anytime algorithms for learning anytime classifiers saher ... - Technion

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Technion - Computer Science Department - Ph.D. Thesis PHD-2008-12 - 2008 e. For the scenarios where ρ l or ρ c are unknown, we assume two binary functions f l () and f c (), which can be queried by the learner and the classifier respectively to find our whether their resources have been exhausted. In this work we propose a novel framework that can be applied in the following constraint combinations: • Contract learning, unlimited classification (CLUC): the learner is aware of ρ l . The classifier is not limited in the resources it can use (ρ c = ∞). If the environment does not involve test costs (AC = 0) and the misclassification costs are uniform (M = M U , a matrix with zeros on the main diagonal and ones elsewhere) the objective of the resulted classifier is to maximize accuracy. Formally, CLUC(E, A, 0, M U , ρ l , ∞) → h(e). In the more general case, where test costs exist and misclassification costs may vary, the goal is to learn a classifier that minimizes the total cost of classification. Formally, CLUC(E, A, AC, M, ρ l , ∞) → h(e). • Interruptible learning, unlimited classification (ILUC): similar to CLUC but the learning time is not preallocated. Formally, ILUC(E, A, 0, M U , f l (), ∞) → h(e) in the cost-insenstive case, and ILUC(E, A, AC, M, f l (), ∞) → h(e) in the cost-sensitive case. • Contract learning, pre-contract classification (CLPC): the learner is aware of both ρ l and ρ c . It produces a classifier that uses at most ρ c (the classifier does not benefit from any remaining surplus). Formally, CLPC(E, A, AC, M, ρ l , ρ c ) → h(e). • Interruptible learning, pre-contract classification (ILPC): similar to CLPC but the learning time is not preallocated. Formally, ILPC(E, A, AC, M, f l (), ρ c ) → h(e). • Contract learning, contract classification (CLCC): the learner is aware of ρ l but not of ρ c , which becomes available right before classification. The learner must produce a classifier that can operate under different cost constraints. The produced classifier should be act according to the provided ρ c . Formally, CLCC(E, A, AC, M, ρ l ) → h(e, ρ c ). • Interruptible learning, contract classification (ILCC): similar to CLCC but the learning time is not predetermined. Formally, ILCC(E, A, AC, M, f l ()) → h(e, ρ c ). • Contract learning, interruptible classification (CLIC): the learner is aware of ρ l . Neither the learner nor the classifier are provided with ρ c . The learner must produce a classifier that utilizes the available resources until 16
Technion - Computer Science Department - Ph.D. Thesis PHD-2008-12 - 2008 interrupted and queried for a solution. Formally, CLIC(E, A, AC, M, ρ l ) → h(e, f c ()). • Interruptible learning, interruptible classification (ILIC): similar to CLIC but the learning time is unknown. Formally, ILIC(E, A, AC, M, f l (), ρ c ) → h(e, f c ()). In Chapter 3 we present LSID3, a contract algorithm for learning classifiers that aim to maximize accuracy, without bounds on testing costs: LSID3(E, A, 0, M U , ρ l , ∞) → h(e). Next, we introduce IIDT, a general method to convert our contract learners into interruptible ones, and instantiate it for LSID3. Chapter 4 presents ACT, a contract algorithm for inducing trees that aim to minimize the total cost of classification without bounds on their classification budget: ACT(E, A, AC, M, ρ l , ∞) → h(e). ACT can be converted into an interruptible learner using the IIDT procedure. In Chapter 5 we introduce TATA, a framework for learning resource-bounded classifiers. TATA can operate when the testing budget is known to the learner (Pre-contract-TATA(E, A, AC, M, ρ l , ρ c ) → h(e)), when it is known to the classifier but not to the learner (Contract-TATA(E, A, AC, M, ρ l ) → h(e, ρ c )), and when it is not predetermined (Interruptible-TATA(E, A, AC, M, ρ l ) → h(e, f c ())). We also explain how to adapt these algorithms for interruptible learning scenarios. 17
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