Test: max y , h w T Ψ ( x , y , h )

1. h y x Modeling Latent Variable Uncertainty for Loss-based Learning M. Pawan Kumar Ben Packer Daphne Koller http://cvc.centrale-ponts.fr http://dags.stanford.edu Aim:Accurate parameter estimation from weakly supervised datasets Results Objective Minimize Rao’s Dissimilarity Coefficient Known ground-truth LV values at test time Object Detection Latent Variable Models Pw(yi,hi|xi) Pθ(hi|yi,xi) HOG Features y : output x : input minθ,wΣiΣhΔ(yi,h,yi(w),hi(w))Pθ(h|yi,xi) Encourages prediction with correct output and high probabilityLV Values known during training No object scale variation -βΣh,h’Δ(yi,h,yi,h’)Pθ(h|yi,xi)Pθ(h’|yi,xi) h : latent variables (LV) Values unknown during training Latent Space = All possible pixel positions Property 1 If loss function is independent of h, we recover latent SVM y = “Deer” x h Object Detection Optimization • Predict the image class y • Predict the object location h Block coordinate descent over (w,θ) y Fix delta distribution; Optimize conditional distribution Latent SVM Linear prediction rule with parameter w Case I: Delta distribution predicts correct output, y = y(w) hi(w) Train: minwΣiΔ(yi,yi(w),hi(w)) Test: maxy,hwTΨ(x,y,h) hi(w) Ψ: joint feature vector Δ: loss function; measures risk Statistically Significant Not Statistically Significant ✔ Employs a user-defined loss function (with restricted form) ✖ Does not model uncertainty in LV Increase the probability of the predicted LV h(w) Action Detection Case II: Delta distribution predicts incorrect output, y ≠ y(w) exp(θTΨ(x,y,h)) The EM Algorithm Pθ(y,h|x) = Z Poselet Features Train: maxθΣiΣhilog (Pθ(yi,hi|xi)) Test: maxy,hθTΨ(x,y,h) Large object scale variation ✔ Models uncertainty in LV Increase the diversity of the conditional distribution Fix conditional distribution; Optimize delta distribution ✖ Does not model accuracy of LV prediction (yi,hi(w)) ✖ Does not employ a user-defined loss function Latent Space = Top k person detections (yi,hi(w)) Overview Two distributions for two tasks Models uncertainty in LV Predict correct output and high probability LV Pθ(hi|yi,xi) Difference-of-convex upper bound of expected loss hi Efficient concave-convex procedure similar to latent SVM Models predicted output and LV Pw(yi,hi|xi) Property 2 If Pθis modeled as delta, we recover iterative latent SVM (yi,hi) (yi(w),hi(w)) Ideally, the two learned distributions should match exactly Code available at http://cvc.centrale-ponts.fr/personnel/pawan Statistically Significant Statistically Significant Limited representational power prevents exact match