# Time Series Anomaly Detection with label-free Model Selection

arXiv: https://arxiv.org/abs/2106.07473 · HTML: https://mlsanity.com/paper/2106.07473/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 34 references that are in the map.
- First posted on arXiv 11 Jun 2021.

## Builds on (most cited first, 9 of 9)

- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [LSTM-based Encoder-Decoder for Multi-sensor Anomaly Detection](https://mlsanity.com/paper/1607.00148/) (2016)
- [Extended Isolation Forest](https://mlsanity.com/paper/1811.02141/) (2018)
- [Toward Supervised Anomaly Detection](https://mlsanity.com/paper/1401.6424/) (2014)
- [Anomaly Detection in Univariate Time-series: A Survey on the State-of-the-Art](https://mlsanity.com/paper/2004.00433/) (2020)
- [Predictive Inference Is Free with the Jackknife+-after-Bootstrap](https://mlsanity.com/paper/2002.09025/) (2020)
- [Anomaly Detection by Robust Statistics](https://mlsanity.com/paper/1707.09752/) (2017)
- [Boosted Embeddings for Time Series Forecasting](https://mlsanity.com/paper/2104.04781/) (2021)
- [Automatic Hyperparameter Tuning Method for Local Outlier Factor, with Applications to Anomaly Detection](https://mlsanity.com/paper/1902.00567/) (2019)

## Built on by (most cited first, 3 of 3)

- [mTSBench: Benchmarking Multivariate Time Series Anomaly Detection and Model Selection at Scale](https://mlsanity.com/paper/2506.21550/) (2025)
- [A Reliable Framework for Human-in-the-Loop Anomaly Detection in Time Series](https://mlsanity.com/paper/2405.03234/) (2024)
- [RAMSeS: Robust and Adaptive Model Selection for Time-Series Anomaly Detection Algorithms](https://mlsanity.com/paper/2602.21766/) (2026)

## Abstract (arXiv)

Anomaly detection for time-series data becomes an essential task for many data-driven applications fueled with an abundance of data and out-of-the-box machine-learning algorithms. In many real-world settings, developing a reliable anomaly model is highly challenging due to insufficient anomaly labels and the prohibitively expensive cost of obtaining anomaly examples. It imposes a significant bottleneck to evaluate model quality for model selection and parameter tuning reliably. As a result, many existing anomaly detection algorithms fail to show their promised performance after deployment. In this paper, we propose LaF-AD, a novel anomaly detection algorithm with label-free model selection for unlabeled times-series data. Our proposed algorithm performs a fully unsupervised ensemble learning across a large number of candidate parametric models. We develop a model variance metric that quantifies the sensitivity of anomaly probability with a bootstrapping method. Then it makes a collective decision for anomaly events by model learners using the model variance. Our algorithm is easily parallelizable, more robust for ill-conditioned and seasonal data, and highly scalable for a large number of anomaly models. We evaluate our algorithm against other state-of-the-art methods on a synthetic domain and a benchmark public data set.