# Learning from Snapshots of Discrete and Continuous Data Streams

arXiv: https://arxiv.org/abs/2412.06079 · HTML: https://mlsanity.com/paper/2412.06079/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 16 references that are in the map.
- First posted on arXiv 8 Dec 2024.

## Builds on (most cited first, 7 of 7)

- [Online Learning with Feedback Graphs: Beyond Bandits](https://mlsanity.com/paper/1502.07617/) (2015)
- [An Information-Theoretic Approach to Minimax Regret in Partial Monitoring](https://mlsanity.com/paper/1902.00470/) (2019)
- [An efficient algorithm for learning with semi-bandit feedback](https://mlsanity.com/paper/1305.2732/) (2013)
- [Efficient and Parsimonious Agnostic Active Learning](https://mlsanity.com/paper/1506.08669/) (2015)
- [List Online Classification](https://mlsanity.com/paper/2303.15383/) (2023)
- [Minimax Regret for Partial Monitoring: Infinite Outcomes and Rustichini's Regret](https://mlsanity.com/paper/2202.10997/) (2022)
- [The Dimension of Self-Directed Learning](https://mlsanity.com/paper/2402.13400/) (2024)

## Built on by (most cited first, 2 of 2)

- [AdaKoop: Efficient Modeling of Nonlinear Dynamics from Nonstationary Data Streams with Koopman Operator Regression](https://mlsanity.com/paper/2606.04930/) (2026)
- [Improving scalable oversight with co-trained monitors](https://mlsanity.com/paper/2609.36049/) (2026)

## Abstract (arXiv)

Imagine a smart camera trap selectively clicking pictures to understand animal movement patterns within a particular habitat. These "snapshots", or pieces of data captured from a data stream at adaptively chosen times, provide a glimpse of different animal movements unfolding through time. Learning a continuous-time process through snapshots, such as smart camera traps, is a central theme governing a wide array of online learning situations. In this paper, we adopt a learning-theoretic perspective in understanding the fundamental nature of learning different classes of functions from both discrete data streams and continuous data streams. In our first framework, the textitupdate-and-deploy setting, a learning algorithm discretely queries from a process to update a predictor designed to make predictions given as input the data stream. We construct a uniform sampling algorithm that can learn with bounded error any concept class with finite Littlestone dimension. Our second framework, known as the blind-prediction setting, consists of a learning algorithm generating predictions independently of observing the process, only engaging with the process when it chooses to make queries. Interestingly, we show a stark contrast in learnability where non-trivial concept classes are unlearnable. However, we show that adaptive learning algorithms are necessary to learn sets of time-dependent and data-dependent functions, called pattern classes, in either framework. Finally, we develop a theory of pattern classes under discrete data streams for the blind-prediction setting.