A Sticky HDPHMM for Systems with State Persistence

1
A Sticky HDP-HMM for Systems with State
Persistence

• Emily Fox, Erik Sudderth, Michael Jordan, and
  Alan Willsky
• ICML 2008
• Helsinki, Finland

2
Application Speaker Diarization
Total of people
High probability of self-transition
Multi-modal emissions
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Application Maneuvering Target Tracking

• HMM emissions exogenous input driving dynamical
  system
• Unknown number of maneuver modes

Dynamical System
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HDP Prior on Infinite HMM

• Nonparametric Bayesian prior on HMMs with unknown
  state space cardinality
• Encourages use of sparse subset of infinite state
  space
• Allows new states to be created as more data are
  observed

• Inadequately captures temporal state persistence

Infinite HMM Beal, et.al., NIPS 2002HDP-HMM
Teh, et. al., JASA 2006
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Outline

• Background HDP-HMM
• Sticky HDP-HMM
• Capturing multimodal emissions
• Speaker diarization

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Hidden Markov Models
states
Time
observations
State
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Hidden Markov Models
states
observations
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Hidden Markov Models
states
observations
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Hidden Markov Models
states
observations
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HDP-HMM
Time
State

• Dirichlet process (DP)
• State space of unbounded size
• Model complexity adapts to observations
• Hierarchical
• Ties state transition distributions
• Shared sparsity

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HDP-HMM
Stick-breaking construction for DP(g, H)

• Average transition distribution

Stick of unit probability mass
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HDP-HMM

• Average transition distribution
• State-specific transition distributions

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Sensitivity to Noise

• HDP-HMM inadequately models temporal persistence
  of states
• DP bias insufficient to prevent unrealistically
  rapid dynamics
• Reduces predictive performance of inferred model

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Sticky HDP-HMM Part I
State-specific base measure
Increased probability of self-transition
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Direct Assignment Sampler

• Marginalize
• Transition densities
• Emission parameters
• Sequentially sample

Conjugate base measure Þ closed form
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Blocked Resampling
HDP-HMM weak limit approximation
HDP-HMM weak limit approximation
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Hyperparameters

• Place priors on hyperparameters and learn them
  from data
• Weakly informative priors
• All results use the same settings

hyperparameters
can be set using the data
Related self-transition parameter Beal, et.al.,
NIPS 2002
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Results Gaussian Emissions
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Results Fast Switching
Observations
True statesequence
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Outline

• Background
• Sticky HDP-HMM
• Capturing multimodal emissions
• Speaker diarization

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Issues with Multimodal Emissions
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Sticky HDP-HMM Part II

• Approximate multimodal emissions with infinite
  Gaussian mixture
• Temporal state persistence disambiguates model

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Results Mixture Emissions
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Speaker Diarization
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Processing of Features

• Features 19-dim MFCCs
• Features similar between speakers gt challenging
  problem
• Speakers look different over time
• Note
• No training data
• Just input the raw features

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Results 21 meetings
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Results Meeting 1
Sticky DER 1.26 ICSI DER 7.56
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Results Meeting 2
Sticky DER 24.06 ICSI DER 22.00
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Conclusion

• Examined limitations of original HDP-HMM
• Presented sticky HDP-HMM with
• Parameter allowing bias towards self-transitions
• DP emission densities for each HMM state
• Simple and effective addition to the original
  HDP-HMM
• Able to learn a wide range of dynamics, even when
  state persistence is not present in the data

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Results Fast Switching
Observations
True statesequence
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NIST Rich Transcription Evaluations

• Competition for past 6 years
• Many teams compete
• Highly engineered systems
• Large team
• Years to develop

WOW ICSI has lt 10DER