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Big data are produced by various sources. Most often, they are distributedly stored at computing farms or clouds. Analytics on the Hadoop Distributed File System (HDFS) then follows the MapReduce programming model. According to the Lambda architecture of Nathan Marz and James Warren, this is the batch layer. It is complemented by the speed layer, which aggregates and integrates incoming data streams in real time. When considering big data and small devices, obviously, we imagine the small devices being hosts of the speed layer, only. Analytics on the small devices is restricted by memory and computation resources.

The interplay of streaming and batch analytics offers a multitude of configurations. In this talk, we discuss opportunities for using sophisticated models for learning spatio-temporal models. In particular, we investigate graphical models, which generate the probabilities for connected (sensor) nodes. First, we present spatio-temporal random fields that take as input data from small devices, are computed at a server, and send results to -possibly different — small devices. Second, we go even further: the Integer Markov Random Field approximates the likelihood estimates such that it can be computed on small devices. We illustrate our learning models by applications from traffic management.

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- 1. Big Data and Small Decives Katharina Morik, Artificial Intelligence, TU Dortmund University, Germany
- 2. Overview ! Big data -- small devices ! Graphical Models ! Computation on the batch layer ! Computation on the speed layer ! Integer Random Fields ! Spatio-Temporal Random Fields ! Traffic Scenarios ! Using the streams framework
- 3. Big data – small devices ! Machine learning for the enhancement of small devices ! Machine learning on small devices ! Reduce ! Computational complexity ! Memory consumption ! Communication ! Energy
- 4. Overview ! Big data -- small devices ! Graphical Models ! Computation on the batch layer ! Computation on the speed layer ! Integer Random Fields ! Spatio-Temporal Random Fields ! Traffic Scenarios ! Using the streams framework
- 5. Graphical Models ! Graph G=(V,E) ! Multi-variate random variable X with finite discrete domain X ! Mapping joint vertex assignment into vector space φ(x): X --> Rd ! Parameter to be learned: θ in Rd CRF : p ( ! ! y x) = 1 ! ( x) Z θ, Σ exp θi φi ( ! x) ! y, i " # $ % & ' 1 a = exp(−ln a) Σ = exp θi φi ( ! x) ! y, i " # $ % & ' ! ( x) − ln Z θ, ) * + , - . ! x ( ) − A θ ( ) )* = exp θ,φ ! y, ,- MRF : p( ! x) = 1 Z θ ( ) Σ exp θi φi ! (x) i " # $ % & ' ! x ( ) − A θ ( ) )* = exp θ,φ ,-
- 6. Note: vectors are sparse φ(x): ( /* Nodes*/ 1. red, /*dom(lights)*/ 2. yellow, 3. green, 4. wet, /*dom(rain)*/ 5. dry, 6. jam, /*dom(jam)*/ 7. free, /*Edges*/ 1. red, dry, /* edge lights-rain*/ 2. yellow, dry, 3. green, dry, 4. red, wet, 5. yellow, wet, 6. green, wet, 7. red, jam, /*edge lights-jam*/ 8. yellow, jam, 9. green, jam, 10. red, free, 11. yellow, free, 12. green, free, 13. dry, free, /*edge rain-jam*/ 14. dry, jam, 15. wet, free, 16. wet, jam) ) ! x1:(red,dry,free) Lights Rain Jam {jam, free} {dry, wet} {red, yellow, green}
- 7. Conditional Random Field: Likelihood
- 8. Markov Random Field: Likelihood
- 9. Markov Random Field: Estimation and Prediction
- 10. Belief propagation ! Actually computing the expected probability of parameters given θ by message passing for each direction.
- 11. Note: vectors are sparse φ(x): ( /* Nodes*/ 1. red, /*dom(lights)*/ 2. yellow, 3. green, 4. wet, /*dom(rain)*/ 5. dry, 6. jam, /*dom(jam)*/ 7. free, /*Edges*/ 1. red, dry, /* edge lights-rain*/ 2. yellow, dry, 3. green, dry, 4. red, wet, 5. yellow, wet, 6. green, wet, 7. red, jam, /*edge lights-jam*/ 8. yellow, jam, 9. green, jam, 10. red, free, 11. yellow, free, 12. green, free, 13. dry, free, /*edge rain-jam*/ 14. dry, jam, 15. wet, free, 16. wet, jam) ) ! x1:(red,dry,free) ! φ(x1)= (1,0,0,0,1,0,1,1,0,0,0,0,0,0, 0,0,1,0,0,1,0,0,0) ! d = 23 Lights Rain Jam {jam, free} {dry, wet} {red, yellow, green}
- 12. Belief propagation example Π Σ mv→u (y) = exp θvu=xy +θv=x ( ) mwu (x) Lights Rain Jam {jam, free} {dry, wet} {red, yellow, green} w∈Nv−{u} x∈ℵv Compute for each node u and each of its neighbors and each of the states
- 13. Parallel Belief Propagation (GPU) ! Data Parallel: all node and neighbor pairs become blocks with b threads. A thread computes the msg v" u. ! Thread-cooperative: all node and instance pairs become blocks. A thread computes partial outgoing messages. These are cooperatively processed by all threads in a block. Partial messages are merged afterwards. ! Nico Piatkowski (2011) Parallel Algorithms for GPU Accelerated Probabilistic Inference ! http://biglearn.org/2011/files/papers/biglearn2011_submission_28.pdf
- 14. File Prefetching for Smartphone Energy Saving ! Accessing files that are stored in cache consumes less energy than accessing those on the hard disc. ! Prefetching files which soon will be accessed allows for grouping requests to a batched one. This saves energy. " Prediction of file access saves energy! Given a system call: 1,open,1812,179,178,201,200,firefox,/etc/hosts,524288,438,7 Predict: hosts full Prefetch: hosts 2,read,1812,179,178,201,200,firefox,/etc/hosts,4096,361 3,read,1812,179,178,201,200,firefox,/etc/hosts,4096,0 4,close,1812,179,178,201,200,firefox,/etc/hosts timestamp, syscall, thread-id, process-id, parent, user, group, exec, file, parameters (optional) 14
- 15. Results: Memory ! Naive Bayes models use less memory than those of regular CRF. ! Implementing CRF on GPGPU reduces memory needs. ! CRF on GPU scales best. 15 1600 1400 1200 1000 800 600 400 200 0 67k 202k 337k 472k 606k NB memory CRF memory GPU CRF memory Felix Jungermann, Nico Piatkowski, Katharina Morik (2010) Enhancing Ubiquitous Systems Through System Call Mining, LACIS at ICDM http://www.computer.org/csdl/proceedings/ icdmw/2010/4257/00/4257b338-abs.html
- 16. Overview ! Big data -- small devices ! Graphical Models ! Computation on the batch layer ! Computation on the speed layer ! Integer Random Fields ! Spatio-Temporal Random Fields ! Traffic Scenarios ! Using the streams framework
- 17. Graphical models on resource-restricted processors ! Floating point arithmetics (real) costs more clock cycles than integer arithmetics. ! “The most obvious technique to conserve power is to reduce the number of cycles it takes to complete a workload.” (Intel 64, IA-32 architectures optimization reference manual, guidelines for extending battery life). ! Restrict the parameter space of MRF Sandy Bridge ARM 11 Real Int Real Int + 3 1 8 1 * 5 3 8 4-5 / 14 13-15 19 - Bit - 3 - 2 shift Clock cycles for arithmetics on different processors: Real vs. integer. θ ∈{0,1,...,K}⊂ Ν
- 18. Parameter space transformation ! Graph model tree-structured ! Transform the parameter space: ηi (θ) = θi ln 2 MRF : p( ! x) = 1 Z θ ( ) Σ exp θi φi ! (x) i " # $ % & ' ! x ( ) − A θ ( ) )* = exp θ,φ +, IntegerMRF : p( ! x) = exp η θ ( ),φ ! x ( ) )* +, = 2 θ ,φ x ( ) −A η θ ( ) ( ) )* +, = 2 θ ,φ (x) 2 θ ,φ (y) y∈ℵ Σ
- 19. Integer belief propagation ! Simply replacing the exp(.) by 2(.) is not sufficient ! Overflows are normally avoided by normalization. ! Normalization is impossible in integer division. ! Magnitude of messages corresponds to probability ! Use the length of each message ! Bit-length is similar to log Π Σ mv→u (y) = exp θvu=xy +θv=x ( ) mwu (x) w∈Nv−{u} x∈ℵv m! v→u (y) = 2 (θvu=xy+θv=x ) Σ m! wu (x) x∈ℵv Π w∈Nv−{u} βv→u (y) = max x∈ℵv Σ θvu=xy +θv=x + βwu (x) w∈Nv−{u}
- 20. Evaluation: accuracy 0.95 0.9 0.85 Int, deg=4 Int, deg=8 Int, deg=16 1000 2000 3000 4000 5000 6000 7000 8000 ! Different vertex degrees ! Up to 8000 nodes in the graph ! 100 runs of IntMRF ! Real MRF is 100% accuracy. # Scalable!
- 21. Integer models use less clock cycles and memory ! Integer MRF shows ! high accuracy: 86 – 92% of full MRF for up to 8 states and 8000 nodes ! high speed-up: 2.56 Raspberry Pie and 2.34 for Sandy Bridge ! Graphical models can now be computed on small devices. ! Using less clock cycles really saves energy. Nico Piatkowski, Sangkyun Lee, Katharina Morik (2014) The Integer Approximation of Undirected Graphical Models, ICPRAM http://www-ai.cs.uni-dortmund.de/ PublicPublicationFiles/piatkowski_etal_2014a.pdf
- 22. Overview ! Big data -- small devices ! Graphical Models ! Computation on the batch layer ! Computation on the speed layer ! Integer Random Fields ! Spatio-Temporal Random Fields ! Traffic Scenarios ! Using the streams framework
- 23. Spatio-temporal random fields ! The spatio-temporal graph is trained to predict each node’s maximum a posteriori probability with the marginal probabilities. ! Generative model predicting all nodes. ! Dimension T x |V0| x | X| + [(T-1)(|V0|+3|E0|)+ |E0|] x |X|2 ! Remember: vectors are sparse we have to exploit that! User queries: Given traffic densities at all nodes at t1, t2, t3, what is the probability of traffic density at node A at time t5? Given state “jam” at place A ts, which other places have a higher probability for “jam” in ts < t < te?
- 24. Training efficiently ! Reparametrization ! Sparseness and smoothness ! There are not many changes over time ! Small ratio of non-zero entries ! Regularization ! L1 and L2 norm now penalizing difference θ(t-1) and θ(t) ! STRF uses 8 times less memory than MRF model ! Its distributed optimization converges about 2 times faster.
- 25. Compressible parametrization ! STRF is 8 times smaller than MRF model ! The ratio of non-zero entries is quite small already for quite small L1 regularization ! STRF’s distributed optimization converges faster than MRF: ! Run MRF for 100 iterations, record the likelihood value; ! Run STRF until it reaches the same result of the objective function. ! Compare seconds.
- 26. Evaluation: accuracy ! Smaller state spaces result in higher accuracies. ! Again, for MRF accuracy 100%. # State space is important! 1 0.8 0.6 0.4 Int, |X|=2 Int, |X|=4 Int, |X|=8 Int, |X|=16 0 1000 2000 3000 4000 5000 6000 7000 8000
- 27. Flood in the City ! The city of Dublin suffers from flood due to rainfall and tide. Wanted: ! Optimal traffic regulations based on traffic predictions. ! Insight EU Project www.insight-ict.eu Intelligent Synthesis and Real-time Response using Massive Streaming of Heterogeneous Data Coordinator: Dimitrios Gunopoulos, Univ. Athens, Greece
- 28. Smart trip modeling for Dublin ! Open Street Map " graph topology ! Open Trip Planner: user query (v,w), route planning based on traffic costs. ! Traffic costs learned: ! Spatio-temporal random field based on sensor data stream; ! Gaussian process estimates values for non-sensor locations. ! Framework for real-time processing of data streams, XML configuration of data flow, connecting data, traffic model and planner. 7:00 8:00 v v w w
- 29. Constructing the spatio-temporal graph of Dublin OpenStreetMap streets segmented according to junctions. 966 sensors transmit traffic flow every 6 minutes (www.dublinked.ie). Aggregate sensor readings for 30 minutes, aggregate sensor nodes by 7NN. Traffic flow discretized into 6 intervals of density. 48 time layers for each day (48* 30=1440 minutes make a day). Training for every weekday. Predicting density of each node and edge – interpreted as costs.
- 30. Using STRF for smart trip modeling -- Evaluation ! Confusion matrix of predicting the number of vehicles (6 intervals) for all sensors and all half hours following 1 pm on Fridays, tested on March 1.,8.,15.,22.,29. ! given the traffic at 1 p.m. (bold is true). Predicted 0 1-5 6-20 21- 30 31-60 61- Prec True 0 840 32 10 6 3 0 0.943 1-5 2 632 498 3 0 1 0.556 6-20 91 156 12169 2006 83 25 0.838 21-30 32 0 1223 5637 717 14 0.739 31-60 43 0 60 893 1945 29 0.655 61- 0 0 16 3 12 35 0.530 Recall 0.833 0.771 0.871 0.659 0.705 0.34 Environment Energy Engineering
- 31. Confusion Matrices for Cluster-Based Discretization (all t) Friday 0-7 8-12 13-21 22 - Precision 0-7 139 518 38 551 45 350 50 501 0.5093 8-12 37 419 51 284 37 153 27 112 0.3396 13-21 23 535 25 863 115 081 66 171 0.4989 22- 22 387 18 034 58229 205 822 0.6760 Recall 0.6260 0.3881 0.4499 0.5887 Saturday 0-7 8-12 13-21 22 - Precision 0-7 167 073 57 448 34 370 16 590 0.6065 8-12 46 944 102 703 68 194 26 181 0.4209 13-21 31 626 45 606 140 866 51 136 0.5232 22- 19 365 25 737 46 949 89 301 0.4937 Recall 0.6304 0.4437 0.4859 0.4874
- 32. Smart traffic for smart cities ! Spatio-temporal modeling is natural for traffic prediction. ! Several questions can be answered using the same learned model. ! The answers come along with their probabilities. This might be helpful for decision makers. ! Integration of Spatio-temporal random fields into the Open Trip Planner and Gaussian information completion resulted in an excellent navigation system. Piatkowski, Lee, Morik (2013) Spatio-temporal random fields: compressible representation and distributed estimation, Machine Learning Journal 93:1, 115 – 140. Liebig, Piatkowski, Bockermann, Morik (2014) Predictive Trip Planning – Smart Routing in Smart Cities, Mining Urban Data Workshop at 17th Intern. Conf. on Extending Database Technology.
- 33. Overview ! Introduction ! Big data ! Small devices ! Graphical Models ! Computation on the batch layer ! Computation on the speed layer ! Integer Random Fields ! Spatio-Temporal Random Fields ! Traffic Scenarios ! Using the streams framework
- 34. Streams framework ! Open-source Java environment for abstract orchestration of streaming functions by Christian Bockermann, GNU AGPL license. ! High-level API for sources, processing nodes, executable on the STORM engine and topology. ! Graph of nodes can be used for distributed processing. ! Easy integration of MOA library. ! Eases integration of various engines. Christian Bockermann, Hendrik Blom 2012 The Streams Framework Tech.Rep. SFB 876 http://www-ai.cs.uni-dortmund.de/ PublicPublicationFiles/ bockermann_blom_2012c.pdf
- 35. Stream Processing Engines ! Fault tolerance by resending not acknowledged data (streams) vs. sophisticated recovery methods (MillWheel). ! State management by storing state in process context (streams) vs. links to distributed storage systems (Samza, MillWheel on Apache Cassandra, BigTable). ! Explicit partitioning by flow graph vs. built upon distributed computing environment managed by a central node.
- 36. Comparison of stream processing engines Christian Bockermann A Survey of the Stream Processing Landscape 2014 TechRep. SFB 876 http://sfb876.tu-dortmund.de/ PublicPublicationFiles/ bockermann_2014b.pdf
- 37. Streams framework ! Streams to map reduce for an easy execution in Hadoop reading HDFS files.
- 38. Conclusion ! Complex models such as MRF can be computed on small devices such as smartphones. ! Graphical Models ! Parallel BP using GPU ! Approximation to Integer Random Fields ! Spatio-Temporal Random Fields ! Using the streams framework for integrating processes (e.g. MOA for learning) and real-time processing and documentation.
- 39. References ! Nico Piatkowski (2011) Parallel Algorithms for GPU Accelerated Probabilistic Inference http://biglearn.org/2011/files/papers/ biglearn2011_submission_28.pdf ! Felix Jungermann, Nico Piatkowski, Katharina Morik (2010) Enhancing Ubiquitous Systems Through System Call Mining, LACIS at ICDM http://www.computer.org/csdl/proceedings/ icdmw/2010/4257/00/4257b338-abs.html ! Nico Piatkowski, Sangkyun Lee, Katharina Morik (2014) The Integer Approximation of Undirected Graphical Models, ICPRAM http://www-ai.cs.uni-dortmund.de/ PublicPublicationFiles/ piatkowski_etal_2014a.pdf ! Piatkowski, Lee, Morik (2013) Spatio-temporal random fields: compressible representation and distributed estimation, Machine Learning Journal 93:1, 115 – 140. ! Liebig, Piatkowski, Bockermann, Morik (2014) Predictive Trip Planning – Smart Routing in Smart Cities, Mining Urban Data Workshop at 17th Intern. Conf. on Extending Database Technology. ! Streams framework Christian Bockermann, Hendrik Blom 2012 The Streams Framework Tech.Rep. SFB 876 http://www-ai.cs.uni-dortmund.de/ PublicPublicationFiles/ bockermann_blom_2012c.pdf ! Christian Bockermann (2014) A Survey of the Stream Processing Landscape TechRep. SFB 876 http://sfb876.tu-dortmund.de/ PublicPublicationFiles/ bockermann_2014b.pdf ! For streams software (not just scripts!) check: http://www-ai.cs.uni-dortmund.de/ SOFTWARE/streams/

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