# Exponentially Weighted Moving Models

arXiv: https://arxiv.org/abs/2404.08136 · HTML: https://mlsanity.com/paper/2404.08136/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 29 references that are in the map.
- First posted on arXiv 11 Apr 2024.

## Builds on (most cited first, 3 of 3)

- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Fitting Laplacian Regularized Stratified Gaussian Models](https://mlsanity.com/paper/2005.01752/) (2020)

## Built on by (most cited first, 4 of 4)

- [ReliabilityRAG: Effective and Provably Robust Defense for RAG-based Web-Search](https://mlsanity.com/paper/2509.23519/) (2025)
- [Optimal Empirical Risk Minimization under Temporal Distribution Shifts](https://mlsanity.com/paper/2507.13287/) (2025)
- [GaiaFlow: Semantic-Guided Diffusion Tuning for Carbon-Frugal Search](https://mlsanity.com/paper/2602.15423/) (2026)
- [Multi-objective optimization and quantum hybridization of equivariant deep learning interatomic potentials](https://mlsanity.com/paper/2602.16908/) (2026)

## Abstract (arXiv)

An exponentially weighted moving model (EWMM) for a vector time series fits a new data model each time period, based on an exponentially fading loss function on past observed data. The well known and widely used exponentially weighted moving average (EWMA) is a special case that estimates the mean using a square loss function. For quadratic loss functions EWMMs can be fit using a simple recursion that updates the parameters of a quadratic function. For other loss functions, the entire past history must be stored, and the fitting problem grows in size as time increases. We propose a general method for computing an approximation of EWMM, which requires storing only a window of a fixed number of past samples, and uses an additional quadratic term to approximate the loss associated with the data before the window. This approximate EWMM relies on convex optimization, and solves problems that do not grow with time. We compare the estimates produced by our approximation with the estimates from the exact EWMM method.