Mixture Modeling and Inference for Recognition of Multiple Recurring Unknown Patterns Zeyu You, Raviv Raich, Yonghong Huang (presenter) School of Electrical Engineering and Computer Science Oregon State University Corvallis, Oregon 97331-5501 Intel Labs, 2111 Northeast 25th Avenue, Hillsboro, Oregon 97124

Overview Motivation Single Pattern recognition Multiple Pattern recognition Results Conclusions / future work

Motivation Previous work on Single template recognition Target: Multiple template recognition

Single Pattern Recognition Approach: Statistical Model MLE for s:

Approach cont. Solve MLE by Robust Initialization for s*: Finding position containing s (Complete graph -> Bi-partite graph approximation) Finding the estimated s Refinement: MM solver for iterative updates on s

Multiple Pattern Recognition MLE Approach: Statistical Model S->Sk Unknown parameter: Vector of template probabilities α Templates {s1, s2 ,…,sk} Hidden parameter: Template indicator vector [K1,…,KN] Position vector [J1,…,JN]

Solution Complete Data Likelihood function: Expectation Maximization G(Xi/sk) is the ith bag PDF which has the same form as single pattern model PDF Expectation Maximization Robust Initialization Majorization Minimization for Refinement

Expectation Maximization E-step: M-step: Single template ML

Challenges Non-convex optimization for each M-step No guarantees on global optimal solution Sensitive to the initialization

Learning Signatures Consider each activation template as a bag containing all possible delay windows Map an item in each bag to one of K unknown patterns

Solution on Inner Iteration Robust Initialization( ): where weight wik is Find the k’th template Refinement using Majorization-Minimization: For each k, find delays:

Experiment Results Synthetic Data: Real World Data: MSE Analysis Detection Error Real World Data: Similar AUC on the single pattern task Increased AUC on the multiple pattern task

Synthetic Data: Template Estimation MSE No. bags Length No of instances K=3

Data Resources Appliance activation ground truth: Pecan Street Project A research and development organization Developing and testing advanced technology, business model, and customer behavior for advanced energy management system Voltage measurement: Intel’s BEST device Source: Pecan Street Project

Experiments on Real-world Data AUC of a single template model [ICASSP’14] vs. mixture model with K=1 [WCCI’14] Note the proposed model for K=1 is trained on the same filter dataset. Maintained the same performance

Real-world Data Detection ROC changes significantly as K increases for some device, but not all devices: Air conditioning ROC Oven ROC

Test with different K AUCs of mixture model by varying K K-pattern model captures the variations in patterns. AUC significantly increased as K=3 vs. single pattern model. Over-fitting can be overcome using Cross-Validation.

Conclusions Single pattern Model: Mixture pattern Model: Statistical single pattern model Robust initialization Refinement using MM Mixture pattern Model: Statistical K-pattern model Problem and solutions Experiment results: significant improvements over the single pattern model

Future Work Learning in the presence of outliers Learning from large datasets Trade-off: training time complexity for accurate templates Transfer learning Test on homes which are not included in the training data Classification framework

Thanks ! Questions?

Gradient Descent Steepest Descent Newton’s