The Annals of Statistics

Hierarchical testing designs for pattern recognition

Gilles Blanchard and Donald Geman

Full-text: Open access

Abstract

We explore the theoretical foundations of a “twenty questions” approach to pattern recognition. The object of the analysis is the computational process itself rather than probability distributions (Bayesian inference) or decision boundaries (statistical learning). Our formulation is motivated by applications to scene interpretation in which there are a great many possible explanations for the data, one (“background”) is statistically dominant, and it is imperative to restrict intensive computation to genuinely ambiguous regions.

The focus here is then on pattern filtering: Given a large set $\mathcal {Y}$ of possible patterns or explanations, narrow down the true one Y to a small (random) subset $\widehat{Y}\subset\mathcal{Y}$ of “detected” patterns to be subjected to further, more intense, processing. To this end, we consider a family of hypothesis tests for YA versus the nonspecific alternatives YAc. Each test has null type I error and the candidate sets $A\subset\mathcal{Y}$ are arranged in a hierarchy of nested partitions. These tests are then characterized by scope (|A|), power (or type II error) and algorithmic cost.

We consider sequential testing strategies in which decisions are made iteratively, based on past outcomes, about which test to perform next and when to stop testing. The set is then taken to be the set of patterns that have not been ruled out by the tests performed. The total cost of a strategy is the sum of the “testing cost” and the “postprocessing cost” (proportional to ||) and the corresponding optimization problem is analyzed. As might be expected, under mild assumptions good designs for sequential testing strategies exhibit a steady progression from broad scope coupled with low power to high power coupled with dedication to specific explanations. In the assumptions ensuring this property a key role is played by the ratio cost/power. These ideas are illustrated in the context of detecting rectangles amidst clutter.

Article information

Source
Ann. Statist., Volume 33, Number 3 (2005), 1155-1202.

Dates
First available in Project Euclid: 1 July 2005

Permanent link to this document
https://projecteuclid.org/euclid.aos/1120224099

Digital Object Identifier
doi:10.1214/009053605000000174

Mathematical Reviews number (MathSciNet)
MR2195632

Zentralblatt MATH identifier
1072.62052

Subjects
Primary: 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20] 62L05: Sequential design 68T10: Pattern recognition, speech recognition {For cluster analysis, see 62H30}
Secondary: 62H15: Hypothesis testing 68T45: Machine vision and scene understanding 90B40: Search theory

Keywords
Classification sequential hypothesis testing hierarchical designs coarse-to-fine search pattern recognition scene interpretation

Citation

Blanchard, Gilles; Geman, Donald. Hierarchical testing designs for pattern recognition. Ann. Statist. 33 (2005), no. 3, 1155--1202. doi:10.1214/009053605000000174. https://projecteuclid.org/euclid.aos/1120224099


Export citation

References

  • Amit, Y. (2002). 2D Object Detection and Recognition. MIT Press, Cambridge, MA.
  • Amit, Y. and Geman, D. (1999). A computational model for visual selection. Neural Computation 11 1691--1715.
  • Amit, Y., Geman, D. and Fan, X. (2004). A coarse-to-fine strategy for multiclass shape detection. IEEE Trans. Pattern Analysis and Machine Intelligence 26 1606--1621.
  • Bellman, R. (1961). Adaptive Control Processes: A Guided Tour. Princeton Univ. Press.
  • Blackwell, D. and Girschick, M. A. (1954). Theory of Games and Statistical Decisions. Wiley, New York.
  • Blanchard, G. and Geman, D. (2003). Hierarchical testing designs for pattern recognition. Technical Report 2003-07, Département de Mathématiques, Univ. de Paris-Sud.
  • Breiman, L., Friedman, J., Olshen, R. and Stone, C. (1984). Classification and Regression Trees. Wadsworth, Belmont, CA.
  • Chernoff, H. (1972). Sequential Analysis and Optimal Design. SIAM, Philadelphia.
  • Cootes, T. F. and Taylor, C. J. (1996). Locating faces using statistical feature detectors. In Proc. Second International Conference on Automatic Face and Gesture Recognition 204--209. IEEE Press, New York.
  • DeGroot, M. H. (1970). Optimal Statistical Decisions. McGraw--Hill, New York.
  • Desimone, R., Miller, E. K., Chelazzi, L. and Lueschow, A. (1995). Multiple memory systems in visual cortex. In The Cognitive Neurosciences (M. S. Gazzaniga, ed.) 475--486. MIT Press, Cambridge, MA.
  • Dietterich, T. (2000). The divide-and-conquer manifesto. In Proc. Eleventh International Conference on Algorithmic Learning Theory. Lecture Notes in Artificial Intelligence 1968 13--26. Springer, New York.
  • Fleuret, F. (2000). Détection hiérarchique de visages par apprentissage statistique. Ph.D. dissertation, Univ. Paris VI, Jussieu.
  • Fleuret, F. and Geman, D. (2001). Coarse-to-fine face detection. International J. Computer Vision 41 85--107.
  • Fritsch, J. and Finke, M. (1998). Applying divide and conquer to large scale pattern recognition tasks. Neural Networks: Tricks of the Trade. Lecture Notes in Comput. Sci. (G. B. Orr and K.-R. Müller, eds.) 1524 315--342. Springer, New York.
  • Garey, M. R. (1972). Optimal binary identification procedures. SIAM J. Appl. Math. 23 173--186.
  • Geman, D. and Jedynak, B. (2001). Model-based classification trees. IEEE Trans. Inform. Theory 47 1075--1082.
  • Geman, S., Bienenstock, E. and Doursat, R. (1992). Neural networks and the bias/variance dilemma. Neural Computation 4 1--58.
  • Geman, S., Manbeck, K. and McClure, D. (1995). Coarse-to-fine search and rank-sum statistics in object recognition. Technical report, Div. Applied Mathematics, Brown Univ.
  • Jung, F. (2001). Reconnaissance d'objets par focalisation et detection de changements. Ph.D. dissertation, Ecole Polytechnique, Paris.
  • Jung, F. (2002). Detecting new buildings from time-varying aerial stereo pairs. Technical report, IGN.
  • Osuna, E., Freund, R. and Girosit, F. (1997). Training support vector machines: An application to face detection. In Proc. Computer Vision and Pattern Recognition 130--136. IEEE Press, New York.
  • Puterman, M. (1994). Markov Decision Processes. Wiley, New York.
  • Rowley, H. A., Baluja, S. and Kanade, T. (1998). Neural network-based face detection. IEEE Trans. Pattern Analysis and Machine Intelligence 20 23--38.
  • Socolinsky, D. A., Neuheisel, J. D., Priebe, C. E., De Vinney, J. and Marchette, D. (2002). Fast face detection with a boosted cccd classifier. Technical report, Johns Hopkins Univ.
  • Sung, K.-K. and Poggio, T. (1998). Example-based learning for view-based human face detection. IEEE Trans. Pattern Analysis and Machine Intelligence 20 39--51.
  • Thorpe, S., Fize, D. and Marlot, C. (1996). Speed of processing in the human visual system. Nature 381 520--522.
  • Trouvé, A. and Yu, Y. (2002). Entropy reduction strategies on tree structured retrieval spaces. In Proc. Colloquium on Mathematics and Computer Science. II. Algorithms, Trees, Combinatorics and Probabilities (B. Chauvin, P. Flajolet, D. Gardy and A. Mokkadem, eds.) 513--525. Birkhäuser, Basel.
  • Viola, P. and Jones, M. J. (2001). Robust real-time face detection. In Proc. Eighth IEEE International Conference on Computer Vision 2 747. IEEE Press, New York.
  • Yuille, A. L., Hallinan, P. and Cohen, D. S. (1992). Feature extraction from faces using deformable templates. International J. Computer Vision 8 99--111.