Doubly Optimized Calibrated Support Vector Machine (DOC-SVM): an algorithm for joint optimization of discrimination and calibration.

Historically, probabilistic models for decision support have focused on discrimination, e.g., minimizing the ranking error of predicted outcomes. Unfortunately, these models ignore another important aspect, calibration, which indicates the magnitude of correctness of model predictions. Using discrimination and calibration simultaneously can be helpful for many clinical decisions. We investigated tradeoffs between these goals, and developed a unified maximum-margin method to handle them jointly. Our approach called, Doubly Optimized Calibrated Support Vector Machine (DOC-SVM), concurrently optimizes two loss functions: the ridge regression loss and the hinge loss. Experiments using three breast cancer gene-expression datasets (i.e., GSE2034, GSE2990, and Chanrion's datasets) showed that our model generated more calibrated outputs when compared to other state-of-the-art models like Support Vector Machine (p=0.03, p=0.13, and p<0.001) and Logistic Regression (p=0.006, p=0.008, and p<0.001). DOC-SVM also demonstrated better discrimination (i.e., higher AUCs) when compared to Support Vector Machine (p=0.38, p=0.29, and p=0.047) and Logistic Regression (p=0.38, p=0.04, and p<0.0001). DOC-SVM produced a model that was better calibrated without sacrificing discrimination, and hence may be helpful in clinical decision making

Performance and Optimization Abstractions for Large Scale Heterogeneous Systems in the Cactus/Chemora Framework

We describe a set of lower-level abstractions to improve performance on modern large scale heterogeneous systems. These provide portable access to system- and hardware-dependent features, automatically apply dynamic optimizations at run time, and target stencil-based codes used in finite differencing, finite volume, or block-structured adaptive mesh refinement codes. These abstractions include a novel data structure to manage refinement information for block-structured adaptive mesh refinement, an iterator mechanism to efficiently traverse multi-dimensional arrays in stencil-based codes, and a portable API and implementation for explicit SIMD vectorization. These abstractions can either be employed manually, or be targeted by automated code generation, or be used via support libraries by compilers during code generation. The implementations described below are available in the Cactus framework, and are used e.g. in the Einstein Toolkit for relativistic astrophysics simulations

Optimization and Abstraction: A Synergistic Approach for Analyzing Neural Network Robustness

In recent years, the notion of local robustness (or robustness for short) has emerged as a desirable property of deep neural networks. Intuitively, robustness means that small perturbations to an input do not cause the network to perform misclassifications. In this paper, we present a novel algorithm for verifying robustness properties of neural networks. Our method synergistically combines gradient-based optimization methods for counterexample search with abstraction-based proof search to obtain a sound and ({\delta}-)complete decision procedure. Our method also employs a data-driven approach to learn a verification policy that guides abstract interpretation during proof search. We have implemented the proposed approach in a tool called Charon and experimentally evaluated it on hundreds of benchmarks. Our experiments show that the proposed approach significantly outperforms three state-of-the-art tools, namely AI^2 , Reluplex, and Reluval