# Sequential online prediction in the presence of outliers and change points: an instant temporal structure learning approach

## TL;DR

This paper introduces the INTEL algorithm for sequential online prediction that effectively detects outliers and change points in streaming data by instantaneously learning temporal structures using a mixture of Gaussian processes.

## Contribution

The paper presents a novel instant temporal structure learning method that adjusts hyper-parameters for regime shifts, improving prediction robustness in the presence of outliers and change points.

## Key findings

- Significantly outperforms benchmark methods in experiments
- Effectively detects outliers and change points in real datasets
- Instant learning adapts to regime shifts efficiently

## Abstract

In this paper, we consider sequential online prediction (SOP) for streaming data in the presence of outliers and change points. We propose an INstant TEmporal structure Learning (INTEL) algorithm to address this problem. Our INTEL algorithm is developed based on a full consideration of the duality between online prediction and anomaly detection. We first employ a mixture of weighted Gaussian process models (WGPs) to cover the expected possible temporal structures of the data. Then, based on the rich modeling capacity of this WGP mixture, we develop an efficient technique to instantly learn (capture) the temporal structure of the data that follows a regime shift. This instant learning is achieved only by adjusting one hyper-parameter value of the mixture model. A weighted generalization of the product of experts (POE) model is used for fusing predictions yielded from multiple GP models. An outlier is declared once a real observation seriously deviates from the fused prediction. If a certain number of outliers are consecutively declared, then a change point is declared. Extensive experiments are performed using a diverse of real datasets. Results show that the proposed algorithm is significantly better than benchmark methods for SOP in the presence of outliers and change points.