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Maximum A Posteriori (MAP) Estimation Pieter Abbeel UC Berkeley EECS

Maximum A Posteriori (MAP) Estimation Pieter Abbeel UC Berkeley EECS. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A A A A A A A A A A. Overview. Filtering: Smoothing: MAP:. X 0. X 0. X 0. X t-1. X t-1. X t-1. X t. X t. X t. X t+1.

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Maximum A Posteriori (MAP) Estimation Pieter Abbeel UC Berkeley EECS

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  1. Maximum A Posteriori (MAP) Estimation Pieter Abbeel UC Berkeley EECS TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAAAAA

  2. Overview • Filtering: • Smoothing: • MAP: X0 X0 X0 Xt-1 Xt-1 Xt-1 Xt Xt Xt Xt+1 Xt+1 XT XT z0 z0 z0 zt-1 zt-1 zt-1 zt zt zt zt+1 zt+1 zT zT

  3. MAP Naively solving by enumerating all possible combinations of x_0,…,x_Tis exponential in T ! • Generally:

  4. MAP --- Complete Algorithm • O(T n2)

  5. Kalman Filter (aka Linear Gaussian) setting • Summations  integrals • But: can’t enumerate over all instantations • However, we can still find solution efficiently: • the joint conditional P(x0:T | z0:T) is a multivariate Gaussian • for a multivariate Gaussian the most likely instantiation equals the mean  we just need to find the mean of P(x0:T | z0:T) • the marginal conditionals P(xt | z0:T) are Gaussians with mean equal to the mean of xt under the joint conditional, so it suffices to find all marginal conditionals • We already know how to do so: marginal conditionals can be computed by running the Kalman smoother.

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