Statistical Problems in Computer Vision

Transcription

1 V and ML Statistical Problems in omputer Vision Machine Learning and Perception Group Microsoft Research ambridge SI Meeting, ambridge, 26th September 2011 Statistical Problems in omputer Vision Microsoft Research ambridge

2 V and ML V and ML omputer Vision 1. model uncertainty: we do not know the correct model, 2. task ambiguity: humans solve ambiguous high-level vision tasks consistently, 3. data availability: large amounts of image data available. Statistical Problems in omputer Vision Microsoft Research ambridge

3 V and ML V and ML omputer Vision 1. model uncertainty: we do not know the correct model, 2. task ambiguity: humans solve ambiguous high-level vision tasks consistently, 3. data availability: large amounts of image data available. This short talk: statistical problems in common computer vision models Statistical Problems in omputer Vision Microsoft Research ambridge

4 V and ML V and ML Simple omputer Vision Tasks Image retrieval, matching, registration (Lowe, IV 1999) Frontal face detection (Viola and Jones, VPR 2001) Image classification (Gehler and Nowozin, IV 2009) Statistical Problems in omputer Vision Microsoft Research ambridge

5 V and ML V and ML Simple omputer Vision Tasks ommon properties successfully reduced to simple task and output (classification, nearest-neighbor retrieval, etc.) inexpensive annotation simple models are state-of-the-art Statistical Problems in omputer Vision Microsoft Research ambridge

6 V and ML V and ML omplex omputer Vision Tasks Human pose estimation (Ferrari et al., VPR 2008) Scene understanding (Gould et al., IV 2009) Object detection (veringham et al., VO 2010 report) ction/ctivity recognition (Laptev et al., IV 2007) Statistical Problems in omputer Vision Microsoft Research ambridge

7 V and ML V and ML omplex omputer Vision Tasks ommon properties structured prediction of multiple dependent variables ground truth data expensive to obtain performance improvements by structured models learning and test-time inference is challenging Statistical Problems in omputer Vision Microsoft Research ambridge

8 V and ML V and ML onditional Random Fields (RF) wd X i V D D D D Yi D D D w w w w Undirected graphical model on discrete random variables Y p(y x, w), image x (always observed), labelling y, parameters w Parameters w carry no meaning by themselves Prediction by minimizing expected loss l under the model, z = f (x) = argmin z y p(y x) [l(y, z)] Statistical Problems in omputer Vision Microsoft Research ambridge

9 V and ML V and ML Problem 1: asics Number of variables varies, structure determined by x, replicated Parameters shared, but all interactions are conditioned on x Parameter estimation: how to define consistency? hallenging even for a linear chain model, see (Sinn, Poupart, ISTTS 2011) D D D D D D Statistical Problems in omputer Vision Microsoft Research ambridge

10 V and ML V and ML Problem 2: Misspecification and Loss Model error typically dominates everything else Model quality is measured in terms of prediction loss on holdout data Loss function is task-specific and structured p w p p ut we know that, Minimizing the expected loss under a misspecified model is a bad idea, except for the log-loss (Liang, Jordan, IML 2008), (Pletscher, Nowozin, Kohli, Rother, DGM 2011) Different adverse effect due to approximate inference (Lacoste-Julien, Husźar, Ghahramani, ISTTS 2011) doption of loss-centric paradigms, empirical risk minimization, structured SVM Statistical Problems in omputer Vision Microsoft Research ambridge

11 V and ML V and ML Problem 2: Misspecification and Loss Model error typically dominates everything else Model quality is measured in terms of prediction loss on holdout data Loss function is task-specific and structured p w p p ut we know that, Minimizing the expected loss under a misspecified model is a bad idea, except for the log-loss (Liang, Jordan, IML 2008), (Pletscher, Nowozin, Kohli, Rother, DGM 2011) Different adverse effect due to approximate inference (Lacoste-Julien, Husźar, Ghahramani, ISTTS 2011) doption of loss-centric paradigms, empirical risk minimization, structured SVM Statistical Problems in omputer Vision Microsoft Research ambridge

12 V and ML V and ML Problem 2: Misspecification and Loss Model error typically dominates everything else Model quality is measured in terms of prediction loss on holdout data Loss function is task-specific and structured p w p p ut we know that, Minimizing the expected loss under a misspecified model is a bad idea, except for the log-loss (Liang, Jordan, IML 2008), (Pletscher, Nowozin, Kohli, Rother, DGM 2011) Different adverse effect due to approximate inference (Lacoste-Julien, Husźar, Ghahramani, ISTTS 2011) doption of loss-centric paradigms, empirical risk minimization, structured SVM Statistical Problems in omputer Vision Microsoft Research ambridge

13 V and ML V and ML Problem 3: Intractability and Special lasses High-treewidth models on discrete variables xact inference and estimation generally intractable MP, max y p(y x) remains tractable for special classes (permuted submodular energies) D D D D D D Open problem: are there similar subclasses of models for which guarantees on the quality of probabilistic inference or estimation can be provided? Statistical Problems in omputer Vision Microsoft Research ambridge

14 V and ML V and ML Thank you! Feedback most welcome: Sebastian.Nowozin@microsoft.com Statistical Problems in omputer Vision Microsoft Research ambridge