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Part II: Practical Implementations. Modeling the Classes. Stochastic Discrimination. Algorithm for Training a SD Classifier. Generate projectable weak model. Evaluate model w.r.t. training set, check enrichment. Check uniformity w.r.t. existing collection. Add to discriminant.

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## Part II: Practical Implementations.

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**Modeling the Classes**Stochastic Discrimination**Algorithm for Training a SD Classifier**Generate projectable weak model Evaluate model w.r.t. training set, check enrichment Check uniformity w.r.t. existing collection Add to discriminant**2D Example**• Adapted from [Kleinberg, PAMI, May 2000]**An “r=1/2” random subset in the feature space that**covers ½ of all the points**Watch how many such subsets cover a particular point, say,**(2,17) (2,17)**Out**In In It’s in 1/2 models Y = ½ = 0.5 It’s in 2/3 models Y = 2/3 = 0.67 It’s in 0/1 models Y = 0/1 = 0.0 In In In It’s in 3/4 models Y = ¾ = 0.75 It’s in 4/5 models Y = 4/5 = 0.8 It’s in 5/6 models Y = 5/6 = 0.83**Out**In In It’s in 6/8 models Y = 6/8 = 0.75 It’s in 7/9 models Y = 7/9 = 0.77 It’s in 5/7 models Y = 5/7 = 0.72 In Out Out It’s in 8/10 models Y = 8/10 = 0.8 It’s in 8/11 models Y = 8/11 = 0.73 It’s in 8/12 models Y = 8/12 = 0.67**Fraction of “r=1/2” random subsets covering point (2,17)**as more such subsets are generated**Fractions of “r=1/2” random subsets covering several**selected points as more such subsets are generated**Distribution of model coverage for all points in space,**with 100 models**Distribution of model coverage for all points in space,**with 200 models**Distribution of model coverage for all points in space,**with 300 models**Distribution of model coverage for all points in space,**with 400 models**Distribution of model coverage for all points in space,**with 500 models**Distribution of model coverage for all points in space,**with 1000 models**Distribution of model coverage for all points in space,**with 2000 models**Distribution of model coverage for all points in space,**with 5000 models**Introducing enrichment:**For any discrimination to happen, the models must have some difference in coverage for different classes.**Class distribution**A biased (enriched) weak model • Enforcing enrichment (adding in a bias): require each subset to cover more points of one class than another**Distribution of model coverage for points in each class,**with 100 enriched weak models**Distribution of model coverage for points in each class,**with 200 enriched weak models**Distribution of model coverage for points in each class,**with 300 enriched weak models**Distribution of model coverage for points in each class,**with 400 enriched weak models**Distribution of model coverage for points in each class,**with 500 enriched weak models**Distribution of model coverage for points in each class,**with 1000 enriched weak models**Distribution of model coverage for points in each class,**with 2000 enriched weak models**Distribution of model coverage for points in each class,**with 5000 enriched weak models**Error rate decreases as number of models increases**Decision rule: if Y < 0.5 then class 2 else class 1**Training Set**Test Set • Sparse Training Data: Incomplete knowledge about class distributions**Distribution of model coverage for points in each class,**with 100 enriched weak models Training Set Test Set**Distribution of model coverage for points in each class,**with 200 enriched weak models Training Set Test Set**Distribution of model coverage for points in each class,**with 300 enriched weak models Training Set Test Set**Distribution of model coverage for points in each class,**with 400 enriched weak models Training Set Test Set**Distribution of model coverage for points in each class,**with 500 enriched weak models Training Set Test Set**Distribution of model coverage for points in each class,**with 1000 enriched weak models Training Set Test Set**Distribution of model coverage for points in each class,**with 2000 enriched weak models Training Set Test Set**No discrimination!**• Distribution of model coverage for points in each class, with 5000 enriched weak models Training Set Test Set**Models of this type, when enriched for training set, are not**necessarily enriched for test set Training Set Test Set Random model with 50% coverage of space**Introducing projectability:**Maintain local continuity of class interpretations. Neighboring points of the same class should share similar model coverage.**Class distribution**A projectable model • Allow some local continuity in model membership, so that interpretation of a training point can generalize to its immediate neighborhood**Distribution of model coverage for points in each class,**with 100 enriched, projectable weak models Training Set Test Set**Distribution of model coverage for points in each class,**with 300 enriched, projectable weak models Training Set Test Set**Distribution of model coverage for points in each class,**with 400 enriched, projectable weak models Training Set Test Set**Distribution of model coverage for points in each class,**with 500 enriched, projectable weak models Training Set Test Set**Distribution of model coverage for points in each class,**with 1000 enriched, projectable weak models Training Set Test Set**Distribution of model coverage for points in each class,**with 2000 enriched, projectable weak models Training Set Test Set**Distribution of model coverage for points in each class,**with 5000 enriched, projectable weak models Training Set Test Set**Promoting uniformity:**All points in the same class should have equal likelihood to be covered by a model of each particular rating. Retain models that cover the points whose coverage by current collection is less

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