How to Find MAP Compute features Define the energy function Solve the Combinatorial Optimization Activity/Object labels for the past and future Sample Possible Futures [Koppula et al RSS/ICML, Kitani et al ECCV, Jiang et al. RSS/CVPR, Lan et al ECCV, Hu et al RSS/ICRA ]
Shortcomings Compute features Define the energy function Solve the Combinatorial Optimization Activity/Object labels for the past and future Sample Possible Futures We also need probabilities in addition to MAP solution (future is unknown)
Shortcomings Compute features Define the energy function Solve the Combinatorial Optimization Activity/Object labels for the past and future Sample Possible Futures We also need probabilities in addition to MAP solution (future is unknown) on Space with dimension~ 1o6xT ~ 103600 (#ObjLabels#Objectsx#ActLabels)Time
Tale of Two Approaches Graphical Models (discriminative) Can handle exponentially large space Recursive Bayesian (generative) Can compute full belief and reason about uncertinity
HMM – Recursive Belief Estimation HMM Derivation [Rabiner] belt( y ) / p( y t = y | x 1, . . . , x t) | {z } ↵t(y) p( x t+1, . . . , x T | y t = y ) | {z } t(y) ↵t( y t) = p( x t| y t) X yt 1 ↵t 1( y t 1)p( y t| y t 1) t( y t) = X yt+1 p( x t+1| y t+1) t+1( y t+1)p( y t+1| y t)
rCRF: Algorithm in a Nutshell Compute energy function for frame-wise CRF Forward-Backward loop for message passing Compute the energy function of rCRF Sample by using Lagrangian relaxation [Batra et al]
rCRF: Algorithm in a Nutshell All extensions of recursive belief estimation framework are applicable For example, • Non-Markovian edges (eg. skip- connections, auto-regressive HMM, Input-Output HMM)
Efficiency and Accuracy Improvement rCRF is 30x faster than the state-of-the-art algorithms and runs in real-time Accurate handling of uncertainty also increases accuracy
Computes probabilities for past/present/future with no random sampling rCRF: Algorithm O ⇣ (TNOLOLA)3 ⌘ ! O ⇣ T (NOLOLA)3 ⌘ Finds all plausible solutions Extends existing learned models and inference algorithms
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