MoTM: Towards a Foundation Model for Time Series Imputation based on Continuous Modeling

TL;DR

This paper introduces MoTM, a novel foundation model for time series imputation that leverages a mixture of implicit neural representations to handle various missing data scenarios and distribution shifts.

Contribution

MoTM combines multiple INRs trained on different time series patterns with a ridge regressor for adaptive, out-of-domain imputation, advancing foundation models in time series analysis.

Findings

Robust in-domain and out-of-domain imputation performance

Effective handling of diverse missing data scenarios

Generalizes well across different sampling rates

Abstract

Recent years have witnessed a growing interest for time series foundation models, with a strong emphasis on the forecasting task. Yet, the crucial task of out-of-domain imputation of missing values remains largely underexplored. We propose a first step to fill this gap by leveraging implicit neural representations (INRs). INRs model time series as continuous functions and naturally handle various missing data scenarios and sampling rates. While they have shown strong performance within specific distributions, they struggle under distribution shifts. To address this, we introduce MoTM (Mixture of Timeflow Models), a step toward a foundation model for time series imputation. Building on the idea that a new time series is a mixture of previously seen patterns, MoTM combines a basis of INRs, each trained independently on a distinct family of time series, with a ridge regressor that adapts to the observed context at inference. We demonstrate robust in-domain and out-of-domain generalization across diverse imputation scenarios (e.g., block and pointwise missingness, variable sampling rates), paving the way for adaptable foundation imputation models.