We address the problem of detecting distribution changes in multivariate data streams by means of histograms. Histograms are very general and flexible models, which have been relatively ignored in the change-detection literature as they often require a number of bins that grows unfeasibly with the data dimension. We present QuantTree, a recursive binary splitting scheme that adaptively defines the histogram bins to ease the detection of any distribution change. Our design scheme implies that i) we can easily control the overall number of bins and ii) the bin probabilities do not depend on the distribution of stationary data. This latter is a very relevant aspect in change detection, since thresholds of tests statistics based on these histograms (e.g., the Pearson statistic or the total variation) can be numerically computed from univariate and synthetically generated data, yet guaranteeing a controlled false positive rate. Our experiments show that the proposed histograms are very effective in detecting changes in high dimensional data streams, and that the resulting thresholds can effectively control the false positive rate, even when the number of training samples is relatively small.

QuantTree: Histograms for change detection in multivariate data streams

Boracchi G.;Carrera D.;
2018

Abstract

We address the problem of detecting distribution changes in multivariate data streams by means of histograms. Histograms are very general and flexible models, which have been relatively ignored in the change-detection literature as they often require a number of bins that grows unfeasibly with the data dimension. We present QuantTree, a recursive binary splitting scheme that adaptively defines the histogram bins to ease the detection of any distribution change. Our design scheme implies that i) we can easily control the overall number of bins and ii) the bin probabilities do not depend on the distribution of stationary data. This latter is a very relevant aspect in change detection, since thresholds of tests statistics based on these histograms (e.g., the Pearson statistic or the total variation) can be numerically computed from univariate and synthetically generated data, yet guaranteeing a controlled false positive rate. Our experiments show that the proposed histograms are very effective in detecting changes in high dimensional data streams, and that the resulting thresholds can effectively control the false positive rate, even when the number of training samples is relatively small.
35th International Conference on Machine Learning, ICML 2018
File in questo prodotto:
File Dimensione Formato  
2018_icml2018quanttree.pdf

Accesso riservato

Dimensione 1.98 MB
Formato Adobe PDF
1.98 MB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1126168
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 10
  • ???jsp.display-item.citation.isi??? 13
social impact