Unsupervised Mining of Statistical Temporal Structures in Video Liu ze yuan May 15,2011

What purpose does Markov Chain Monte-Carlo(MCMC) serve in this chapter? Quiz of the Chapter

 1 Introduction  1.1Keywords  1.2 Examples  1.3 Structure discovery problem  1.4 Characteristics of video structure  1.5 Approach  2 Methods  Hierarchical Hidden Markov Models  Learning HHMM parameters with EM  Bayesian model adaptation  Feature selection for unsupervised learning  3 Experiments & Results  4 Conclusion Agenda

 Algorithms for discovering statistical structures and finding informative features from videos in an unsupervised setting.  Effective solutions to video indexing require detection and recognition of structures and events.  We focus on temporal structures 1 Introduction

 Hierarchical hidden Markov Model(HHMM)  Hidden Markov model(HMM)  Markov Chain Monte-Carlo(MCMC)  Dynamic Bayesian network(DBN)  Bayesian Information criteria(BIC)  Maximum Likelihood(ML)  Expectation Maximization(EM) 1.1 Introduction: keywords

 General to various domains and applicable at different levels  At the lowest level, repeating color schemes in a video  At the mid level, seasonal trends in web traffics  At the highest level, genetic functional regions 1.2Introduction: examples

 The problem of identifying structure consists of two parts: finding and locating.  The former is referred as training, while the latter is referred to as classification.  Hidden Markov Model(HMM) is a discrete state-space stochastic model with efficient learning algorithm that works well for temporally correlated data streams and successful application. However, due to domain restrictions, we propose a new algorithm that fully unsupervised statistical techniques. 1.3 Introduction: the structure discovery problem

 Fixed domain: audio-visual streams  The structures have the following properties:  Video structure are in a discrete state-space  features are stochastic  sequences are correlated in time  Focus on dense structures  Assumptions  Within events, states are discrete and Markov  Observations are associated with states under Gaussian 1.4 Introduction: Characteristics of Video Structure

 Model the temporal, dependencies in video and generic structure of events in a unified statistical framework  Model recurring events in each video as HMM and HHMM, where the state inference and parameter estimation learned using EM  Developed algorithms to address model selection and feature selection problems  Bayesian learning techniques for model complexity  Bayesian Information Criteria as model posterior  Filter-wrapper method for feature selection 1.5 Introduction: Approach

 Use two-level hierarchical hidden Markov model  Higher- level elements correspond to semantic events and lower-levels elements represent variations  Special case of Dynamic Bayesian Network  Could be extended to more levels and feature distribution is not constrained to a mixture of Gaussians 2 Hierarchical Hidden Markov Models(HHMM)

2. Hierarchical Hidden Markov Models: Graphical Representation

 Generalization to HMM with a hierarchical control structure.  Bottom-up structure 2 Hierarchical Hidden Markov Models: Structure of HHMM

 (1) supervised learning  (2) unsupervised learning  (3) a mixture of the above 2 Hierarchical Hidden Markov Models: Structure of HHMM: applications

 Multi-level hidden state inference with HHMM is O(T 3 );however, not optimal due to some other algorithm with O(T).  A generalized forward-backward algorithm for hidden state inference  A generalized EM algorithm for parameter estimation with O(DT*|Q| 2D ). 2 Complexity of Inferencing and Learning with HHMM

 Representations of states and parameter set of an HHMM  Scope of EM is the basic parameter estimation  Model size given and Learned over a per-defined feature set 2 Learning HHMM parameter with EM

2 Learning HHMM parameters with EM: representing an HHMM The entire configuration of the hierarchical states from top to bottom with N-ary and D-digit integer. Whole parameter set theta of an HHMM is represented by the followings:

2 Learning HHMM parameters with EM: Overview of EM algorithm

 Parameter learning for HHMM using EM is known to converge to a local max and predefined model structures.  It has drawbacks, thus we adopt and Bayesian model.  use a Markov Chain Monte Carlo(MCMC) to maximize Bayesian information criterion 2 Bayesian Model adaptation

 A class of algorithms designed to solve high dimensional optimization problems  MCMC iterates between two steps  new model sample based on current model and stat of data  Decision step computes an acceptance probability based on fitness of the proposed new model  Converge to global optimum 2 Overview of MCMC

 Model adaptation for HHMM involves an iterative procedure.  Based on the current model, compute a probability profile involving EM, split(d),merge(d) and swap(d)  Certain formula to determine whether a proposed move is accepted 2 MCMC for HHMM

 Select a relevant and compact feature subset that fits the HHMM model  Task of feature selection is divided into two aspect:  Eliminating irrelevant and redundant ones 2 Feature selection for unsupervised learning

 Suppose the feature is a discrete set  e.g F={ f 1, …,f D }  Markov blanket filtering to eliminate redundant features  A human operator needed to decide on whether to iterate 2 Feature selection for unsupervised learning: feature selection algorithm

2 Feature selection for unsupervised learning: evaluating information gain

 After wrapping information gain criterion, we are left with possible redundancy.  Need to apply Markov blanket to solve this matter  Iterative algorithm with a threshold less than 5% 2 Feature selection for unsupervised learning: finding a Markov blanket

 Computes a value that influences decision on whether to accept it.  Initialization and convergence issues exist, so randomization. 2 Feature selection for unsupervised learning: normalized BIC

3 Experiments & Results Sports videos represent an interesting structure discovery

 We compare the learning accuracy of four different learning schemes against the ground truth  Supervised HMM  Supervised HHMM  Unsupervised HHMM without model adaptation  Unsupervised HHMM with model adaptation  EM  MCMC 3 Experiments & Results: parameter and structure learning

Run each of the four algorithm for 15 times with random starting points

 Test the performance of the automatic feature selection method on the two video clips  For the Spain case, the evaluation has an accuracy of 74.8% and the Korea clip achieves an accuracy of 74.5% 3 Experiments & Results: feature selection

 Conduct the baseball video clip on a different domain  HHMM learning with full model adaptation  Consistent results and agree with intuition 3 Experiments & Results: testing on a different domain

 Simplified HHMM boils down to a sub-HMM but left to right model with skips  Fully connected general 2-level HHMM model  Results show the constrained model is 2.3% lower than the fully connected model, but more modeling power 3 Experiments & Results: comparing to HHMM with simplifying constraints

 In this chapter, we proposed algorithms for unsupervised discovery of structure from video sequences.  We model video structures using HHMM with parameters learned using EM and MCMC.  We test them out on two different video clips and achieve results comparable to its supervised learning counterparts  Application to many other domains and simplified constraints. 4 Conclusion

 It serves to solve high dimensional optimization problems Solution to the Quiz

 Questions? Q&A