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Many stochastic continuous-state dynamical systems can be modeled as probabilistic programs with nonlinear non-polynomial updates in non-nested loops. We present two methods, one approximate and one exact, to automatically compute, without sampling, moment-based invariants for such probabilistic programs as closed-form solutions parameterized by the loop iteration. The exact method applies to probabilistic programs with trigonometric and exponential updates and is embedded in the Polar tool. The approximate method for moment computation applies to any nonlinear random function as it exploits the theory of polynomial chaos expansion to approximate non-polynomial updates as the sum of orthogonal polynomials. This translates the dynamical system to a non-nested loop with polynomial updates, and thus renders it conformable with the Polar tool that computes the moments of any order of the state variables. We evaluate our methods on an extensive number of examples ranging from modeling monetary policy to several physical motion systems in uncertain environments. The experimental results demonstrate the advantages of our approach with respect to the current state-of-the-art.

Sequence-independent lifting is a procedure for strengthening valid inequalities of an integer program. We generalize the sequence-independent lifting method of Gu, Nemhauser, and Savelsbergh (GNS lifting) for cover inequalities and correct an error in their proposed generalization. We obtain a new sequence-independent lifting technique -- piecewise-constant (PC) lifting -- with a number of interesting properties. We derive a broad set of sufficient conditions under which PC lifting is facet defining. To our knowledge, this is the first characterization of facet-defining sequence-independent liftings that are efficiently computable from the underlying cover. Finally, we demonstrate via experiments that PC lifting can be a useful alternative to GNS lifting. We test our new lifting techniques atop a number of novel cover cut generation routines, which prove to be effective in experiments with CPLEX.

Convolutional neural networks have shown to be widely applicable to a large number of fields when large amounts of labelled data are available. The recent trend has been to use models with increasingly larger sets of tunable parameters to increase model accuracy, reduce model loss, or create more adversarially robust models -- goals that are often at odds with one another. In particular, recent theoretical work raises questions about the ability for even larger models to generalize to data outside of the controlled train and test sets. As such, we examine the role of the number of hidden layers in the ResNet model, demonstrated on the MNIST, CIFAR10, CIFAR100 datasets. We test a variety of parameters including the size of the model, the floating point precision, and the noise level of both the training data and the model output. To encapsulate the model's predictive power and computational cost, we provide a method that uses induced failures to model the probability of failure as a function of time and relate that to a novel metric that allows us to quickly determine whether or not the cost of training a model outweighs the cost of attacking it. Using this approach, we are able to approximate the expected failure rate using a small number of specially crafted samples rather than increasingly larger benchmark datasets. We demonstrate the efficacy of this technique on both the MNIST and CIFAR10 datasets using 8-, 16-, 32-, and 64-bit floating-point numbers, various data pre-processing techniques, and several attacks on five configurations of the ResNet model. Then, using empirical measurements, we examine the various trade-offs between cost, robustness, latency, and reliability to find that larger models do not significantly aid in adversarial robustness despite costing significantly more to train.

Tissue segmentation is a routine preprocessing step to reduce the computational cost of whole slide image (WSI) analysis by excluding background regions. Traditional image processing techniques are commonly used for tissue segmentation, but often require manual adjustments to parameter values for atypical cases, fail to exclude all slide and scanning artifacts from the background, and are unable to segment adipose tissue. Pen marking artifacts in particular can be a potential source of bias for subsequent analyses if not removed. In addition, several applications require the separation of individual cross-sections, which can be challenging due to tissue fragmentation and adjacent positioning. To address these problems, we develop a convolutional neural network for tissue and pen marking segmentation using a dataset of 200 H&E stained WSIs. For separating tissue cross-sections, we propose a novel post-processing method based on clustering predicted centroid locations of the cross-sections in a 2D histogram. On an independent test set, the model achieved a mean Dice score of 0.981$\pm$0.033 for tissue segmentation and a mean Dice score of 0.912$\pm$0.090 for pen marking segmentation. The mean absolute difference between the number of annotated and separated cross-sections was 0.075$\pm$0.350. Our results demonstrate that the proposed model can accurately segment H&E stained tissue cross-sections and pen markings in WSIs while being robust to many common slide and scanning artifacts. The model with trained model parameters and post-processing method are made publicly available as a Python package called SlideSegmenter.

In this paper, a comparison analysis between geometric impedance controls (GICs) derived from two different potential functions on SE(3) for robotic manipulators is presented. The first potential function is defined on the Lie group, utilizing the Frobenius norm of the configuration error matrix. The second potential function is defined utilizing the Lie algebra, i.e., log-map of the configuration error. Using a differential geometric approach, the detailed derivation of the distance metric and potential function on SE(3) is introduced. The GIC laws are respectively derived from the two potential functions, followed by extensive comparison analyses. In the qualitative analysis, the properties of the error function and control laws are analyzed, while the performances of the controllers are quantitatively compared using numerical simulation.

We propose a predictor-corrector adaptive method for the study of hyperbolic partial differential equations (PDEs) under uncertainty. Constructed around the framework of stochastic finite volume (SFV) methods, our approach circumvents sampling schemes or simulation ensembles while also preserving fundamental properties, in particular hyperbolicity of the resulting systems and conservation of the discrete solutions. Furthermore, we augment the existing SFV theory with a priori convergence results for statistical quantities, in particular push-forward densities, which we demonstrate through numerical experiments. By linking refinement indicators to regions of the physical and stochastic spaces, we drive anisotropic refinements of the discretizations, introducing new degrees of freedom (DoFs) where deemed profitable. To illustrate our proposed method, we consider a series of numerical examples for non-linear hyperbolic PDEs based on Burgers' and Euler's equations.

We propose policy gradient algorithms for robust infinite-horizon Markov decision processes (MDPs) with non-rectangular uncertainty sets, thereby addressing an open challenge in the robust MDP literature. Indeed, uncertainty sets that display statistical optimality properties and make optimal use of limited data often fail to be rectangular. Unfortunately, the corresponding robust MDPs cannot be solved with dynamic programming techniques and are in fact provably intractable. We first present a randomized projected Langevin dynamics algorithm that solves the robust policy evaluation problem to global optimality but is inefficient. We also propose a deterministic policy gradient method that is efficient but solves the robust policy evaluation problem only approximately, and we prove that the approximation error scales with a new measure of non-rectangularity of the uncertainty set. Finally, we describe an actor-critic algorithm that finds an $\epsilon$-optimal solution for the robust policy improvement problem in $\mathcal{O}(1/\epsilon^4)$ iterations. We thus present the first complete solution scheme for robust MDPs with non-rectangular uncertainty sets offering global optimality guarantees. Numerical experiments show that our algorithms compare favorably against state-of-the-art methods.

When using ordinal patterns, which describe the ordinal structure within a data vector, the problem of ties appeared permanently. So far, model classes were used which do not allow for ties; randomization has been another attempt to overcome this problem. Often, time periods with constant values even have been counted as times of monotone increase. To overcome this, a new approach is proposed: it explicitly allows for ties and, hence, considers more patterns than before. Ties are no longer seen as nuisance, but to carry valuable information. Limit theorems in the new framework are provided, both, for a single time series and for the dependence between two time series. The methods are used on hydrological data sets. It is common to distinguish five flood classes (plus 'absence of flood'). Considering data vectors of these classes at a certain gauge in a river basin, one will usually encounter several ties. Co-monotonic behavior between the data sets of two gauges (increasing, constant, decreasing) can be detected by the method as well as spatial patterns. Thus, it helps to analyze the strength of dependence between different gauges in an intuitive way. This knowledge can be used to asses risk and to plan future construction projects.

We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.

High spectral dimensionality and the shortage of annotations make hyperspectral image (HSI) classification a challenging problem. Recent studies suggest that convolutional neural networks can learn discriminative spatial features, which play a paramount role in HSI interpretation. However, most of these methods ignore the distinctive spectral-spatial characteristic of hyperspectral data. In addition, a large amount of unlabeled data remains an unexploited gold mine for efficient data use. Therefore, we proposed an integration of generative adversarial networks (GANs) and probabilistic graphical models for HSI classification. Specifically, we used a spectral-spatial generator and a discriminator to identify land cover categories of hyperspectral cubes. Moreover, to take advantage of a large amount of unlabeled data, we adopted a conditional random field to refine the preliminary classification results generated by GANs. Experimental results obtained using two commonly studied datasets demonstrate that the proposed framework achieved encouraging classification accuracy using a small number of data for training.