# Online Detection of Changes in Moment-Based Projections: When to Retrain Deep Learners or Update Portfolios?

arXiv: https://arxiv.org/abs/2302.07198 · HTML: https://mlsanity.com/paper/2302.07198/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 41 references that are in the map.
- First posted on arXiv 14 Feb 2023.

## Builds on (most cited first, 6 of 6)

- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [Regularized M-estimators with nonconvexity: Statistical and algorithmic theory for local optima](https://mlsanity.com/paper/1305.2436/) (2013)
- [Statistical guarantees for sparse deep learning](https://mlsanity.com/paper/2212.05427/) (2022)
- [Restricted Strong Convexity of Deep Learning Models with Smooth Activations](https://mlsanity.com/paper/2209.15106/) (2022)
- [Projection inference for high-dimensional covariance matrices with structured shrinkage targets](https://mlsanity.com/paper/2211.02368/) (2022)

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

- [ARC: Augmented-Rank Conformalization for Changepoint Localization --- Finite-Sample Validity and Distribution-Robust Efficiency](https://mlsanity.com/paper/2608.08424/) (2026)
- [Context-Adaptive Thresholding for Conditionally Representative Monitoring and Classification](https://mlsanity.com/paper/2609.26652/) (2026)

## Abstract (arXiv)

Training deep learning neural networks often requires massive amounts of computational ressources. We propose to sequentially monitor network predictions to trigger retraining only if the predictions are no longer valid. This can reduce drastically computational costs and opens a door to green deep learning. Our approach is based on the relationship to projected second moments monitoring, a problem also arising in other areas such as computational finance. Various open-end as well as closed-end monitoring rules are studied under mild assumptions on the training sample and the observations of the monitoring period. The results allow for high-dimensional non-stationary time series data and thus, especially, non-i.i.d. training data. Asymptotics is based on Gaussian approximations of projected partial sums allowing for an estimated projection vector. Estimation of projection vectors is studied both for classical non-ℓ0-sparsity as well as under sparsity. For the case that the optimal projection depends on the unknown covariance matrix, hard- and soft-thresholded estimators are studied. The method is analyzed by simulations and supported by synthetic data experiments.