Advection-diffusion equations describe a large family of natural transport processes, e.g., fluid flow, heat transfer, and wind transport. They are also used for optical flow and perfusion imaging computations. We develop a machine learning model, D^2-SONATA, built upon a stochastic advection-diffusion equation, which predicts the velocity and diffusion fields that drive 2D/3D image time-series of transport. In particular, our proposed model incorporates a model of transport atypicality, which isolates abnormal differences between expected normal transport behavior and the observed transport. In a medical context such a normal-abnormal decomposition can be used, for example, to quantify pathologies. Specifically, our model identifies the advection and diffusion contributions from the transport time-series and simultaneously predicts an anomaly value field to provide a decomposition into normal and abnormal advection and diffusion behavior. To achieve improved estimation performance for the velocity and diffusion-tensor fields underlying the advection-diffusion process and for the estimation of the anomaly fields, we create a 2D/3D anomaly-encoded advection-diffusion simulator, which allows for supervised learning. We further apply our model on a brain perfusion dataset from ischemic stroke patients via transfer learning. Extensive comparisons demonstrate that our model successfully distinguishes stroke lesions (abnormal) from normal brain regions, while reconstructing the underlying velocity and diffusion tensor fields.
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ACM/IEEE第23屆模型驅動工程語言和系統國際會議，是模型驅動軟件和系統工程的首要會議系列，由ACM-SIGSOFT和IEEE-TCSE支持組織。自1998年以來，模型涵蓋了建模的各個方面，從語言和方法到工具和應用程序。模特的參加者來自不同的背景，包括研究人員、學者、工程師和工業專業人士。MODELS 2019是一個論壇，參與者可以圍繞建模和模型驅動的軟件和系統交流前沿研究成果和創新實踐經驗。今年的版本將為建模社區提供進一步推進建模基礎的機會，并在網絡物理系統、嵌入式系統、社會技術系統、云計算、大數據、機器學習、安全、開源等新興領域提出建模的創新應用以及可持續性。
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We introduce a family of stochastic optimization methods based on the Runge-Kutta-Chebyshev (RKC) schemes. The RKC methods are explicit methods originally designed for solving stiff ordinary differential equations by ensuring that their stability regions are of maximal size.In the optimization context, this allows for larger step sizes (learning rates) and better robustness compared to e.g. the popular stochastic gradient descent method. Our main contribution is a convergence proof for essentially all stochastic Runge-Kutta optimization methods. This shows convergence in expectation with an optimal sublinear rate under standard assumptions of strong convexity and Lipschitz-continuous gradients. For non-convex objectives, we get convergence to zero in expectation of the gradients. The proof requires certain natural conditions on the Runge-Kutta coefficients, and we further demonstrate that the RKC schemes satisfy these. Finally, we illustrate the improved stability properties of the methods in practice by performing numerical experiments on both a small-scale test example and on a problem arising from an image classification application in machine learning.
Second-order optimization methods are among the most widely used optimization approaches for convex optimization problems, and have recently been used to optimize non-convex optimization problems such as deep learning models. The widely used second-order optimization methods such as quasi-Newton methods generally provide curvature information by approximating the Hessian using the secant equation. However, the secant equation becomes insipid in approximating the Newton step owing to its use of the first-order derivatives. In this study, we propose an approximate Newton sketch-based stochastic optimization algorithm for large-scale empirical risk minimization. Specifically, we compute a partial column Hessian of size ($d\times m$) with $m\ll d$ randomly selected variables, then use the \emph{Nystr\"om method} to better approximate the full Hessian matrix. To further reduce the computational complexity per iteration, we directly compute the update step ($\Delta\boldsymbol{w}$) without computing and storing the full Hessian or its inverse. We then integrate our approximated Hessian with stochastic gradient descent and stochastic variance-reduced gradient methods. The results of numerical experiments on both convex and non-convex functions show that the proposed approach was able to obtain a better approximation of Newton\textquotesingle s method, exhibiting performance competitive with that of state-of-the-art first-order and stochastic quasi-Newton methods. Furthermore, we provide a theoretical convergence analysis for convex functions.
We present a novel neural-networks-based algorithm to compute optimal transport maps and plans for strong and weak transport costs. To justify the usage of neural networks, we prove that they are universal approximators of transport plans between probability distributions. We evaluate the performance of our optimal transport algorithm on toy examples and on the unpaired image-to-image style translation task.
Constituting highly informative network embeddings is an important tool for network analysis. It encodes network topology, along with other useful side information, into low-dimensional node-based feature representations that can be exploited by statistical modeling. This work focuses on learning context-aware network embeddings augmented with text data. We reformulate the network-embedding problem, and present two novel strategies to improve over traditional attention mechanisms: ($i$) a content-aware sparse attention module based on optimal transport, and ($ii$) a high-level attention parsing module. Our approach yields naturally sparse and self-normalized relational inference. It can capture long-term interactions between sequences, thus addressing the challenges faced by existing textual network embedding schemes. Extensive experiments are conducted to demonstrate our model can consistently outperform alternative state-of-the-art methods.
We advocate the use of implicit fields for learning generative models of shapes and introduce an implicit field decoder for shape generation, aimed at improving the visual quality of the generated shapes. An implicit field assigns a value to each point in 3D space, so that a shape can be extracted as an iso-surface. Our implicit field decoder is trained to perform this assignment by means of a binary classifier. Specifically, it takes a point coordinate, along with a feature vector encoding a shape, and outputs a value which indicates whether the point is outside the shape or not. By replacing conventional decoders by our decoder for representation learning and generative modeling of shapes, we demonstrate superior results for tasks such as shape autoencoding, generation, interpolation, and single-view 3D reconstruction, particularly in terms of visual quality.
Tumor detection in biomedical imaging is a time-consuming process for medical professionals and is not without errors. Thus in recent decades, researchers have developed algorithmic techniques for image processing using a wide variety of mathematical methods, such as statistical modeling, variational techniques, and machine learning. In this paper, we propose a semi-automatic method for liver segmentation of 2D CT scans into three labels denoting healthy, vessel, or tumor tissue based on graph cuts. First, we create a feature vector for each pixel in a novel way that consists of the 59 intensity values in the time series data and propose a simplified perimeter cost term in the energy functional. We normalize the data and perimeter terms in the functional to expedite the graph cut without having to optimize the scaling parameter $\lambda$. In place of a training process, predetermined tissue means are computed based on sample regions identified by expert radiologists. The proposed method also has the advantage of being relatively simple to implement computationally. It was evaluated against the ground truth on a clinical CT dataset of 10 tumors and yielded segmentations with a mean Dice similarity coefficient (DSC) of .77 and mean volume overlap error (VOE) of 36.7%. The average processing time was 1.25 minutes per slice.
Deep learning (DL) is a high dimensional data reduction technique for constructing high-dimensional predictors in input-output models. DL is a form of machine learning that uses hierarchical layers of latent features. In this article, we review the state-of-the-art of deep learning from a modeling and algorithmic perspective. We provide a list of successful areas of applications in Artificial Intelligence (AI), Image Processing, Robotics and Automation. Deep learning is predictive in its nature rather then inferential and can be viewed as a black-box methodology for high-dimensional function estimation.
Image foreground extraction is a classical problem in image processing and vision, with a large range of applications. In this dissertation, we focus on the extraction of text and graphics in mixed-content images, and design novel approaches for various aspects of this problem. We first propose a sparse decomposition framework, which models the background by a subspace containing smooth basis vectors, and foreground as a sparse and connected component. We then formulate an optimization framework to solve this problem, by adding suitable regularizations to the cost function to promote the desired characteristics of each component. We present two techniques to solve the proposed optimization problem, one based on alternating direction method of multipliers (ADMM), and the other one based on robust regression. Promising results are obtained for screen content image segmentation using the proposed algorithm. We then propose a robust subspace learning algorithm for the representation of the background component using training images that could contain both background and foreground components, as well as noise. With the learnt subspace for the background, we can further improve the segmentation results, compared to using a fixed subspace. Lastly, we investigate a different class of signal/image decomposition problem, where only one signal component is active at each signal element. In this case, besides estimating each component, we need to find their supports, which can be specified by a binary mask. We propose a mixed-integer programming problem, that jointly estimates the two components and their supports through an alternating optimization scheme. We show the application of this algorithm on various problems, including image segmentation, video motion segmentation, and also separation of text from textured images.
Image segmentation is the process of partitioning the image into significant regions easier to analyze. Nowadays, segmentation has become a necessity in many practical medical imaging methods as locating tumors and diseases. Hidden Markov Random Field model is one of several techniques used in image segmentation. It provides an elegant way to model the segmentation process. This modeling leads to the minimization of an objective function. Conjugate Gradient algorithm (CG) is one of the best known optimization techniques. This paper proposes the use of the Conjugate Gradient algorithm (CG) for image segmentation, based on the Hidden Markov Random Field. Since derivatives are not available for this expression, finite differences are used in the CG algorithm to approximate the first derivative. The approach is evaluated using a number of publicly available images, where ground truth is known. The Dice Coefficient is used as an objective criterion to measure the quality of segmentation. The results show that the proposed CG approach compares favorably with other variants of Hidden Markov Random Field segmentation algorithms.
In this paper, we study the optimal convergence rate for distributed convex optimization problems in networks. We model the communication restrictions imposed by the network as a set of affine constraints and provide optimal complexity bounds for four different setups, namely: the function $F(\xb) \triangleq \sum_{i=1}^{m}f_i(\xb)$ is strongly convex and smooth, either strongly convex or smooth or just convex. Our results show that Nesterov's accelerated gradient descent on the dual problem can be executed in a distributed manner and obtains the same optimal rates as in the centralized version of the problem (up to constant or logarithmic factors) with an additional cost related to the spectral gap of the interaction matrix. Finally, we discuss some extensions to the proposed setup such as proximal friendly functions, time-varying graphs, improvement of the condition numbers.
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