Cost-sensitive Dynamic Feature Selection
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1 Cost-sensitive Dynamic Feature Selection He He 1, Hal Daumé III 1 and Jason Eisner 2 1 University of Maryland, College Park 2 Johns Hopkins University June 30, 2012 He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
2 Dynamic Feature Selection Feature selection in real life is a sequential decision-making process. He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
3 Dynamic Feature Selection Feature selection in real life is a sequential decision-making process. Observation cost Decision coughing free cold flu H1N1 sore throat free cold flu H1N1 headache free cold flu H1N1 He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
4 Dynamic Feature Selection Feature selection in real life is a sequential decision-making process. Observation cost Decision coughing free cold flu H1N1 sore throat free cold flu H1N1 headache free cold flu H1N1 temperature (101 ) $1 cold flu H1N1 nasal swab test (pos.) $10 cold flu H1N1 viral culture test (pos.) $50 cold flu H1N1 molecular test (pos.) $100 cold flu H1N1 blood test (pos.) $100 cold flu H1N1 He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
5 Dynamic Feature Selection Feature selection in real life is a sequential decision-making process. Observation cost Decision coughing free cold flu H1N1 sore throat free cold flu H1N1 headache free cold flu H1N1 temperature (101 ) $1 cold flu H1N1 nasal swab test (pos.) $10 cold flu H1N1 viral culture test (pos.) $50 cold flu H1N1 molecular test (pos.) $100 cold flu H1N1 blood test (pos.) $100 cold flu H1N1 He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
6 Dynamic Feature Selection Feature selection in real life is a sequential decision-making process. Observation cost Decision coughing free cold flu H1N1 sore throat free cold flu H1N1 headache free cold flu H1N1 temperature (101 ) $1 cold flu H1N1 nasal swab test (neg.) $10 cold flu H1N1 He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
7 Dynamic Feature Selection Feature selection in real life is a sequential decision-making process. Observation cost Decision coughing free cold flu H1N1 sore throat free cold flu H1N1 headache free cold flu H1N1 temperature (101 ) $1 cold flu H1N1 nasal swab test (neg.) $10 cold flu H1N1 viral culture test (pos.) $50 cold flu H1N1 molecular test (pos.) $100 cold flu H1N1 blood test (pos.) $100 cold flu H1N1 He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
8 Cost-sensitive Dynamic Feature Selection Feature Cost Computation time Data acquisition expense Dynamic Selection Based on previous selected features and their values Compute features on-the-run Given a pretrained classifier and feature cost, Goal Sequentially select features for each instance at test time Achieve a user-specified accuracy-cost trade-off He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
9 Dynamic Feature Selection as an MDP He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
10 Dynamic Feature Selection as an MDP At time step t, for one example, State s t Selected features and their values Action a t A t Acquire some features or stop Policy π Map from state to action: π(s t ) = a t Reward r r(s t, a t ) = margin(s t, a t ) λ cost(s t, a t ) margin: score of the true class - highest score of other classes λ: trade-off parameter He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
11 Imitation Learning Oracle Demonstrate optimal actions π (s) = at Agent Learn a policy to mimic the oracle s behavior π(s t ) = a t Imitation via Supervised Classification Training examples {(φ(s π ), π (s))} Feature: φ(s) label: π (s) classifier: ˆπ Minimize a surrogate loss l(s, π) w.r.t. to π, e.g. hinge loss in SVM. He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
12 Forward Selection Oracle Select the feature that yields the maximum immediate reward He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
13 Forward Selection Oracle Select the feature that yields the maximum immediate reward r(s t, a t ) = margin(s t, a t ) cost(s t, a t ) λ = 1, cost scaled to [0, 1], H1N1=positive order feat. marg. cost reward 1 coughing, sore throat, headache He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
14 Forward Selection Oracle Select the feature that yields the maximum immediate reward r(s t, a t ) = margin(s t, a t ) cost(s t, a t ) λ = 1, cost scaled to [0, 1], H1N1=positive order feat. marg. cost reward 1 coughing, sore throat, headache temperature nasal swab test viral culture test molecular test blood test He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
15 Forward Selection Oracle Select the feature that yields the maximum immediate reward r(s t, a t ) = margin(s t, a t ) cost(s t, a t ) λ = 1, cost scaled to [0, 1], H1N1=positive order feat. marg. cost reward 1 coughing, sore throat, headache temperature (101 ) nasal swab test viral culture test molecular test blood test He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
16 Forward Selection Oracle Select the feature that yields the maximum immediate reward r(s t, a t ) = margin(s t, a t ) cost(s t, a t ) λ = 1, cost scaled to [0, 1], H1N1=positive order feat. marg. cost reward 1 coughing, sore throat, headache temperature nasal swab test (pos.) viral culture test molecular test blood test He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
17 Forward Selection Oracle Select the feature that yields the maximum immediate reward r(s t, a t ) = margin(s t, a t ) cost(s t, a t ) λ = 1, cost scaled to [0, 1], H1N1=positive order feat. marg. cost reward 1 coughing, sore throat, headache temperature nasal swab test viral culture test (pos.) molecular test blood test He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
18 Forward Selection Oracle Select the feature that yields the maximum immediate reward r(s t, a t ) = margin(s t, a t ) cost(s t, a t ) λ = 1, cost scaled to [0, 1], H1N1=positive order feat. marg. cost reward 1 coughing, sore throat, headache temperature nasal swab test viral culture test molecular test (pos.) blood test He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
19 Forward Selection Oracle Select the feature that yields the maximum immediate reward r(s t, a t ) = margin(s t, a t ) cost(s t, a t ) λ = 1, cost scaled to [0, 1], H1N1=positive order feat. marg. cost reward 1 coughing, sore throat, headache temperature nasal swab test viral culture test molecular test blood test (pos.) He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
20 Forward Selection Oracle Select the feature that yields the maximum immediate reward r(s t, a t ) = margin(s t, a t ) cost(s t, a t ) λ = 1, cost scaled to [0, 1], H1N1=positive order feat. marg. cost reward 1 coughing, sore throat, headache temperature 2 nasal swab test (pos.) viral culture test molecular test blood test He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
21 Forward Selection Oracle Select the feature that yields the maximum immediate reward r(s t, a t ) = margin(s t, a t ) cost(s t, a t ) λ = 1, cost scaled to [0, 1], H1N1=positive order feat. marg. cost reward 1 coughing, sore throat, headache temperature (101 ) nasal swab test (pos.) viral culture test molecular test blood test He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
22 Forward Selection Oracle Select the feature that yields the maximum immediate reward r(s t, a t ) = margin(s t, a t ) cost(s t, a t ) λ = 1, cost scaled to [0, 1], H1N1=positive order feat. marg. cost reward 1 coughing, sore throat, headache temperature (101 ) nasal swab test (pos.) viral culture test (pos.) molecular test blood test He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
23 Forward Selection Oracle Select the feature that yields the maximum immediate reward r(s t, a t ) = margin(s t, a t ) cost(s t, a t ) λ = 1, cost scaled to [0, 1], H1N1=positive order feat. marg. cost reward 1 coughing, sore throat, headache temperature (101 ) nasal swab test (pos.) viral culture test (pos.) molecular test 5 blood test (pos.) He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
24 Forward Selection Oracle Select the feature that yields the maximum immediate reward r(s t, a t ) = margin(s t, a t ) cost(s t, a t ) λ = 1, cost scaled to [0, 1], H1N1=positive order feat. marg. cost reward 1 coughing, sore throat, headache temperature (101 ) nasal swab test (pos.) viral culture test (pos.) molecular test (pos.) blood test (pos.) He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
25 Forward Selection Oracle Select the feature that yields the maximum immediate reward Stop in the global maximum-reward state free nasal swab test temperature viral culture test stop r(s t, a t ) = margin(s t, a t ) cost(s t, a t ) λ = 1, cost scaled to [0, 1], H1N1=positive order feat. marg. cost reward 1 coughing, sore throat, headache temperature (101 ) nasal swab test (pos.) viral culture test (pos.) molecular test (pos.) blood test (pos.) He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
26 Forward Selection Oracle Select the feature that yields the maximum immediate reward Stop in the global maximum-reward state free nasal swab test temperature viral culture test stop Have access to the ground truth, only available during training r(s t, a t ) = margin(s t, a t ) cost(s t, a t ) λ = 1, cost scaled to [0, 1], H1N1=positive order feat. marg. cost reward 1 coughing, sore throat, headache temperature (101 ) nasal swab test (pos.) viral culture test (pos.) molecular test (pos.) blood test (pos.) He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
27 Policy Features At step 2, compute φ(s 2 ) feat. cold flu H1N1 cost free swab He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
28 Policy Features selected features e.g. free = coughing, sore throat, headache; nasal swab test = pos. At step 2, compute φ(s 2 ) feat. cold flu H1N1 cost free swab He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
29 Policy Features selected features e.g. free = coughing, sore throat, headache; nasal swab test = pos. confidence score and its change e.g. 0.04, 0.23, 0.73; 0.16, 0.27, 0.43 At step 2, compute φ(s 2 ) feat. cold flu H1N1 cost free swab He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
30 Policy Features selected features e.g. free = coughing, sore throat, headache; nasal swab test = pos. confidence score and its change e.g. 0.04, 0.23, 0.73; 0.16, 0.27, 0.43 Does the guess change? e.g. Yes At step 2, compute φ(s 2 ) feat. cold flu H1N1 cost free swab He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
31 Policy Features selected features e.g. free = coughing, sore throat, headache; nasal swab test = pos. confidence score and its change e.g. 0.04, 0.23, 0.73; 0.16, 0.27, 0.43 Does the guess change? e.g. Yes cost and its change e.g. 0.04; 0.04 At step 2, compute φ(s 2 ) feat. cold flu H1N1 cost free swab He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
32 Policy Features selected features e.g. free = coughing, sore throat, headache; nasal swab test = pos. confidence score and its change e.g. 0.04, 0.23, 0.73; 0.16, 0.27, 0.43 Does the guess change? e.g. Yes cost and its change e.g. 0.04; 0.04 cost divided by confidence score e.g. 1.00, 5.75, At step 2, compute φ(s 2 ) feat. cold flu H1N1 cost free swab He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
33 Policy Features selected features e.g. free = coughing, sore throat, headache; nasal swab test = pos. confidence score and its change e.g. 0.04, 0.23, 0.73; 0.16, 0.27, 0.43 Does the guess change? e.g. Yes cost and its change e.g. 0.04; 0.04 cost divided by confidence score e.g. 1.00, 5.75, current guess e.g. H1N1 At step 2, compute φ(s 2 ) feat. cold flu H1N1 cost free swab He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
34 Imitation Learning via Classification s π : states visited by π T : task horizon J(π): task loss (negative reward) of π Theorem Ross & Bagnell (2010) Let E sπ [l(s, π)] = ɛ, then J(π) J(π ) + T 2 ɛ. He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
35 Imitation Learning via Classification s π : states visited by π T : task horizon J(π): task loss (negative reward) of π Theorem Ross & Bagnell (2010) Let E sπ [l(s, π)] = ɛ, then J(π) J(π ) + T 2 ɛ. Why do we have quadratically increasing loss? He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
36 Imitation Learning via Classification s π : states visited by π T : task horizon J(π): task loss (negative reward) of π Theorem Ross & Bagnell (2010) Let E sπ [l(s, π)] = ɛ, then J(π) J(π ) + T 2 ɛ. Why do we have quadratically increasing loss? Trains only under states the oracle visited Ignores the difference between the oracle s and the agent s state distribution He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
37 Dataset Aggregation (DAgger) (Ross et al. (2011)) Let π 1 = π. In iteration i, execute policy π i and collect dataset D i = {(φ(s πi ), π (s))}; learn π i+1 from the aggregated dataset D 1 D2 Di. Return the best policy evaluated on validation set. He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
38 Dataset Aggregation (DAgger) (Ross et al. (2011)) Let π 1 = π. In iteration i, execute policy π i and collect dataset D i = {(φ(s πi ), π (s))}; learn π i+1 from the aggregated dataset D 1 D2 Di. Return the best policy evaluated on validation set. Qt π (s, π): t-step cost of executing π initially then running π 1 ɛ N = min N π Π N i=1 E s πi [l(s, π)] Theorem Ross et al. (2011) For DAgger, if QT π t+1 (s, π) Qπ T t+1 (s, π ) u and N is Õ(uT ), there is a policy π π 1:N s.t. J(π) J(π ) + ut ɛ N + O(1). He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
39 Coaching The oracle s policy can be too good to learn! Far from the agent s learning space Policy features are insufficient He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
40 Coaching The oracle s policy can be too good to learn! Far from the agent s learning space use kernels Policy features are insufficient more descriptive features He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
41 Coaching The oracle s policy can be too good to learn! Far from the agent s learning space use kernels Overhead! Policy features are insufficient more descriptive features He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
42 Coaching The oracle s policy can be too good to learn! Far from the agent s learning space use kernels Overhead! Policy features are insufficient more descriptive features Hope action (McAllester et al. (2010); Chiang et al. (2009)) Combines the current policy s preference and the reward: ã t = arg max a A t η score πi (a) + r(s t, a) instead of a t = arg max a A t r(s t, a) He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
43 Experimental Results Baselines ( w /cost, Forward): add feature statically from a ranked list Trade-off: λ = (0, 0.1, 0.25, 0.5, 1, 1.5, 2) Coaching: initialize η to 1 and decrease by e 1 in each iteration accuracy w /cost 0.70 Forward DAgger 0.65 Coaching Oracle average cost per example Figure: Radar (binary). He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
44 Experimental Results accuracy w /cost Forward 0.5 DAgger Coaching Oracle average cost per example 1.0 Figure: Digit (10 classes). accuracy w /cost 0.70 Forward DAgger 0.65 Coaching Oracle average cost per example 1.0 Figure: Segmentation (7 classes). He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
45 Conclusion and Future Work Conclusion Feature selection as an MDP Imitation learning techniques Iterative policy training Coaching as a local update method Future Work Include feature dependency using feature templates Learn feature weights jointly with the policy Apply to ensemble learning (select model dynamically) Structured prediction problem where policy features might require inference under features selected so far feature cost may need to be inferred at runtime He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
46 Bibliography Chiang, David, Knight, Kevin, and Wang, Wei. 11,001 new features for statistical machine translation. In NAACL-HLT, McAllester, D., Hazan, T., and Keshet, J. Direct loss minimization for structured prediction. In NIPS, Ross, Stéphane and Bagnell, J. Andrew. Efficient reductions for imitation learning. In AISTATS, Ross, Stéphane., Gordon, Geoffrey J., and Bagnell, J. Andrew. A reduction of imitation learning and structured prediction to no-regret online learning. In AISTATS, He He, Hal Daumé III and Jason Eisner Cost-sensitive Dynamic Feature Selection June 30, / 14
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