# Latent Temporal Flows for Multivariate Analysis of Wearables Data

arXiv: https://arxiv.org/abs/2210.07475 · HTML: https://mlsanity.com/paper/2210.07475/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 53 references that are in the map.
- First posted on arXiv 14 Oct 2022.

## Builds on (most cited first, 24 of 24)

- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Generating Sequences With Recurrent Neural Networks](https://mlsanity.com/paper/1308.0850/) (2013)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [Residual Flows for Invertible Generative Modeling](https://mlsanity.com/paper/1906.02735/) (2019)
- [Towards K-means-friendly Spaces: Simultaneous Deep Learning and Clustering](https://mlsanity.com/paper/1610.04794/) (2016)
- [Time Series Data Augmentation for Deep Learning: A Survey](https://mlsanity.com/paper/2002.12478/) (2020)
- [Input complexity and out-of-distribution detection with likelihood-based generative models](https://mlsanity.com/paper/1909.11480/) (2019)
- [High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes](https://mlsanity.com/paper/1910.03002/) (2019)
- [Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flows](https://mlsanity.com/paper/2002.06103/) (2020)
- [A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised Learning](https://mlsanity.com/paper/1710.05741/) (2017)
- [Benchmarking Deep Learning Interpretability in Time Series Predictions](https://mlsanity.com/paper/2010.13924/) (2020)
- [Deep Factors for Forecasting](https://mlsanity.com/paper/1905.12417/) (2019)
- [Temporal Latent Auto-Encoder: A Method for Probabilistic Multivariate Time Series Forecasting](https://mlsanity.com/paper/2101.10460/) (2021)
- [Temporal Dependencies in Feature Importance for Time Series Predictions](https://mlsanity.com/paper/2107.14317/) (2021)
- [Low-rank Characteristic Tensor Density Estimation Part II: Compression and Latent Density Estimation](https://mlsanity.com/paper/2106.10591/) (2021)

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

- [Samba: Synchronized Set-of-Sequences Modeling for Multiple Object Tracking](https://mlsanity.com/paper/2410.01806/) (2024)
- [Jointly Modeling Spatio-Temporal Features of Tactile Signals for Action Classification](https://mlsanity.com/paper/2404.15279/) (2024)

## Abstract (arXiv)

Increased use of sensor signals from wearable devices as rich sources of physiological data has sparked growing interest in developing health monitoring systems to identify changes in an individual's health profile. Indeed, machine learning models for sensor signals have enabled a diverse range of healthcare related applications including early detection of abnormalities, fertility tracking, and adverse drug effect prediction. However, these models can fail to account for the dependent high-dimensional nature of the underlying sensor signals. In this paper, we introduce Latent Temporal Flows, a method for multivariate time-series modeling tailored to this setting. We assume that a set of sequences is generated from a multivariate probabilistic model of an unobserved time-varying low-dimensional latent vector. Latent Temporal Flows simultaneously recovers a transformation of the observed sequences into lower-dimensional latent representations via deep autoencoder mappings, and estimates a temporally-conditioned probabilistic model via normalizing flows. Using data from the Apple Heart and Movement Study (AH&MS), we illustrate promising forecasting performance on these challenging signals. Additionally, by analyzing two and three dimensional representations learned by our model, we show that we can identify participants' VO2max, a main indicator and summary of cardio-respiratory fitness, using only lower-level signals. Finally, we show that the proposed method consistently outperforms the state-of-the-art in multi-step forecasting benchmarks (achieving at least a 10% performance improvement) on several real-world datasets, while enjoying increased computational efficiency.