TY  - JOUR
A1  - Cvetković, Nada
A1  - Conrad, Tim
A1  - Lie, Han Cheng
T1  - A convergent discretization method for transition path theory for diffusion processes
JF  - Multiscale modeling & simulation : a SIAM interdisciplinary journal
N2  - Transition path theory (TPT) for diffusion processes is a framework for analyzing the transitions of multiscale ergodic diffusion processes between disjoint metastable subsets of state space. Most methods for applying TPT involve the construction of a Markov state model on a discretization of state space that approximates the underlying diffusion process. However, the assumption of Markovianity is difficult to verify in practice, and there are to date no known error bounds or convergence results for these methods. We propose a Monte Carlo method for approximating the forward committor, probability current, and streamlines from TPT for diffusion processes. Our method uses only sample trajectory data and partitions of state space based on Voronoi tessellations. It does not require the construction of a Markovian approximating process. We rigorously prove error bounds for the approximate TPT objects and use these bounds to show convergence to their exact counterparts in the limit of arbitrarily fine discretization. We illustrate some features of our method by application to a process that solves the Smoluchowski equation on a triple-well potential.
KW  - ergodic diffusion processes
KW  - transition paths
KW  - rare events
KW  - Monte Carlo
KW  - methods
Y1  - 2021
U6  - https://doi.org/10.1137/20M1329354
SN  - 1540-3459
SN  - 1540-3467
VL  - 19
IS  - 1
SP  - 242
EP  - 266
PB  - Society for Industrial and Applied Mathematics
CY  - Philadelphia
ER  - 
TY  - JOUR
A1  - Freitas da Cruz, Harry
A1  - Pfahringer, Boris
A1  - Martensen, Tom
A1  - Schneider, Frederic
A1  - Meyer, Alexander
A1  - Böttinger, Erwin
A1  - Schapranow, Matthieu-Patrick
T1  - Using interpretability approaches to update "black-box" clinical prediction models
BT  - an external validation study in nephrology
JF  - Artificial intelligence in medicine : AIM
N2  - Despite advances in machine learning-based clinical prediction models, only few of such models are actually deployed in clinical contexts. Among other reasons, this is due to a lack of validation studies. In this paper, we present and discuss the validation results of a machine learning model for the prediction of acute kidney injury in cardiac surgery patients initially developed on the MIMIC-III dataset when applied to an external cohort of an American research hospital. To help account for the performance differences observed, we utilized interpretability methods based on feature importance, which allowed experts to scrutinize model behavior both at the global and local level, making it possible to gain further insights into why it did not behave as expected on the validation cohort. The knowledge gleaned upon derivation can be potentially useful to assist model update during validation for more generalizable and simpler models. We argue that interpretability methods should be considered by practitioners as a further tool to help explain performance differences and inform model update in validation studies.
KW  - Clinical predictive modeling
KW  - Nephrology
KW  - Validation
KW  - Interpretability
KW  - methods
Y1  - 2021
U6  - https://doi.org/10.1016/j.artmed.2020.101982
SN  - 0933-3657
SN  - 1873-2860
VL  - 111
PB  - Elsevier
CY  - Amsterdam
ER  -