Maximum a posteriori map estimation pieter abbeel uc berkeley eecs
Download
1 / 5

Maximum A Posteriori (MAP) Estimation Pieter Abbeel UC Berkeley EECS - PowerPoint PPT Presentation


  • 118 Views
  • Uploaded on

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.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Maximum A Posteriori (MAP) Estimation Pieter Abbeel UC Berkeley EECS' - selia


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
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.: AAAAAAAAAAAAA


Overview
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


Maximum a posteriori map estimation pieter abbeel uc berkeley eecs
MAP

Naively solving by enumerating all possible combinations of x_0,…,x_Tis exponential in T !

  • Generally:



Kalman filter aka linear gaussian setting
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.