Probabilistic Aggregation in Distributed Networks

1
Probabilistic Aggregation in Distributed Networks

• Ling Huang, Ben Zhao,
• Anthony Joseph and John Kubiatowicz
• hling, ravenben, adj, kubitrong_at_eecs.berkeley.ed
  u
• June, 2004

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Outline

• Background
• Motivation
• Statistical properties of real life data streams
• Problem of existing approaches
• Our Approach
• Reduce communication overhead
• Recover from loss
• Evaluation
• Conclusion and future work

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Background

• Aggregate functions
• MIN, MAX, AVG, COUNT, , etc.
• In-Network hierarchical processing
• Query propagation
• Tree construction
• Aggregates computed epoch by epoch
• Addressing fault-tolerance
• Multi-root
• Multi-tree
• Reliable transmission

4
Motivation

• Data aggregation is an important function for all
  network infrastructures
• Sensor networks
• P2P networks
• Network monitoring and intrusion detection
  systems
• Exact result not achievable in face of loss and
  faults
• High cost when adding fault-tolerance
• Low communication overhead, accurate
  approximation is crucial
• But, its difficult to achieve

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Observation Comparison of Data Streams
Three real-world data traces and a random trace
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Statistical Properties of Data Streams
Relative Increment is defined as
There is temporal correlation in real data
stream, by which we can leverage to maintain
aggregate data accuracy, while reducing
communication overhead and recovering from data
loss.
Density estimation for relative increment
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Problems in Existing Approaches

• Few approach exploits the temporal properties and
  is designed to handle data loss
• Simple last-value algorithm for data loss
  recovery in TAG
• Multi-root/tree make things worse by consuming
  more resource
• Fragile for large process groups
• Need all relevant nodes for participation
• Difficult to trade accuracy for communication
  overhead
• Good applications need this tradeoff
• Only need approximation
• But, minimize resource consumption
• Centralize solution of adaptive filtering
  proposed by Olston et.al.

8
Our Approach

• Probabilistic data aggregation a scalable and
  robust approach
• Exploit and leverage statistical properties of
  data stream in temporal domain
• Apply statistical algorithms to data aggregation
• Develop protocol that handles loss and failures
  as essential part of normal operations
• Nodes participate in aggregation and
  communication according to statistical sampling
  algorithm
• In the absence of data, estimate value using time
  series algorithms
• Differentiate between voluntary and involuntary
  Loss

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Reducing Communication Overhead

• Trade off between accuracy and resource
  consumption
• Allow selective participation of nodes while
  maintaining aggregate accuracy
• Node participates in the operation with certain
  probability, which is the design parameter of the
  algorithm
• Sampling strategies
• Uniform Sampling all nodes use the identical
  sampling rate
• Subtree-size based Sampling sampling rate of a
  node is proportional to the size of its subtree
• Variance based sampling a sensor only reports a
  new value if it is above or below a threshold
  percentage its last reported value.

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Performance of Sampling algorithms

• As fewer nodes participate, overall accuracy
  decreases for all algorithms.
• Uniform sampling performs worst.
• Variance based sampling is most accurate,

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Observation Long-Term Pattern in Data
Daily patterns in a weekly data stream
Data source bandwidth measurements for the CUDI
network interface on an Abilene router with
5-minute average.
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Two Level Representation of Data
Monday Data
The data stream can be decomposed into two
layers the long trend (pattern), which changes
slowly the residual, high frequency but low
amplitude.
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Recovering From Loss

• Traditional Approaches
• Last seen data as approximation for current epoch
• Linear Prediction
• Two-Level data representation and prediction
• Long term trend B-spline estimation
• High frequency residual ARMA modeling
• ARMA stands for AutoRegressive and Moving Average
  model, which is a standard time series technique
  to model chaotic data stream

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Two-Level Data Prediction

• B-spline modeling for long term trend
• Piecewise continuous, low-degree B-spline can
  represent complex shapes
• Least-square B-spline regression for two-level
  decomposition
• B-Spline extension for future forecasting
• ARMA forecasting for transient oscillation
• System Identification to determine the order of
  the model
• Parameter estimation by optimization algorithm
• Low complexity recursive equation for future
  forecasting
• Statistical properties for the calibration of
  prediction results

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Performance of Prediction Algorithms
Performance of Prediction Algorithms For MAX
Operation in Lossless Environment
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Performance of Prediction Algorithms
Performance of prediction algorithms in lossy
environments. Average loss rate of the network is
20. The ration of loss rate between wide-area
links and local links is 31.
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Summary of Results

• All prediction algorithms are effective in
  improving the accuracy of aggregation results
• Two-level prediction approach perform the best in
  all situations
• Achieve more than 90 of accuracy even under each
  node nonparticipation with rate up to 60
• Is effective even in a high loss environment

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Conclusion and Future Work

• Apply statistical algorithms to data aggregation
  system
• quantify the statistical properties of real-world
  measurement data
• propose the concept of probabilistic
  participation of nodes
• propose multi-level prediction mechanism to
  recover from sampling and data loss
• Uniqueness multi-level prediction enables high
  accuracy even under high loss and voluntary
  non-participation
• Future Work
• Develop online algorithm and exploit tradeoff
  between prediction accuracy and computation and
  storage cost
• Build real system for applications with health
  monitoring, traffic measurement and router
  statistics aggregation
• Real system implementation and Deployment

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The Danger of Prediction