# Managing Incompleteness, Complexity and Scale in Big Data

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1 Managing Incompleteness, Complexity and Scale in Big Data Nick Duffield Electrical and Computer Engineering Texas A&M University

2 Three Challenges for Big Data Complexity Problem: high-dimensional data with complex dependence between variables, difficult to model Solution: machine learning dominant relationships Incompleteness Problem: not all quantities can be directly measured Solution: statistically infer what we want from what we have Scale Problem: huge datasets: costly to store, slow to compute Solution: smart data reduction retains ability to answer most important queries

3 Big Data Complexity: Customer Experience Packet loss and delay; line quality; service parameters Objective Metrics of Network Performance? Noisy measures of customer experience Customer care calls; social media; keyword analysis Which objective metrics closely associated with customer dissatisfaction? If known, remediate and prevent future troubles Solution: (machine) learn metrics (and values), service settings, most associated with occurrence of customer calls. Set action thresholds. Monitor metrics, take action when thresholds exceed Operational savings Reduce call volume to customer care center, reduce churn Reverse problem Learn calling patterns and keywords most predictive of network problem

4 Incompleteness: Internet tomography What ISPs want Origin-Destination (OD) traffic rates between any two routers What ISPs have Measured traffic rates on each link Linear relation Link_Rates = A. OD_Rates A = routing matrix encodes which links that OD traffic traverses Solve? Under-constrained problem Different possible sets of OD_Rates yield the same set of measured Link_rates

5 Internet Tomography Gravity Model? OD_Rate(A à B) =const. Rate(Aà ALL) Rate(ALLà B) Can measure Rate(Aà ALL) at links emanating from A Problem with gravity! Gravity model is not a solution of Link_Rates = A. OD_Rates Solution: Tomogravity Use solution closest to gravity model! Penalized likelihood solution Quick to compute, good accuracy In daily use in ISPs, Routers M 2 gravity model solution Tomogravity = least square solution constraint subspace L = A.M M 1

6 Big Data Scale ISP operations generate 100s of Terabytes of usage measurement data daily Passive traffic measurements by (core) routers Session-level traffic summaries (flow records) Each flow record reports IP source and destination, #packets, bytes, timing,.. Core routers stream flow records to collectors for analysis Used widely in network management timescale from months (planning) to seconds (security) Still need tomo-gravity outside core!

7 Managing Data Scale through Sampling Turn Big Data into Smaller Data Savings in storage, bandwidth; speed up queries Reference sampling Reuse samples over multiple retrospective queries Know query class in advance, but not specific query Smart sampling matches data characteristics to analysis requirements E.g. uniform sampling is useless on heavy tails Streaming constraints Sample to be computable in small time per item Big data constraint often not met in classical methods

8 Statistically Optimal Stream Sampling Aim: Sample fraction of flow records Use to answer queries approximately Problem: heavy tails 10% of the flow records report 90% of bytes Uniform sampling misses most of the 10% Big hit on accuracy Solution: Statistically optimal non-uniform sampling algorithms (minimal estimation variance) Computationally feasible for stream sampling In use in ISPs

9 Taming the Heavy Tail Distribution of traffic estimates Uniform sampling Smart sampling

10 Next: Streaming ISP Graph Data ISP Communications Graph from Flow Records node = IP address; edge = flow from source to destination compromise control flooding Hard to detect against background Known attacks: Signature matching based on subgraphs, flow features, timing Unknown attacks: exploratory & retrospective analysis Smart sampling of subgraphs

11 Sampling + Knowledge Discovery Interplay between sampling and data mining is not well understood Need to understand how ML/DM algorithms are affected by sampling E.g. how big a sample is needed to build an accurate classifier? E.g. what sampling strategy optimizes cluster quality Expect results to be method specific I.e. smart samping + k-means

12 Sampling and Privacy Current focus on privacy-preserving data mining Opportunity for sampling to be part of the solution Naïve sampling provides privacy in expectation Your data remains private if you aren t included in the sample Intuition: uncertainty from sampling contributes to privacy This intuition can be formalized with different privacy models Sampling can be analyzed in the context of differential privacy Sampling alone does not provide differential privacy But applying a DP method to sampled data does guarantee privacy A tradeoff between sampling rate and privacy parameters Understand benefits as well as risks of information flows Network calculus of risk/reward trade-off from information sharing, joining

13 Outlook Big data challenges Incompleteness, complexity, scale Generic problems; transferable solutions Find causal relations in high dimensional data Use machine learning for discovery & prediction Big Data Tomography Solve ill-posed inverse problems with constraints from models and side data Smart Sampling Speed up computations and save on resources Tune sampling to mediate between data and queries Role of sampling in ML/DM, privacy,

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