Search for: All records

Deep Evidential Regression (DER) places a prior on the original Gaussian likelihood and treats learning as an evidence acquisition process to quantify uncertainty. For the validity of the evidence theory, DER requires specialized activation functions to ensure that the prior parameters remain non-negative. However, such constraints will trigger evidence contraction, causing sub-optimal performance. In this paper, we analyse DER theoretically, revealing the intrinsic limitations for sub-optimal performance: the non-negativity constraints on the Normal Inverse-Gamma (NIG) prior parameter trigger the evidence contraction under the specialized activation function, which hinders the optimization of DER performance. On this basis, we design a Non-saturating Uncertainty Regularization term, which effectively ensures that the performance is further optimized in the right direction. Experiments on real-world datasets show that our proposed approach improves the performance of DER while maintaining the ability to quantify uncertainty.

 

This paper introduces a library for cross-simulator comparison of reinforcement learning models in trafc signal control tasks. This library is developed to implement recent state-of-the-art reinforcement learning models with extensible interfaces and unifed crosssimulator evaluation metrics. It supports commonly-used simulators in trafc signal control tasks, including Simulation of Urban MObility(SUMO) and CityFlow, and multiple benchmark datasets for fair comparisons. We conducted experiments to validate our implementation of the models and to calibrate the simulators so that the experiments from one simulator could be referential to the other. Based on the validated models and calibrated environments, this paper compares and reports the performance of current state-of-theart RL algorithms across diferent datasets and simulators. This is the frst time that these methods have been compared fairly under the same datasets with diferent simulators. 

Gradient-based optimization algorithms can be studied from the perspective of limiting ordinary differential equations (ODEs). Motivated by the fact that existing ODEs do not distinguish between two fundamentally different algorithms—Nesterov’s accelerated gradient method for strongly convex functions (NAG-) and Polyak’s heavy-ball method—we study an alternative limiting process that yieldshigh-resolution ODEs. We show that these ODEs permit a general Lyapunov function framework for the analysis of convergence in both continuous and discrete time. We also show that these ODEs are more accurate surrogates for the underlying algorithms; in particular, they not only distinguish between NAG- and Polyak’s heavy-ball method, but they allow the identification of a term that we refer to as “gradient correction” that is present in NAG- but not in the heavy-ball method and is responsible for the qualitative difference in convergence of the two methods. We also use the high-resolution ODE framework to study Nesterov’s accelerated gradient method for (non-strongly) convex functions, uncovering a hitherto unknown result—that NAG- minimizes the squared gradient norm at an inverse cubic rate. Finally, by modifying the high-resolution ODE of NAG-, we obtain a family of new optimization methods that are shown to maintain the accelerated convergence rates of NAG- for smooth convex functions.

 

Patients' longitudinal biomarker changing patterns are crucial factors for their disease progression. In this research, we apply functional principal component analysis techniques to extract these changing patterns and use them as predictors in landmark models for dynamic prediction. The time‐varying effects of risk factors along a sequence of landmark times are smoothed by a supermodel to borrow information from neighbor time intervals. This results in more stable estimation and more clear demonstration of the time‐varying effects. Compared with the traditional landmark analysis, simulation studies show our proposed approach results in lower prediction error rates and higher area under receiver operating characteristic curve (AUC) values, which indicate better ability to discriminate between subjects with different risk levels. We apply our method to data from the Framingham Heart Study, using longitudinal total cholesterol (TC) levels to predict future coronary heart disease (CHD) risk profiles. Our approach not only obtains the overall trend of biomarker‐related risk profiles, but also reveals different risk patterns that are not available from the traditional landmark analyses. Our results show that high cholesterol levels during young ages are more harmful than those in old ages. This demonstrates the importance of analyzing the age‐dependent effects of TC on CHD risk.