Binomial early stopping times

2021 ◽  
pp. 1-17
Author(s):  
Nick Mulgan
Keyword(s):  
Stopping Times ◽  
Early Stopping

scholarly journals Cardiovascular consequences of discontinuing low-dose rivaroxaban in people with chronic coronary or peripheral artery disease

Heart ◽  
2021 ◽  
pp. heartjnl-2020-318758
Author(s):  
Gilles R Dagenais ◽  
Leanne Dyal ◽  
Jacqueline J Bosch ◽  
Darryl P Leong ◽  
Victor Aboyans ◽  
...  
Keyword(s):  
Peripheral Artery Disease ◽  
Low Dose ◽  
Cardiovascular Death ◽  
Stroke Rate ◽  
Early Stopping ◽  
Peripheral Artery ◽  
Once Daily ◽  
Registration Number ◽  
Artery Disease

ObjectiveIn patients with chronic coronary or peripheral artery disease enrolled in the Cardiovascular Outcomes for People Using Anticoagulation Strategies trial, randomised antithrombotic treatments were stopped after a median follow-up of 23 months because of benefits of the combination of rivaroxaban 2.5 mg two times per day and aspirin 100 mg once daily compared with aspirin 100 mg once daily. We assessed the effect of switching to non-study aspirin at the time of early stopping.MethodsIncident composite of myocardial infarction, stroke or cardiovascular death was estimated per 100 person-years (py) during randomised treatment (n=18 278) and after study treatment discontinuation to non-study aspirin (n=14 068).ResultsDuring randomised treatment, the combination compared with aspirin reduced the composite (2.2 vs 2.9/100 py, HR: 0.76, 95% CI 0.66 to 0.86), stroke (0.5 vs 0.8/100 py, HR: 0.58, 95% CI 0.44 to 0.76) and cardiovascular death (0.9 vs 1.2/100 py, HR: 0.78, 95% CI 0.64 to 0.96). During 1.02 years after early stopping, participants originally randomised to the combination compared with those randomised to aspirin had similar rates of the composite (2.1 vs 2.0/100 py, HR: 1.08, 95% CI 0.84 to 1.39) and cardiovascular death (1.0 vs 0.8/100 py, HR: 1.26, 95% CI 0.85 to 1.86) but higher stroke rate (0.7 vs 0.4/100 py, HR: 1.74, 95% CI 1.05 to 2.87) including a significant increase in ischaemic stroke during the first 6 months after switching to non-study aspirin.ConclusionDiscontinuing study rivaroxaban and aspirin to non-study aspirin was associated with the loss of cardiovascular benefits and a stroke excess.Trial registration numberNCT01776424.

scholarly journals Quit When You Can: Efficient Evaluation of Ensembles by Optimized Ordering

2021 ◽  
Vol 17 (4) ◽  
pp. 1-20
Author(s):  
Serena Wang ◽  
Maya Gupta ◽  
Seungil You
Keyword(s):  
Optimization Problem ◽  
Optimal Solution ◽  
Combinatorial Optimization Problem ◽  
Joint Optimization ◽  
Early Stopping ◽  
Time Approximation ◽  
Approximation Bound ◽  
Evaluation Time ◽  
Speed Up ◽  
Real World Problems

Given a classifier ensemble and a dataset, many examples may be confidently and accurately classified after only a subset of the base models in the ensemble is evaluated. Dynamically deciding to classify early can reduce both mean latency and CPU without harming the accuracy of the original ensemble. To achieve such gains, we propose jointly optimizing the evaluation order of the base models and early-stopping thresholds. Our proposed objective is a combinatorial optimization problem, but we provide a greedy algorithm that achieves a 4-approximation of the optimal solution under certain assumptions, which is also the best achievable polynomial-time approximation bound. Experiments on benchmark and real-world problems show that the proposed Quit When You Can (QWYC) algorithm can speed up average evaluation time by 1.8–2.7 times on even jointly trained ensembles, which are more difficult to speed up than independently or sequentially trained ensembles. QWYC’s joint optimization of ordering and thresholds also performed better in experiments than previous fixed orderings, including gradient boosted trees’ ordering.

scholarly journals Pricing Perpetual American Put Options with Asset-Dependent Discounting

2021 ◽  
Vol 14 (3) ◽  
pp. 130
Author(s):  
Jonas Al-Hadad ◽  
Zbigniew Palmowski
Keyword(s):  
Value Function ◽  
Asset Price ◽  
Stopping Times ◽  
Martingale Measure ◽  
Put Options ◽  
American Put Options ◽  
Exact Calculations ◽  
Negative Exponential ◽  
American Put ◽  
The Value Function

The main objective of this paper is to present an algorithm of pricing perpetual American put options with asset-dependent discounting. The value function of such an instrument can be described as VAPutω(s)=supτ∈TEs[e−∫0τω(Sw)dw(K−Sτ)+], where T is a family of stopping times, ω is a discount function and E is an expectation taken with respect to a martingale measure. Moreover, we assume that the asset price process St is a geometric Lévy process with negative exponential jumps, i.e., St=seζt+σBt−∑i=1NtYi. The asset-dependent discounting is reflected in the ω function, so this approach is a generalisation of the classic case when ω is constant. It turns out that under certain conditions on the ω function, the value function VAPutω(s) is convex and can be represented in a closed form. We provide an option pricing algorithm in this scenario and we present exact calculations for the particular choices of ω such that VAPutω(s) takes a simplified form.

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