We present a new methodology to answer these questions. The methodology comprises modeling between-study disagreement, capturing nonlinear dose-response relationships, detecting outliers, and accounting for nonlinear observation mechanisms inherent in how studies report results. It is now used to analyze more than 470 risk-outcome pairs in the Global Burden of Disease study, conducted by IHME and collaborators. We present the main model, highlight the role of optimization, and include recent results for select risk-outcome pairs of interest.

We also extend this algorithm to address clustering problems (a class of unsupervised learning). Preliminary numerical results have demonstrated that our algorithm is able to solve problems with hundreds of samples to global optimality within a reasonable amount of time, while state-of-the-art global solvers can only deal with tens of samples. Moreover, global optimization can significantly improve performance on several datasets compared with local optimal algorithms, such as k-means.

In this talk, we present robust statistical methods to identify two different knee-points in capacity degradation data of Li-ion cells. Following this identification step, we show how machine learning algorithms can be employed to successfully predict the occurrence of these knee-points from the first few discharge cycles of a cell's life. We rely on feature engineering to overcome the challenge of working with a very small, yet high-dimensional data set and we quantify the uncertainty of the predictions to build trust in our models.

We use machine learning Neural Network techniques to build independent capacity and IR predictor models achieving a MAPE of 0.4\% and 1.6\%, respectively. We then use the IR model to synthesize internal resistance data to complete the dataset from Attia et al 2020 for which no IR data was logged.

We present a CT reconstruction approach which unrolls a standard iterative algorithm and trains it end-to-end as a DNN. The DNN consists of fixed layers, corresponding to the basic iterative algorithm, as well as trainable layers, which have the effect of perturbing the solution between iterations. The trainable layers can be viewed as replacing the negative gradient of an unknown penalty function or regularizer, which can vary with the iteration number. In numerical experiments, we test the approach on sparse-view and limited-angle CT problems, and study the effect of network architecture on the effectiveness of the algorithm. The proposed method provides significant improvement over the basic iterative algorithm, as well as total variation minimization approach. Joint work with Yiran Jia, Noah McMichael, Pedro Mokarzel, and Dong Si (UW Bothell).

Abstract: An ecological threshold occurs at a point along an environmental stress gradient at which there is a discontinuous change in the conditional distribution of a biological response. Traditionally, ecological thresholds are estimated from the discontinuities in the central tendency (e.g., slope) using a piecewise linear regression model (PLRM). However, thresholds can also be manifested as changes in the range of natural variation (e.g., conditional variance) for a given level of the environmental stress. In this paper, we defined a Bayesian PLRM by incorporating experts’ knowledge about the relationships between the biological response relative to environmental stress represented via prior distributions. The posterior distributions of the thresholds are obtained by combining the information in the data with experts’ prior knowledge, and optimized via Gibbs sampling and the Metropolis algorithm. We applied our method to two datasets relating an index of the health of marsh-nesting bird communities to habitat alteration (areal extent of land development adjacent to wetlands) within the Detroit River Area of Concern. Our preliminary analysis identified two potential thresholds - one manifested via the change in slope and the other observed from increased variance across the environmental stress gradient.

To fill in this gap, we formulate the problem of clinical trial design into an optimization problem involving high-dimensional integration, and propose a novel computational solution based on Monte-Carlo and smoothing methods. Our method utilizes the modern techniques of General-Purpose computing on Graphics Processing Units for large-scale parallel computing. Compared to a published method in three-dimensional problems, our approach is more accurate and 133 times faster. This advantage increases when dimensionality increases. Our method is scalable to higher-dimensional problems since the precision bound of our estimated study power is a finite number not affected by dimensionality.