Subset Models for Multivariate Time Series Forecast

1st MulTiSA, ICDE 2024

Raphael Saldanha, Victor Ribeiro, Eduardo Pena, Marcel Pedroso, Reza Akbarinia, Patrick Valduriez, Fabio Porto

Inria (FR), LNCC (BR)

2024-05-13

Introduction

  • Abundant multivariate time series, good opportunity for forecasting machine learning methods
  • Data may present intrinsic diversity of samples, affecting model’s performance on different parts of the input
  • Global models: use all available time series
  • Local models: use only time series pertaining to each sample
  • Data subsets models: our proposal

Case example

  • Dengue disease is transmitted by mosquitoes and is a Public Health concern. Record number cases on 2024 in Brazil, tendency to increase with global warming
  • A typical forecasting model is targeted to predict number of cases based on climate indicators (rain and temperature)
  • A global model would use data from all municipalities, facing difficulties related to distinct temporal and spatial disease transmission patterns

Objective

  • Propose a subset modeling framework
  • Accommodate regional variations across diverse units (e.g. municipalities)
  • Cost-effective training with robust prediction capabilities in comparison with global models

Subset modeling framework

  1. Identify subsets within the dataset with similar patterns
  2. Train models for each subset
  3. Use the model trained on the subset data for prediction

Datasets

  • Dengue dataset. Weekly cases count, from 2011 to 2020, for 333 municipalities.
  • Climate dataset. Average maximum and minimum temperature, total precipitation. Same time and spatial units and coverage.
  • All indicators were standardized (with zero mean and one SD)

Experimental setup

  • Identify data subsets considering dengue cases and covariates patterns across municipalities with DTW distance.
    • Select the optimum number of subsets (\(k\)) considering silhouette score
  • Train random forest Global Model with and without the subset id feature information
  • Train random forest Subsets Models
  • Evaluate forecasting model’s performance on test data

Clustering results

  • \(k = 5\) returned the highest silhouette score
  • Partition sizes: \(g_1 = 69\), \(g_2 = 62\), \(g_3 = 82\), \(g_4 = 102\), \(g_5 = 18\)

Model results

Conclusions and next steps

  • We specifically addressed and formalized the subsets approach in a multivariate time series setting
  • Subsets models rendered better performance than global models on 116 municipalities from 333 (34.83%)
  • Subsets models overall performance is related to the partition’s size. Bigger partitions (more municipalities) have more training data.
  • Further work may advance on clustering strategies (constraints in size and featured-based approaches) and apply different learners on model training

Thanks!

Contact and more info at

rfsaldanha.github.io