity.com/paper/2010.02433/) (2020)
- [Classification with Costly Features as a Sequential Decision-Making Problem](https://mlsanity.com/paper/1909.02564/) (2019)
- [Reinforcement Learning with Efficient Active Feature Acquisition](https://mlsanity.com/paper/2011.00825/) (2020)
- [Estimating Conditional Mutual Information for Dynamic Feature Selection](https://mlsanity.com/paper/2306.03301/) (2023)
- [Acquisition Conditioned Oracle for Nongreedy Active Feature Acquisition](https://mlsanity.com/paper/2302.13960/) (2023)
- [A Survey on Active Feature Acquisition Strategies](https://mlsanity.com/paper/2502.11067/) (2025)
- [ASAC: Active Sensing using Actor-Critic models](https://mlsanity.com/paper/1906.06796/) (2019)
- [Active Acquisition for Multimodal Temporal Data: A Challenging Decision-Making Task](https://mlsanity.com/paper/2211.05039/) (2022)
- [Feature-Budgeted Random Forest](https://mlsanity.com/paper/1502.05925/) (2015)
- [A Unified Model for Longitudinal Multi-Modal Multi-View Prediction with Missingness](https://mlsanity.com/paper/2403.12211/) (2024)
- [SoundSieve: Seconds-Long Audio Event Recognition on Intermittently-Powered Systems](https://mlsanity.com/paper/2305.16445/) (2023)

## Built on by (most cited first, 1 of 1)

- [When Does Test-Time Physical Diagnosis Pay? A Frozen Policy Buys Evidence It Never Reads](https://mlsanity.com/paper/2609.22299/) (2026)

## Abstract (arXiv)

In many critical domains, features are not freely available at inference time: each measurement may come with a cost of time, money, and risk. Longitudinal prediction further complicates this setting because both features and labels evolve over time, and missing measurements at earlier timepoints may become permanently unavailable. We propose NOCTA, a Non-Greedy Objective Cost-Tradeoff Acquisition framework that sequentially acquires the most informative features at inference time while accounting for both temporal dynamics and acquisition cost. NOCTA is driven by a novel objective, NOCT, which evaluates a candidate set of future feature-time acquisitions by its expected predictive loss together with its acquisition cost. Since NOCT depends on unobserved future trajectories at inference time, we develop two complementary estimators: (i) NOCT-Contrastive, which learns an embedding of partial observations utilizing the induced distribution over future acquisitions, and (ii) NOCT-Amortized, which directly predicts NOCT for candidate plans with a neural network. Experiments on synthetic and real-world medical datasets demonstrate that both NOCTA estimators outperform existing baselines, achieving higher accuracy at lower acquisition costs.