Parallel HMMs. Parallel Implementation of Hidden Markov Models for Wireless Applications
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1 Parallel HMMs Parallel Implementation of Hidden Markov Models for Wireless Applications Authors Shawn Hymel Virginia Tech) Ihsan Akbar (Harris Corporation) Jeffrey Reed Virginia Tech)
2 Agenda Overview of GPGPU Overview of HMMs Parallelization Results Applications Why Is This Useful? 2
3 General Purpose Processing on GPUs CUDA specific Important Terms: Threads Blocks Grid 3
4 CUDA Code Flow 4
5 This image cannot currently be displayed. Hidden Markov Model Initialization States Observations 0.6 Start Rainy Sunny Walk Shop Clean A B ( A, B, )
6 HMM Canonical Problems Evaluation: P(O λ) Forward Algorithm Backward Algorithm Find the most likely state sequence Viterbi Algorithm Training ( maximize P(O λ) ) Baum Welch Algorithm 6
7 Forward Algorithm Given a model and an observation sequence, calculate P(O λ) T = number of observations N = number of states M = number of possible symbols Initiation: 1( i) i bi 1,... Induction: N Termination P O, i 1,2 N j ia b O t1 t ij j t1 i1 N O i i1 T 7
8 Example of Parallelization N j ia b O t1 t ij j t1 i1 For all j, matrix multiplication α t A N = α' N N N For all j, element by element multiplication N α' b(o t+1 ) α = t+1 We can perform this step in parallel! O(TN 2 ) O(T log N) 8
9 Computational Complexity Serial Parallel Forward Algorithm O(TN 2 ) O(T log N) Viterbi Algorithm O(TN 2 ) O(T log N) Baum Welch Algorithm O(TN 2 ) or O(TMN) O(T log N) 9
10 Test Procedures Time execution of each algorithm (C vs. CUDA) Vary states Vary symbols Vary sequence length Calculate total energy consumption (C vs. CUDA) PowerTOP software Component CPU GPU GPU Core Speed GPU Shader Speed GPU Memory Speed Test Hardware Specification Intel Core 2 Duo 1.30GHz NVIDIA GeForce GT 335M 450 MHz 1080 MHz 1066 MHz CUDA Cores 72 10
11 Speed Results Number of States CPU Runtime (s) GPU Runtime (s) Speed Increase Forward Algorithm x x x x Viterbi Algorithm x x x x Baum Welch Algorithm x x x x 11
12 Energy Consumption Algorithm Power (W) States to C CUDA Break Even Forward ~100 Viterbi ~120 BWA ~70 Energy Consumption for Forward Algorithm Energy Consumed (kwh) Number of States CPU GPU 12
13 Applications Pattern Recognition Spectrum Sensing Signal Classification Specific Emitter Identification Geolocation Modeling Channel Fading Call Drop Prediction 13
14 Why Is This Useful? Evolution of GPUs and multi core processors Smart phones, tablets, SDR Co processor Utilize existing hardware for HMM applications Large number of states 2D/3D HMMs Uses in other fields (speech recognition, computer vision) Extrapolation to other algorithms (pattern recognition) 14
15 Questions? Contact Information Blog: Code: cuda/ Other Good Resources cuhmm: MATLAB: HTK: 15
16 Supporting Slide: Reductions MATLAB example: >> sum(a) Parallelization: C Implementation: sum = 0; for (i = 0; i < length; i++) { sum = sum + A[i]; } Reducing arrays to a single value (e.g. sum) go from O(N) to O(log N) 16
17 Supporting Slide: Timing Results (Forward) Execution Time for Forward Algorithm 600 Vary States Execution Time (s) Number of States Execution Time for Forward Alg. on GPU CPU GPU Execution Time (s) Number of States Execution Time for Forward Algorithm 1.5 Vary Symbols Execution Time (s) Number of Observations CPU GPU 17
18 Supporting Slide: Timing Results (Viterbi) Execution Time for Viterbi Algorithm 600 Vary States Execution Time (s) Number of States Execution Time for Viterbi on GPU CPU GPU Execution Time (s) Number of States Execution Time for Viterbi Algorithm 0.2 Vary Symbols Execution Time (s) Number of Symbols CPU GPU 18
19 Supporting Slide: Timing Results (BWA) Execution Time for Baum Welch Algorithm Vary States Execution Time (s) Number of States Execution Time for BWA on GPU CPU GPU Execution Time (s) Number of States Execution Time for Baum Welch Algorithm 0.55 Vary Symbols Execution Time (s) Number of Symbols CPU GPU 19
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