Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Fast Mining and Dynamic Time-to-Event Prediction over Multi-sensor Data Streams

Kota Nakamura, Koki Kawabata, Yasuko Matsubara, Yasushi Sakurai

TL;DR

TimeCast addresses streaming time-to-event prediction from multi-sensor streams by modeling non-stationary progression through a sequential multi-model framework. It combines a stochastic time-to-event predictor based on a Wiener process $W( au)= u au+oldsymbol{\sigma_B} B( au)$, with $ u=1/f(x_{v,t})$, yielding the event-time distribution $p_{v,t}( au)= rac{1}{ oot 2 ext{}{ ext{2}}oldsymbol{\sigma_B^2 au^3}} imes ext{exp}igl(- rac{(1- au/f(x_{v,t}))^2}{2oldsymbol{\sigma_B^2} au}igr)$, and an interdependency-based descriptor via a sparse Gaussian graphical model with precision matrix $oldsymbol{\\Lambda}$. TimeCast uses a sequential model set $oldsymbol{\\Theta}=igl\{ heta^{(k)}\bigr\}_{k=1}^{K}$ and stage assignments $S$ to capture time-evolving patterns, with learning via alternating optimization and a dynamic-programming-based stage assignment that enforces a nondecreasing stage index over time. The streaming component performs online AdaptivePredict to infer the current stage and predict $p_{w,t_c}( au)$, followed by OnlineModelUpdate that can introduce new stages when drift is detected, all with efficient $O((1+ ext{#iter})K^2)$ amortized cost per step. Across five real datasets, TimeCast achieves higher predictive accuracy and substantially faster runtimes than static baselines, while also revealing interpretable stage transitions and stage-specific interdependencies between sensors, enabling timely maintenance and risk management in industrial and clinical contexts.

Abstract

Given real-time sensor data streams obtained from machines, how can we continuously predict when a machine failure will occur? This work aims to continuously forecast the timing of future events by analyzing multi-sensor data streams. A key characteristic of real-world data streams is their dynamic nature, where the underlying patterns evolve over time. To address this, we present TimeCast, a dynamic prediction framework designed to adapt to these changes and provide accurate, real-time predictions of future event time. Our proposed method has the following properties: (a) Dynamic: it identifies the distinct time-evolving patterns (i.e., stages) and learns individual models for each, enabling us to make adaptive predictions based on pattern shifts. (b) Practical: it finds meaningful stages that capture time-varying interdependencies between multiple sensors and improve prediction performance; (c) Scalable: our algorithm scales linearly with the input size and enables online model updates on data streams. Extensive experiments on real datasets demonstrate that TimeCast provides higher prediction accuracy than state-of-the-art methods while finding dynamic changes in data streams with a great reduction in computational time.

Fast Mining and Dynamic Time-to-Event Prediction over Multi-sensor Data Streams

TL;DR

TimeCast addresses streaming time-to-event prediction from multi-sensor streams by modeling non-stationary progression through a sequential multi-model framework. It combines a stochastic time-to-event predictor based on a Wiener process , with , yielding the event-time distribution , and an interdependency-based descriptor via a sparse Gaussian graphical model with precision matrix . TimeCast uses a sequential model set and stage assignments to capture time-evolving patterns, with learning via alternating optimization and a dynamic-programming-based stage assignment that enforces a nondecreasing stage index over time. The streaming component performs online AdaptivePredict to infer the current stage and predict , followed by OnlineModelUpdate that can introduce new stages when drift is detected, all with efficient amortized cost per step. Across five real datasets, TimeCast achieves higher predictive accuracy and substantially faster runtimes than static baselines, while also revealing interpretable stage transitions and stage-specific interdependencies between sensors, enabling timely maintenance and risk management in industrial and clinical contexts.

Abstract

Given real-time sensor data streams obtained from machines, how can we continuously predict when a machine failure will occur? This work aims to continuously forecast the timing of future events by analyzing multi-sensor data streams. A key characteristic of real-world data streams is their dynamic nature, where the underlying patterns evolve over time. To address this, we present TimeCast, a dynamic prediction framework designed to adapt to these changes and provide accurate, real-time predictions of future event time. Our proposed method has the following properties: (a) Dynamic: it identifies the distinct time-evolving patterns (i.e., stages) and learns individual models for each, enabling us to make adaptive predictions based on pattern shifts. (b) Practical: it finds meaningful stages that capture time-varying interdependencies between multiple sensors and improve prediction performance; (c) Scalable: our algorithm scales linearly with the input size and enables online model updates on data streams. Extensive experiments on real datasets demonstrate that TimeCast provides higher prediction accuracy than state-of-the-art methods while finding dynamic changes in data streams with a great reduction in computational time.
Paper Structure (23 sections, 4 theorems, 19 equations, 8 figures, 4 tables, 2 algorithms)

This paper contains 23 sections, 4 theorems, 19 equations, 8 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Proposed Model
  4. Problem Formulation
  5. TimeCast
  6. Stochastic Time-to-Event Predictor
  7. Interdependency-based descriptor
  8. Sequential Multi-Model Structure
  9. Optimization Algorithms
  10. Learning Algorithm
  11. UpdateStageModels
  12. UpdateAssignments
  13. Streaming Algorithm
  14. Experiments
  15. Conclusion
  16. ...and 8 more sections

Key Result

Lemma 1

The time complexity of the learning algorithm in TimeCast is $O(\#iter \cdot \sum_{v}T_{v})$.

Figures (8)

  • Figure 1: Prediction results of TimeCast over a machine failure-related sensor data stream. The method continuously detects/updates time-evolving stages. Then, it adaptively predicts event probabilities depending on the current stages.
  • Figure 2: An overview of TimeCast for a labeled collection $\mathcal{D}$. The method is based on a sequential multi-model structure, which consists of a stage model set $\Theta=\{\theta^{(k)}\}_{k=1}^{K}$ and a stage assignment set $S$. It adopts a different stage model depending on time-varying behaviors. Each stage model $\theta^{(k)}$ consists of a descriptor $\{\Lambda^{(k)},\mu^{(k)}\}$ and a predictor $\{f^{(k)},\sigma_B^{(k)}\}$.
  • Figure 3: Dynamic programming algorithm for stage assignments. The algorithm efficiently finds the optimal stage assignments by sequentially computing the cost $C_{k,t}$.
  • Figure 4: Comparison of prediction performance. TimeCast consistently outperforms its baselines (lower is better).
  • Figure 5: Prediction accuracy of TimeCast and its variants on MAPE. Each component improves the prediction performance on all datasets (lower is better).
  • ...and 3 more figures

Theorems & Definitions (7)

  • Definition 1: Stage model set: $\Theta$
  • Definition 2: Stage assignment set: $S$
  • Definition 3: Full Parameter Set of TimeCast: $\mathcal{F}$
  • Lemma 1: Proof in Appendix \ref{['sec:app:complexity_learning']}
  • Lemma 2: Proof in Appendix \ref{['sec:app:complexity_streaming']}
  • Lemma 1
  • Lemma 2