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PRML 13.3-13.3.2
12/7/2018
Kazunori Sakai
Outline 2/44
HMM LDS
continuousdiscrete
maximum likelihood
Contents 3/44
Ø13.3 Linear Dynamical Systems
Ø 13.3.1 Inference in LDS
Ø 13.3.2 Learning in LDS
13.3 Linear Dynamical Systems
Motivation behind LDS 5/44
<latexit sha1_base64="nJ4PaDWcGLJqblnlpUarvV5Pz0Y=">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</latexit>
<latexit sha1_base64="x1tYp+agnmgdGSrqolLa6EjSZ4U=">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</latexit>
non-temporal
non-observable:
observable:
Ø non-temporal
<latexit sha1_base64="o67GmM33Y8vOaoVz6/OuD0aLr7Q=">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</latexit>
Ø given a single measurement :
Ø given lots of measurements : <latexit sha1_base64="mPdum5jrJmKamjAFbeyyOqIurhc=">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</latexit>
Ø Estimating z with observable x.
<latexit sha1_base64="u735SM6HSE/2/9viXs16Lj8V89c=">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</latexit>
<latexit sha1_base64="bc4fqIzLwBDwLHOOuyJjINoYgMw=">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</latexit>
<latexit sha1_base64="73hmnNxKpL26KoWdb+HSzGLRL7I=">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</latexit>
<latexit sha1_base64="LkiKuSyEp5KXehLk577ZpwiUM7I=">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</latexit>
<latexit sha1_base64="sKzmamoQ79/qGvrkx8cFxYFIpC8=">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</latexit>
…
<latexit sha1_base64="bc4fqIzLwBDwLHOOuyJjINoYgMw=">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</latexit>
<latexit sha1_base64="LkiKuSyEp5KXehLk577ZpwiUM7I=">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</latexit>
<latexit sha1_base64="sKzmamoQ79/qGvrkx8cFxYFIpC8=">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</latexit>
<latexit sha1_base64="uawi/Z8uf9VnF/qaBxEg4i+rEu8=">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</latexit>
<latexit sha1_base64="SUFUhv9oqsAAGsB6P8yo3McZtA4=">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</latexit>
…
<latexit sha1_base64="73hmnNxKpL26KoWdb+HSzGLRL7I=">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</latexit>
temporal
Ø temporal
Ø will be a new source of error.<latexit sha1_base64="qdCg6MJyW96rZUuCw/An8HcoR1w=">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</latexit>
Motivation behind LDS 6/44
Ø temporal
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Ø change slowly, noise level is high.
Ø change quickly, noise level is low.
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long window
short window
Ø How to form a weighted
average?
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long window.
short window.
Ø More recent observations will contribute more.
weighted window
From HMM to LDS 7/44
mixture models HMM
continuous latent
variable models
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LDS
discrete
continuous
temporalnon-temporal
Requirements 8/44
Ø Efficient algorithm for inference.
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Ø distributions belonging to the exponential family.
same form
※cited from PRML13.2.1-
13.2.2_Enomoto #20
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Linear-Gaussian Models 9/44
PRML 8.1.4
PRML 2.3
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Linear-Gaussian Models 10/44
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Gaussian
Gaussian Mixture Models 11/44
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To measure z using three
noisy sensors.
GMM Gaussian?GMM
Gaussian Mixture Models 12/44
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<latexit sha1_base64="W9zX4+0uNQ8NWUElTYUmFJLd5DQ=">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</latexit>
<latexit sha1_base64="W9zX4+0uNQ8NWUElTYUmFJLd5DQ=">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</latexit>
<latexit sha1_base64="yaAbqRrUlPuqSC26a0Jyq876uaw=">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</latexit>
<latexit sha1_base64="v5oQheRLfUvxPFdgmxuzYTIMf4c=">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</latexit>
Marginal distribution is
a mixture of Gaussian.
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Ø Exact inference will not be practical.
The most probable latent sequence 13/44
Defining the Model 14/44
<latexit sha1_base64="B2PQqwLMb3Bn6RBhDkHvnQOWSws=">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</latexit>
<latexit sha1_base64="Yiq9yzYR6QqxX/Dp0CPdqkXXtOY=">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</latexit>
<latexit sha1_base64="epytwhljqTTAK7BWJ68kchDRyZY=">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</latexit>
Ø The transition distributions.
Ø The emission distributions.
Ø The initial latent variable.
Ø The parameters.
<latexit sha1_base64="Czjh4uGHpjZCWE7ESQFbpccCNKI=">AAADTHichVFNa9RAGH6Taq3V2lUvgpfgsuJByqwKirRQ6UGP267bFpqyTLKzm6GZJCSTlTXsH/APePCkICL+DA968uahP0E8tuBBBZ/MRmy3qBMy88zzvs/7Ma+XhDLTjO1b9syp07Nn5s7Onzu/cGGxdvHSZhbnqS86fhzG6bbHMxHKSHS01KHYTlLBlReKLW9vrbRvDUWayTh6rEeJ2FV8EMm+9LkG1a29cb047GUjhcMpHFcHQnNn7Kw4bij62gWluA68PowPwN88cncfcqX4FLk27dSWg99Ox1OpHGwXiE1JWkd4N5WDQLvjbq3OlphZzknQrECdqtWKax/IpR7F5FNOigRFpIFD4pTh26EmMUrA7VIBLgWSxi5oTPPQ5vAS8OBg97APcNup2Aj3MmZm1D6yhPhTKB1qsM/sLTtgH9k79oX9+GuswsQoaxnh9CZakXQXn11pf/uvSuHUFPxRQdH4R9Wa+nTPVCtRfWKYsg9/EmH49PlB+/5Go7jOXrGv6OAl22fv0UM0PPRfr4uNF6ai1GgEPTE9K1NFhFcuYMuQoQdbH1yO99CIXCBTQMPyRTHA5vS4ToLNW0tN4PU79dXlapRzdJWu0Q3M6y6t0iNqUYd8a8G6bS1bK/Yn+9D+bv+cuNpWpblMx9bM7C+qxM8s</latexit>
Equivalent expression 15/44
<latexit sha1_base64="0ss2Zpka0TQJPnikT8YXONb6Wr0=">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</latexit>
<latexit sha1_base64="ik9tfdtFX2ynmL/dXVeWgbmg+LM=">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</latexit>
<latexit sha1_base64="B2PQqwLMb3Bn6RBhDkHvnQOWSws=">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</latexit>
<latexit sha1_base64="Yiq9yzYR6QqxX/Dp0CPdqkXXtOY=">AAADVHicjVHNahRBEK7ZMRqjJhtFELw0WVYiSOgNQkQNBKLgSZKsmwQyYZnp9Ow2mT9meleTSV7AF/DgScGDePAhPOgLGMgjiMcIXnLwm96BrMa/Hmaq5qv6vqrq8pJAZZrzQ6tinxk5e270/NiFi5fGJ6qTl1ezuJcK2RJxEKfrnpvJQEWypZUO5HqSSjf0ArnmbS8W8bW+TDMVR0/0TiI3Q7cTKV8JVwNqV98nzAmkr6eZE7q66/ksZ8/YPmvDRrB7Q/juEO6kqtPVN9n8IC7cAIHHReB/1RaL5N9q3xrCnabqhO5JwXa1xme4Oey00yidGpVnKa5+JIe2KCZBPQpJUkQafkAuZXg2qEGcEmCblANL4SkTl7RPY+D2kCWR4QLdxreDv40SjfBfaGaGLVAlwJuCyajOP/O3/Ih/4u/4F378R63caBS97MB6A65M2hPPrzW//5MVwmrqnrDAqP+la00+3THdKnSfGKSYQwwU+rsvjpp3V+r5Df6af8UEr/gh/4AZov438WZZrrw0HaWGI+mpmTk0XUS45RyxDBW2EPOB9XAfGso5KnWpX9woFtj4dV2nndXZmQb85du1hfvlKkfpOk3RNPY1Rwv0iJaoRcK6at2zHlgPKweVY9u2RwapFavkXKGfjj3+A+psz18=</latexit>
<latexit sha1_base64="epytwhljqTTAK7BWJ68kchDRyZY=">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</latexit>
13.3.1 Inference in LDS
Form of
must be Gaussian.
The forward equations 17/44
Objective:
Given: <latexit sha1_base64="Czjh4uGHpjZCWE7ESQFbpccCNKI=">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</latexit>
<latexit sha1_base64="YxcfHki3FxOI5VlS3IkyiF3TloM=">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</latexit>
<latexit sha1_base64="r36PINsL4y5XnSmg6HuuFH3wIQI=">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</latexit>
<latexit sha1_base64="YQDoB6vicIORfmQDBT4TLaY7alc=">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</latexit>
: Gaussian
: Gaussian
<latexit sha1_base64="qVsyqP3pPgp/I3xlg1w429MHpaw=">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</latexit>
<latexit sha1_base64="mhjmdTOa0uVELSdV6Wn5MofINOc=">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</latexit>
The forward equations 18/44
<latexit sha1_base64="yRNL12wsxk17kzIHa1myT0Rdv2Y=">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</latexit>
<latexit sha1_base64="2OzvJZxL7ziq92NYE7EIk5MSD6I=">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</latexit>
<latexit sha1_base64="B2PQqwLMb3Bn6RBhDkHvnQOWSws=">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</latexit>
<latexit sha1_base64="Yiq9yzYR6QqxX/Dp0CPdqkXXtOY=">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</latexit>
Ø Determine <latexit sha1_base64="1Mc2Fg7wgHwEK6qpfStmS2HgE9c=">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</latexit>
Assuming
are known.
<latexit sha1_base64="Ihns2iIjfBBhDXsrj4ZqvfuA8lo=">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</latexit>
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The forward equations 19/44
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The forward equations 20/44
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<latexit sha1_base64="qsfcPnTUdCnwfqUqsOsMSkbnGXw=">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</latexit>
<latexit sha1_base64="B1ScmRFSO5/SzaOiE1JllIIxiQg=">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</latexit>
<latexit sha1_base64="lnuvDL+doKvBloxh1r3jqmCt4zQ=">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</latexit>
<latexit sha1_base64="pEqsqyI2JL8rKwkUWD/qE74aHb0=">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</latexit>
<latexit sha1_base64="kPqBZbWM/FmiXzK1/eTI366U0VI=">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</latexit>
The forward equations 21/44
<latexit sha1_base64="CtAvwbIg2MZh5eamvfoE7oqQaDQ=">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</latexit>
<latexit sha1_base64="qsbBRrVS4nfJdrXXtiKltoBJ0Uc=">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</latexit>
<latexit sha1_base64="rugDa+FJau+3iWU9feE+F2nTnXs=">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</latexit>
<latexit sha1_base64="aAOW3VN/iye2qJA+ShvB/5EKBis=">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</latexit>
Ø Using (C.7)
: Kalman gain matrix
Ø Using (C.5)
<latexit sha1_base64="tl0FJVhQlhz/EMY8tOI7wz92ikY=">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</latexit>
Kalman Filter equations 22/44
<latexit sha1_base64="pIkR6/zo+/NnI10EStXya1O9CO4=">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</latexit>
<latexit sha1_base64="NwQ10MQr4OlBCTd6+hYfdIFKrGU=">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</latexit>
observed prediction for <latexit sha1_base64="OQm5cCOMww+hKCKMYwDmwfbiJvk=">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</latexit>
observable space
<latexit sha1_base64="CtAvwbIg2MZh5eamvfoE7oqQaDQ=">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</latexit>
<latexit sha1_base64="IWjwJfbl7EEpC7F8NM1GyFeu3LA=">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</latexit>
<latexit sha1_base64="L18TUq4awKn3Jt/yNA85LSojFSw=">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</latexit>
: unaffected by observations
make the variance small
make the variance large
Example for understanding Kalman gain 23/44
<latexit sha1_base64="az+EbkE13xsIuPBfhto1arK2b8s=">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</latexit>
<latexit sha1_base64="g8yjk7iRNpwCU/lDcCMTE1ulk7E=">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</latexit>
<latexit sha1_base64="TDzk7t+6AE5gtHI2naNc2BYxmiQ=">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</latexit>
<latexit sha1_base64="sxrQ0le2ykzFiU0+e54ud8Eab74=">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</latexit>
<latexit sha1_base64="xEDKDQNPjwnEIC4UFX091kumfgk=">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</latexit>
※cited from
PRML13.3_Taniyama #9
The initial conditions 24/44
<latexit sha1_base64="v4UcvOtQkmGmVzKcn9lRkKKyK6w=">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</latexit>
<latexit sha1_base64="pO2w6P/BxDPXAUwK1I2CAgq1aMQ=">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</latexit>
<latexit sha1_base64="117aRlEfAvnM4kVSrU5YgUZqF20=">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</latexit>
PRML 13.3-13.3.2
PRML 13.3-13.3.2
PRML 13.3-13.3.2
PRML 13.3-13.3.2
PRML 13.3-13.3.2
PRML 13.3-13.3.2
PRML 13.3-13.3.2
PRML 13.3-13.3.2
PRML 13.3-13.3.2
PRML 13.3-13.3.2
PRML 13.3-13.3.2
PRML 13.3-13.3.2
PRML 13.3-13.3.2
PRML 13.3-13.3.2
PRML 13.3-13.3.2
PRML 13.3-13.3.2
PRML 13.3-13.3.2
PRML 13.3-13.3.2
PRML 13.3-13.3.2
PRML 13.3-13.3.2

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PRML 13.3-13.3.2

  • 3. Contents 3/44 Ø13.3 Linear Dynamical Systems Ø 13.3.1 Inference in LDS Ø 13.3.2 Learning in LDS
  • 5. Motivation behind LDS 5/44 <latexit sha1_base64="nJ4PaDWcGLJqblnlpUarvV5Pz0Y=">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</latexit> <latexit 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sha1_base64="73hmnNxKpL26KoWdb+HSzGLRL7I=">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</latexit> temporal Ø temporal Ø will be a new source of error.<latexit 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  • 6. Motivation behind LDS 6/44 Ø temporal <latexit sha1_base64="YAIttKGk1GRBzVFGCHDJMwRFf/A=">AAAC1HichVFLa9RQFP4aX7U+OupGcFMcRtxY74igiIWCGxdS+nCmhU4NSXqnE5rchORmtL1mJW5cuBMXrhRciD/BpYr+ARf9CeKyghsXfrkTES3qCbn33O+c7zz9NApzLcTOmLNv/4GDh8YPTxw5euz4ZOPEyW6eFFkgO0ESJdmK7+UyCpXs6FBHciXNpBf7kVz2N29U9uWhzPIwUbf1VirXYm9Dhf0w8DQht3GxF3t64PfNdumauXKmlxexa9TM3IVb5R0C5qf9Hu2qLN1GU0wLK1N7lXatNFHLfNL4gB7WkSBAgRgSCpp6BA85v1W0IZASW4MhllELrV2ixAS5Bb0kPTyimzw3+FqtUcV3FTO37IBZIv4ZmVNoiU/ildgVH8Vr8Vl8/2ssY2NUtWzx9kdcmbqTj04vffsvK+atMfjFIqP1j6o1+rhqqw1ZfWqRqo9gFGG4/XR36dpiy5wTL8QXdvBc7Ii37EENvwYvF+TiM1tRZjkSd23Psa1CccqGtpwZ1mnrEys4D83IhpkGGFYT5QLbf65rr9K9NN2mvnC5OXu9XuU4zuAsznNfVzCLm5hHh9mf4A3e4b3Tde47D5yHI1dnrOacwm/iPP4B7H+r9g==</latexit> Ø change slowly, noise level is high. Ø change quickly, noise level is low. <latexit sha1_base64="bc4fqIzLwBDwLHOOuyJjINoYgMw=">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</latexit> long window short window Ø How to form a weighted average? <latexit sha1_base64="bc4fqIzLwBDwLHOOuyJjINoYgMw=">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</latexit> long window. short window. Ø More recent observations will contribute more. weighted window
  • 7. From HMM to LDS 7/44 mixture models HMM continuous latent variable models <latexit sha1_base64="v5oQheRLfUvxPFdgmxuzYTIMf4c=">AAACr3ichVHLShxBFD12YjTGxDHZBNxIhpGspFoERVwI2bj0NY7gmEl3W+MU0y+6a0a08QfyAWaRRVRwEfIZLvQHXPgJIUsFNy48XdMQEjG5TVfdOvee+3RjX6VaiKs+68nT/mcDg8+HXgy/fDVSGn29nkadxJNVL/KjZMN1UumrUFa10r7ciBPpBK4va277Q26vdWWSqihc03ux3AqcnVA1ledoQvV64OiW28z2Dxpho1QWk8LI+EPFLpQyClmKSueoYxsRPHQQQCKEpu7DQcpvEzYEYmJbyIgl1JSxSxxgiNwOvSQ9HKJtnjt8bRZoyHceMzVsj1l8/gmZ46iIS/FdXIsL8UP8FHePxspMjLyWPd5ujyvjxsjnt6u3/2UFvDVav1lkVP5RtUYTs6Zaxepjg+R9eL0I3f0v16tzK5VsQpyIX+zgWFyJM/YQdm+802W58tVUlBiOxK7pOTBVhJxyRlvKDNu0NYl1OA/NyBkztdDNJ8oF2n+v66GyPjVpU1+eLi/MF6scxBje4T33NYMFLGIJVWaPcYhvOLJsq2Z9tD71XK2+gvMGf4il7gGsCJw5</latexit> <latexit sha1_base64="yaAbqRrUlPuqSC26a0Jyq876uaw=">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</latexit> <latexit sha1_base64="RZFEUvB84WoF4HrvjkMgga1JH0A=">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</latexit> LDS discrete continuous temporalnon-temporal
  • 8. Requirements 8/44 Ø Efficient algorithm for inference. <latexit sha1_base64="JI0cLEeoo7jV5e9hgB29pQwEW5U=">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</latexit> <latexit sha1_base64="LmmoZuxVtrVyj7NOWxBHb5WJ78s=">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</latexit> Ø distributions belonging to the exponential family. same form ※cited from PRML13.2.1- 13.2.2_Enomoto #20 <latexit sha1_base64="2OzvJZxL7ziq92NYE7EIk5MSD6I=">AAAD1niclVHPa9RAFH5p/FHrj271IngZXFbqwTIpgiIKBS8e+8NtF5qyTLKTzdDJJExmt3ZjvYngyVsPnhQ8iH+DJ8H6D3jonyAeK3jx4Mts0Na1Lk5I8uZ77/veN/OCTIrcULrvTLgnTp46PXlm6uy58xemazMXV/O0p0PeDFOZ6lbAci6F4k0jjOStTHOWBJKvBZv3y/xan+tcpOqh2c74RsK6SkQiZAah9oxDQ9ImBVFkh/hbosNjZnDrM5nFrMQkj8ws8RNm4iDCzADBXwQturG5Tu6RbLTw0aHCx2MEfKHM/7a/QbxDCn8xMBhr4KiErdAJZjolelx9u1anc9QuMhp4VVCHai2mtT3woQMphNCDBDgoMBhLYJDjsw4eUMgQ24ACMY2RsHkOOzCF3B5WcaxgiG7it4u79QpVuC81c8sOsYvEVyOTQIN+pm/pAf1E39Ev9MexWoXVKL1s4z8YcnnWnn5+eeX7WFaCfwPxbxYyGv9wbSCC29atQPeZRcpzhEOF/mD3YOXOcqO4Rl/Tr3iCV3SffsAzqP638M0SX35pHWnL4bBlz5xYFwpvucBcjh06mIsQ6+F9GFQusFMM/fJGcYDen+MaDVbn5zyMl27WF+5Wo5yEK3AVZnFet2ABHsAiNCF0dp33zkdnz225T9yn7rNh6YRTcS7BkeW++AlMi/o5</latexit>
  • 9. Linear-Gaussian Models 9/44 PRML 8.1.4 PRML 2.3 <latexit sha1_base64="VJsPWP3AwH/VbMKtCz+uSz2nQX4=">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</latexit> <latexit sha1_base64="sHIv9x3KiYbMD+soHJ0cDwNbIX0=">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</latexit> <latexit sha1_base64="HQXmn0qFVedEypSv1Ky4hkphM/g=">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</latexit> <latexit sha1_base64="Pik2LQAyauPAiXwEwRV9x/5Ha5g=">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</latexit>
  • 10. Linear-Gaussian Models 10/44 <latexit sha1_base64="vZpsBHFlhJc8AoPoRSJ3o0TzMyw=">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</latexit> <latexit 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  • 11. Gaussian Mixture Models 11/44 <latexit sha1_base64="HVOw9foFXqEx1GW9mDbB225F17k=">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</latexit> <latexit 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sha1_base64="ptJ55NAC3N0FmYoXi/udCEqzoPE=">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</latexit> <latexit 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sha1_base64="yaAbqRrUlPuqSC26a0Jyq876uaw=">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</latexit> <latexit sha1_base64="4cHpXJrwaYnUsPLlp2vsszRb49U=">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</latexit> To measure z using three noisy sensors. GMM Gaussian?GMM
  • 12. Gaussian Mixture Models 12/44 <latexit sha1_base64="GFDDGsZQ8hi8aqlkd08jXTcgeBI=">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</latexit> <latexit 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  • 13. The most probable latent sequence 13/44
  • 14. Defining the Model 14/44 <latexit sha1_base64="B2PQqwLMb3Bn6RBhDkHvnQOWSws=">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</latexit> <latexit sha1_base64="Yiq9yzYR6QqxX/Dp0CPdqkXXtOY=">AAADVHicjVHNahRBEK7ZMRqjJhtFELw0WVYiSOgNQkQNBKLgSZKsmwQyYZnp9Ow2mT9meleTSV7AF/DgScGDePAhPOgLGMgjiMcIXnLwm96BrMa/Hmaq5qv6vqrq8pJAZZrzQ6tinxk5e270/NiFi5fGJ6qTl1ezuJcK2RJxEKfrnpvJQEWypZUO5HqSSjf0ArnmbS8W8bW+TDMVR0/0TiI3Q7cTKV8JVwNqV98nzAmkr6eZE7q66/ksZ8/YPmvDRrB7Q/juEO6kqtPVN9n8IC7cAIHHReB/1RaL5N9q3xrCnabqhO5JwXa1xme4Oey00yidGpVnKa5+JIe2KCZBPQpJUkQafkAuZXg2qEGcEmCblANL4SkTl7RPY+D2kCWR4QLdxreDv40SjfBfaGaGLVAlwJuCyajOP/O3/Ih/4u/4F378R63caBS97MB6A65M2hPPrzW//5MVwmrqnrDAqP+la00+3THdKnSfGKSYQwwU+rsvjpp3V+r5Df6af8UEr/gh/4AZov438WZZrrw0HaWGI+mpmTk0XUS45RyxDBW2EPOB9XAfGso5KnWpX9woFtj4dV2nndXZmQb85du1hfvlKkfpOk3RNPY1Rwv0iJaoRcK6at2zHlgPKweVY9u2RwapFavkXKGfjj3+A+psz18=</latexit> <latexit sha1_base64="epytwhljqTTAK7BWJ68kchDRyZY=">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</latexit> Ø The transition distributions. Ø The emission distributions. Ø The initial latent variable. Ø The parameters. <latexit sha1_base64="Czjh4uGHpjZCWE7ESQFbpccCNKI=">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</latexit>
  • 15. Equivalent expression 15/44 <latexit sha1_base64="0ss2Zpka0TQJPnikT8YXONb6Wr0=">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</latexit> <latexit sha1_base64="ik9tfdtFX2ynmL/dXVeWgbmg+LM=">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</latexit> <latexit sha1_base64="B2PQqwLMb3Bn6RBhDkHvnQOWSws=">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</latexit> <latexit sha1_base64="Yiq9yzYR6QqxX/Dp0CPdqkXXtOY=">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</latexit> <latexit sha1_base64="epytwhljqTTAK7BWJ68kchDRyZY=">AAADN3ichVFNa9RAGH4Tv2r96FYvgiCDy+oKUiYiVESh4MWTbFu3LTRlSbKT3aGTD5LJyjb2D3j04sGTggfxF3j2oH/AQ0/eRPEkFfTgwSezAavFOiHzvvM887wf8/qpkrnmfMeyDx0+cvTY1PHpEydPnZ5pzJ5ZyZMiC0Q3SFSSrfleLpSMRVdLrcRamgkv8pVY9TfvVPzqSGS5TOL7epyKjcgbxDKUgacB9RqPU+YqEeo2cyNPD/2QlWyLbbMerAPrZnIw1FfY7QkfeArEvYo4SPWQuX6i+vk4ggHmRkXNctire1SdPXidq9do8jluFtvvOLXTpHp1ksZbcqlPCQVUUESCYtLwFXmU41snhzilwDaoBJbBk4YXtE3T0Ba4JXDDA7qJfYDTeo3GOFcxc6MOkEXhz6Bk1OLv+Uu+y9/xV/wz//nPWKWJUdUyhvUnWpH2Zh6dW/7+X1UEq2n4WwVF64CqNYV0w1QrUX1qkKqPYBJhtPVkd/nmUqu8xJ/zL+jgGd/hb9BDPPoWvFgUS09NRZnRCHpgeo5MFTFeuQSXI0MfXAiswHtoRC6RaUij6kUxQOfvce13Vq7NOfAXrzcXbtWjnKLzdJHamNc8LdBd6lAX2X9YF6zLVtt+bX+wP9qfJldtq9acpT+W/fUX2QfH7g==</latexit>
  • 17. Form of must be Gaussian. The forward equations 17/44 Objective: Given: <latexit sha1_base64="Czjh4uGHpjZCWE7ESQFbpccCNKI=">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</latexit> <latexit sha1_base64="YxcfHki3FxOI5VlS3IkyiF3TloM=">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</latexit> <latexit sha1_base64="r36PINsL4y5XnSmg6HuuFH3wIQI=">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</latexit> <latexit sha1_base64="YQDoB6vicIORfmQDBT4TLaY7alc=">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</latexit> : Gaussian : Gaussian <latexit sha1_base64="qVsyqP3pPgp/I3xlg1w429MHpaw=">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</latexit> <latexit sha1_base64="mhjmdTOa0uVELSdV6Wn5MofINOc=">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</latexit>
  • 18. The forward equations 18/44 <latexit sha1_base64="yRNL12wsxk17kzIHa1myT0Rdv2Y=">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</latexit> <latexit sha1_base64="2OzvJZxL7ziq92NYE7EIk5MSD6I=">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</latexit> <latexit sha1_base64="B2PQqwLMb3Bn6RBhDkHvnQOWSws=">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</latexit> <latexit sha1_base64="Yiq9yzYR6QqxX/Dp0CPdqkXXtOY=">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</latexit> Ø Determine <latexit sha1_base64="1Mc2Fg7wgHwEK6qpfStmS2HgE9c=">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</latexit> Assuming are known. <latexit sha1_base64="Ihns2iIjfBBhDXsrj4ZqvfuA8lo=">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</latexit> <latexit sha1_base64="y7KPXfqspnGz96IY1tEmOtVafV0=">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</latexit>
  • 19. The forward equations 19/44 <latexit sha1_base64="DclIyGJ/eDSUf0KgLsVUXYWD0No=">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</latexit> <latexit sha1_base64="a8c/4H47Er02uMwHgImL5VSuWts=">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</latexit> <latexit 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sha1_base64="TIVcS+kPQxOhQPm+QKqJDrfJ4CQ=">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</latexit> <latexit 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sha1_base64="L18TUq4awKn3Jt/yNA85LSojFSw=">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</latexit> <latexit sha1_base64="8WgcexPfLp1iUgOa5kZB2oNW8Xw=">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</latexit> <latexit sha1_base64="HVXlNoxExKsh/hEqQF+/ciUdQmM=">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</latexit> <latexit sha1_base64="uJLxcv+Jtu6xlI3g6yk/goMh9As=">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</latexit><latexit sha1_base64="S6bQEcb++XiEIcU89ctPTWhUYkE=">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</latexit> <latexit sha1_base64="QpELeXQL9lFsrq9evs8TJGExVO0=">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</latexit> <latexit sha1_base64="1VdEVha30Dy89ccHIO0sCTD+5kM=">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</latexit>
  • 20. The forward equations 20/44 <latexit sha1_base64="L18TUq4awKn3Jt/yNA85LSojFSw=">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</latexit> <latexit 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  • 21. The forward equations 21/44 <latexit sha1_base64="CtAvwbIg2MZh5eamvfoE7oqQaDQ=">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</latexit> <latexit sha1_base64="qsbBRrVS4nfJdrXXtiKltoBJ0Uc=">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</latexit> <latexit sha1_base64="rugDa+FJau+3iWU9feE+F2nTnXs=">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</latexit> <latexit sha1_base64="aAOW3VN/iye2qJA+ShvB/5EKBis=">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</latexit> Ø Using (C.7) : Kalman gain matrix Ø Using (C.5) <latexit sha1_base64="tl0FJVhQlhz/EMY8tOI7wz92ikY=">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</latexit>
  • 22. Kalman Filter equations 22/44 <latexit sha1_base64="pIkR6/zo+/NnI10EStXya1O9CO4=">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</latexit> <latexit sha1_base64="NwQ10MQr4OlBCTd6+hYfdIFKrGU=">AAADGXichVFLaxRBEK6Z+EjWR1ZzEXJpXFbiIaFHBCUYCOSi5LJ57CaQDcvMpGe3ybyY6d2QDPsH8gdyyEnBg/grxIPBq3hI/kHIMYIXD37TO7irQe1huqq+qq8eXU7sy1RxfmqYY9eu37g5PlG6dfvO3cnyvfuNNOomrqi7kR8lm46dCl+Goq6k8sVmnAg7cHyx4ewu5f6NnkhSGYXraj8W24HdDqUnXVsBapVVM7BVx/FYxhqsz1qQIeQCa/rCUzNs6H4FeHbEXh4JH6JLuZXIdkc9HkFrv2JnmcX6rXKFz3F92FXFKpQKFacWlT9Rk3YoIpe6FJCgkBR0n2xK8W2RRZxiYNuUAUugSe0X1KcSuF1ECUTYQHdxt2FtFWgIO8+ZaraLKj7+BExGVf6Vv+OX/IS/5+f8x19zZTpH3ss+pDPgirg1efhg7ft/WQGkos6QBUb1H10r8ui57lai+1gj+RzuIEPv4OhybX61mj3ib/gFJnjNT/lHzBD2vrlvV8Tqse4o0RxBe3rmQHcR4pUz+FJU2IHPA9bFeyhkzlCpQ738RbFA6891XVUaT+Ys6CtPK4svilWO0zQ9pBns6xkt0kuqUR3VzwwyJoySeWx+ME/Mz4NQ0yg4U/TbMb/8BMWWvFQ=</latexit> observed prediction for <latexit sha1_base64="OQm5cCOMww+hKCKMYwDmwfbiJvk=">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</latexit> observable space <latexit sha1_base64="CtAvwbIg2MZh5eamvfoE7oqQaDQ=">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</latexit> <latexit sha1_base64="IWjwJfbl7EEpC7F8NM1GyFeu3LA=">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</latexit> <latexit sha1_base64="L18TUq4awKn3Jt/yNA85LSojFSw=">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</latexit> : unaffected by observations make the variance small make the variance large
  • 23. Example for understanding Kalman gain 23/44 <latexit sha1_base64="az+EbkE13xsIuPBfhto1arK2b8s=">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</latexit> <latexit sha1_base64="g8yjk7iRNpwCU/lDcCMTE1ulk7E=">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</latexit> <latexit sha1_base64="TDzk7t+6AE5gtHI2naNc2BYxmiQ=">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</latexit> <latexit sha1_base64="sxrQ0le2ykzFiU0+e54ud8Eab74=">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</latexit> <latexit sha1_base64="xEDKDQNPjwnEIC4UFX091kumfgk=">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</latexit> ※cited from PRML13.3_Taniyama #9
  • 24. The initial conditions 24/44 <latexit sha1_base64="v4UcvOtQkmGmVzKcn9lRkKKyK6w=">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</latexit> <latexit sha1_base64="pO2w6P/BxDPXAUwK1I2CAgq1aMQ=">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</latexit> <latexit sha1_base64="117aRlEfAvnM4kVSrU5YgUZqF20=">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</latexit>