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### Generalization error for decision problems [article]

Eric B. Laber, Min Qian
2018 arXiv   pre-print
Define the estimated conditional CDF of U n given β n as follows F Un,n v β = P (b) n K B −1 ( β (b) n − β) 1 U (b) n ≤ v P (b) n K B −1 ( β (b) n − β) , subsequently define u n (β) = F −1 Un,n (1 − α/  ...  and Murphy, 2011; Hirano and Porter, 2012; Laber et al., 2014) .  ...

### Interpretable Dynamic Treatment Regimes [article]

Yichi Zhang, Eric B. Laber, Anastasios Tsiatis, Marie Davidian
2016 arXiv   pre-print
Laber, E. B., K. A. Linn, and L. A. Stefanski (2014). Interactive model building for Qlearning. Biometrika 101 (4), 831-847. Laber, E. B. and Y. Q. Zhao (2015).  ...  Laber, and M. Davidian (2013). Robust estimation of optimal dynamic treatment regimes for sequential treatment decisions. Biometrika 100 (3), 681-694. Zhang, Y., E. B. Laber, A. Tsiatis, and M.  ...  For any f ∈ F δ , we have f ∞ ≤ B and E f 2 ≤ B 2 δ. Thus, by Propositions 1 and 3, where c 2 is some constant that depends on B.  ...

### Interactive Q-Learning for Quantiles

Kristin A. Linn, Eric B. Laber, Leonard A. Stefanski
2017 Figshare
the main paper, the data are generated using the model X 1 ∼ Norm(1 2 , Σ), A 1 , A 2 ∼ Unif{−1, 1} 2 , H 1 = (1, X 1 ) , η H 1 ,A 1 = exp{ C 2 (H 1 γ 0 + A 1 H 1 γ 1 )}, ξ ∼ Norm(0 2 , I 2 ), X 2 = B  ...  The 2 × 2 matrix B A 1 equals The remaining parameters are γ 0 = (1, 0.5, 0) , γ 1 = (−1, −0.5, 0) , β 2,0 = (0.25, −1, 0.5) , and β 2,1 = (1, −0.5, −0.25) , which were chosen to ensure that the mean-optimal  ...

### A spatiotemporal recommendation engine for malaria control [article]

Qian Guan, Brian J. Reich, Eric B. Laber
2020 arXiv   pre-print
Laber et al. (2018) developed a spatiotemporal treatment allocation strategy to slow the spread of white nose syndrome in bats.  ...  We assume at each time t and each health zone l that η lt − η lt−1 = c 0 + b 0 A lt + (c 1 + b 1 A lt )η lt−1 + (c 2 + b 2 A lt ) 1 m l j∈I l η jt−1 + p k=1 β 1k X kl + p k=1 β 2k X kl A lt + lt , (2)  ...

### Thompson Sampling for Pursuit-Evasion Problems [article]

Zhen Li, Nicholas J. Meyer, Eric B. Laber, Robert Brigantic
2018 arXiv   pre-print
Let B L denote the set of distributions over L. A strategy, π E , is an infinite sequence of functions π E,t : dom S t → B L such that π E,t (S t ) has support only on the neighbors of E t .  ...  Similarly, let B L K denote the space of distributions over L K and define a strategy, π W , for the pursuers to be a sequence of maps π W,t : dom H t → B L K such that π W,t (H t ) has support only on  ...

### Comment

Qian Guan, Eric B. Laber, Brian J. Reich
2016 Journal of the American Statistical Association
For binary covariates (e.g., treatment indicators) we take b l (x l ) = x l β l ; for continuous covariates we model b l using M b-spline basis functions, , where ψ 1 , …, ψ M are a fixed b-splines basis  ...  Patients who achieved C and subsequently suffered disease progression (P), were given salvage treatment Z 2,2 ∈ {b 21 , b 22 }, using p(Z 2,2 = b 21 |L i ) = 0.2(L i < 100) + 0.85I(L i ≥ 100).  ...

### Note on Thompson sampling for large decision problems [article]

Tao Hu, Eric B. Laber, Zhen Li, Nick J. Meyer, Krishna Pacifici
2019 arXiv   pre-print
ACKNOWLEDGEMENTS Eric Laber acknowledges support from the National Science Foundation (DMS-1555141, DMS-1557733, DMS-1513579) and the National Institutes of Health (1R01 AA023187-01A1, P01 CA142538).  ...  ., 2011; Laber et al., 2016) , and adaptive management of natural resources wherein management decisions are adjusted over time according to current and forecasted resource availability (McCarthy et al  ...

### Using Decision Lists to Construct Interpretable and Parsimonious Treatment Regimes [article]

Yichi Zhang, Eric B. Laber, Anastasios Tsiatis, Marie Davidian
2015 arXiv   pre-print
., 2013; Laber et al., 2014; Taylor et al., 2014) .  ...  Then we code the observed values x 1j , . . . , x nj into indices b 1j , . . . , b nj according to which interval they fall.  ...

### An imputation method for estimating the learning curve in classification problems [article]

Eric B. Laber, Kerby Shedden, Yang Yang
2012 arXiv   pre-print
More specifically, using β * and p X (x) one could generate B training sets D (1) m , D (2) τ (m) ≈ 1 BN B b=1 (X,Y )∈D * π(X; β * ) · 1{X β (b) m ≤ κ} + (1 − π(X; β * )) · 1{X β (b) m > κ} ≈ 1 BN B b  ...  Using (4), the IMPINT estimator is given bŷ τ II (m) 1 BN B b=1 (X,Y )∈D * Y · 1{X β (b) m ≤ κ} + (1 − Y ) · 1{X β (b) m > κ} , (5) whereβ (b) m =β (b) m (D (b) m ) denotes the maximum likelihood estimator  ...

### Bayesian Nonparametric Policy Search with Application to Periodontal Recall Intervals [article]

Qian Guan, Brian J. Reich, Eric B. Laber, Dipankar Bandyopadhyay
2018 arXiv   pre-print
, Σ b ) , and 1 ∆ l (·) is the indicator function with a point mass at ∆ l .  ...  ., 012a,b; Zhao et al., 2012; Zhang et al., 2013; Zhao et al., 2015; Kosorok and Moodie, 2015; Guan et al., 2016; Zhou and Kosorok, 2017 ).  ...

### iqLearn: Interactive Q-Learning inR

Kristin A. Linn, Eric B. Laber, Leonard A. Stefanski
2015 Journal of Statistical Software
For a list of SMARTs that have finished or are in the field, see The Methodology Center At Pennsylvania State University (2012) and Eric Laber's current list Laber (2013) .  ...  Based on empirical experiments (see Laber et al., 2013) , we recommend choosing the empirical estimator by default, as not much is lost when the true density is normal.  ...

### Set-valued dynamic treatment regimes for competing outcomes

Eric B. Laber, Daniel J. Lizotte, Bradley Ferguson
2014 Biometrics
True preferences' must be expressible as convex combinations Patient preferences cannot change over time For simplicity, we consider the two-stage binary treatment setting, this is not essential (see Laber  ...

### Interactive Q-learning for Probabilities and Quantiles [article]

Kristin A. Linn, Eric B. Laber, Leonard A. Stefanski
2015 arXiv   pre-print
The 2 × 2 matrix B A 1 equals B A 1 =1 =   −0.1 −0.1 0.1 0.1   , B A 1 =−1 =   0.5, −0.1 −0.1 0.5   .  ...  If f (y * τ ) = y * τ , π QIQ 1,τ (h 1 ) = Γ(h 1 , y * τ ) is optimal as it attains the quantile y * τ . b. If f (y * τ ) < y * τ , lim δ↓0 Γ(h 1 , y * τ − δ) is optimal.  ...

### Set-valued dynamic treatment regimes for competing outcomes [article]

Eric B. Laber, Daniel J. Lizotte, Bradley Ferguson
2012 arXiv   pre-print
B.2 CATIE Note that at Phase 1 the regression estimators are non-regular, and that inference in this setting requires additional care as many standard methods are not valid .  ...  (b) Estimate the parameters indexing the working model for the stage-1 Q-function using least squares. That is, regressỸ on H 1 and A 1 using the working model to obtainβ 1 andψ 2 .  ...

### A Robust Method for Estimating Optimal Treatment Regimes

Baqun Zhang, Anastasios A. Tsiatis, Eric B. Laber, Marie Davidian
2012 Biometrics
M SM.I.P k0 is the MSMM method using (B.2)-(B.3) with polynomial of degree k0. M SM.AI.P k0 is the MSMM method using (B.4)-(B.5) with polynomial of degree k0.  ...  Thus, in this scenario, all MSMMs of this form are incorrectly specified.To implement the MSMM method using (B.2)-(B.3) and (B.4)-(B.5), we considered the sequence η j from -2 to 6 with step 0.05 and put  ...
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