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Chapter 15 Probabilistic Reasoning over Time. Chapter 15, Sections 1-5 Outline Time and uncertainty Inference: ltering, prediction, smoothing Hidden Markov.

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Chapter 15 Probabilistic Reasoning over Time

Chapter 15, Sections 1-5 Outline Time and uncertainty Inference: ltering, prediction, smoothing Hidden Markov models Kalman lters (a brief mention) Dynamic Bayesian networks Particle ltering

Time and uncertainty The world changes; we need to track and predict it Diabetes management vs vehicle diagnosis Basic idea: copy state and evidence variables for each time step

Markov processes (Markov chains)

Example

Inference tasks

Filtering

Filtering example

Smoothing

Smoothing example

Most likely explanation

Viterbi example

Hidden Markov models

Country dance algorithm

Kalman lters

Updating Gaussian distributions

Simple 1-D example

General Kalman update

2-D tracking example: ltering

2-D tracking example: smoothing

Where it breaks

Dynamic Bayesian networks

DBNs vs. HMMs

DBNs vs Kalman lters

Exact inference in DBNs

Likelihood weighting for DBNs

Particle ltering

Particle ltering contd.

Particle ltering performance

Chapter 15, Sections 1-5 Summary

Chapter 15, Section 6 Outline Speech as probabilistic inference Speech sounds Word pronunciation Word sequences

Speech as probabilistic inference

Phones

Speech sounds

Phone models

Phone model example

Word pronunciation models

Isolated words

Continuous speech

Language model

Combined HMM

DBNs for speech recognition

Chapter 15, Section 6 Summary Since the mid-1970s, speech recognition has been formulated as probabilistic inference Evidence = speech signal, hidden variables = word and phone sequences "Context" effects (coarticulation etc.) are handled by augmenting state Variability in human speech (speed, timbre, etc., etc.) and background noise make continuous speech recognition in real settings an open problem

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