Diffusion and Poisson flow models have demonstrated remarkable success for a wide range of generative tasks. Nevertheless, their iterative nature results in computationally expensive sampling and the number of function evaluations (NFE) required can be orders of magnitude larger than for single-step methods. Consistency models are a recent class of deep generative models which enable single-step sampling of high quality data without the need for adversarial training. In this paper, we introduce a novel image denoising technique which combines the flexibility afforded in Poisson flow generative models (PFGM)++ with the, high quality, single step sampling of consistency models. The proposed method first learns a trajectory between a noise distribution and the posterior distribution of interest by training PFGM++ in a supervised fashion. These pre-trained PFGM++ are subsequently "distilled" into Poisson flow consistency models (PFCM) via an updated version of consistency distillation. We call this approach posterior sampling Poisson flow consistency models (PS-PFCM). Our results indicate that the added flexibility of tuning the hyperparameter D, the dimensionality of the augmentation variables in PFGM++, allows us to outperform consistency models, a current state-of-the-art diffusion-style model with NFE=1 on clinical low-dose CT images. Notably, PFCM is in itself a novel family of deep generative models and we provide initial results on the CIFAR-10 dataset.
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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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Regularization of inverse problems is of paramount importance in computational imaging. The ability of neural networks to learn efficient image representations has been recently exploited to design powerful data-driven regularizers. While state-of-the-art plug-and-play methods rely on an implicit regularization provided by neural denoisers, alternative Bayesian approaches consider Maximum A Posteriori (MAP) estimation in the latent space of a generative model, thus with an explicit regularization. However, state-of-the-art deep generative models require a huge amount of training data compared to denoisers. Besides, their complexity hampers the optimization involved in latent MAP derivation. In this work, we first propose to use compressive autoencoders instead. These networks, which can be seen as variational autoencoders with a flexible latent prior, are smaller and easier to train than state-of-the-art generative models. As a second contribution, we introduce the Variational Bayes Latent Estimation (VBLE) algorithm, which performs latent estimation within the framework of variational inference. Thanks to a simple yet efficient parameterization of the variational posterior, VBLE allows for fast and easy (approximate) posterior sampling. Experimental results on image datasets BSD and FFHQ demonstrate that VBLE reaches similar performance than state-of-the-art plug-and-play methods, while being able to quantify uncertainties faster than other existing posterior sampling techniques.
Extremal properties of max-autoregressive moving average processes for modelling extreme river flows
Max-autogressive moving average (Max-ARMA) processes are powerful tools for modelling time series data with heavy-tailed behaviour; these are a non-linear version of the popular autoregressive moving average models. River flow data typically have features of heavy tails and non-linearity, as large precipitation events cause sudden spikes in the data that then exponentially decay. Therefore, stationary Max-ARMA models are a suitable candidate for capturing the unique temporal dependence structure exhibited by river flows. This paper contributes to advancing our understanding of the extremal properties of stationary Max-ARMA processes. We detail the first approach for deriving the extremal index, the lagged asymptotic dependence coefficient, and an efficient simulation for a general Max-ARMA process. We use the extremal properties, coupled with the belief that Max-ARMA processes provide only an approximation to extreme river flow, to fit such a model which can broadly capture river flow behaviour over a high threshold. We make our inference under a reparametrisation which gives a simpler parameter space that excludes cases where any parameter is non-identifiable. We illustrate results for river flow data from the UK River Thames.
Deep generative models aim to learn the underlying distribution of data and generate new ones. Despite the diversity of generative models and their high-quality generation performance in practice, most of them lack rigorous theoretical convergence proofs. In this work, we aim to establish some convergence results for OT-Flow, one of the deep generative models. First, by reformulating the framework of OT-Flow model, we establish the $\Gamma$-convergence of the formulation of OT-flow to the corresponding optimal transport (OT) problem as the regularization term parameter $\alpha$ goes to infinity. Second, since the loss function will be approximated by Monte Carlo method in training, we established the convergence between the discrete loss function and the continuous one when the sample number $N$ goes to infinity as well. Meanwhile, the approximation capability of the neural network provides an upper bound for the discrete loss function of the minimizers. The proofs in both aspects provide convincing assurances for OT-Flow.
Stability selection is a widely used method for improving the performance of feature selection algorithms. However, stability selection has been found to be highly conservative, resulting in low sensitivity. Further, the theoretical bound on the expected number of false positives, E(FP), is relatively loose, making it difficult to know how many false positives to expect in practice. In this paper, we introduce a novel method for stability selection based on integrating the stability paths rather than maximizing over them. This yields a tighter bound on E(FP), resulting in a feature selection criterion that has higher sensitivity in practice and is better calibrated in terms of matching the target E(FP). Our proposed method requires the same amount of computation as the original stability selection algorithm, and only requires the user to specify one input parameter, a target value for E(FP). We provide theoretical bounds on performance, and demonstrate the method on simulations and real data from cancer gene expression studies.
Functional integral representations for solutions of the motion equations for wall-bounded incompressible viscous flows, expressed (implicitly) in terms of distributions of solutions to stochastic differential equations of McKean-Vlasov type, are established by using a perturbation technique. These representations are used to obtain exact random vortex dynamics for wall-bounded viscous flows. Numerical schemes therefore are proposed and the convergence of the numerical schemes for random vortex dynamics with an additional force term is established. Several numerical experiments are carried out for demonstrating the motion of a viscous flow within a thin layer next to the fluid boundary.
Due to their flexibility to represent almost any kind of relational data, graph-based models have enjoyed a tremendous success over the past decades. While graphs are inherently only combinatorial objects, however, many prominent analysis tools are based on the algebraic representation of graphs via matrices such as the graph Laplacian, or on associated graph embeddings. Such embeddings associate to each node a set of coordinates in a vector space, a representation which can then be employed for learning tasks such as the classification or alignment of the nodes of the graph. As the geometric picture provided by embedding methods enables the use of a multitude of methods developed for vector space data, embeddings have thus gained interest both from a theoretical as well as a practical perspective. Inspired by trace-optimization problems, often encountered in the analysis of graph-based data, here we present a method to derive ellipsoidal embeddings of the nodes of a graph, in which each node is assigned a set of coordinates on the surface of a hyperellipsoid. Our method may be seen as an alternative to popular spectral embedding techniques, to which it shares certain similarities we discuss. To illustrate the utility of the embedding we conduct a case study in which analyse synthetic and real world networks with modular structure, and compare the results obtained with known methods in the literature.
Numerous Deep Learning (DL) models have been developed for a large spectrum of medical image analysis applications, which promises to reshape various facets of medical practice. Despite early advances in DL model validation and implementation, which encourage healthcare institutions to adopt them, some fundamental questions remain: are the DL models capable of generalizing? What causes a drop in DL model performances? How to overcome the DL model performance drop? Medical data are dynamic and prone to domain shift, due to multiple factors such as updates to medical equipment, new imaging workflow, and shifts in patient demographics or populations can induce this drift over time. In this paper, we review recent developments in generalization methods for DL-based classification models. We also discuss future challenges, including the need for improved evaluation protocols and benchmarks, and envisioned future developments to achieve robust, generalized models for medical image classification.
We formulate a uniform tail bound for empirical processes indexed by a class of functions, in terms of the individual deviations of the functions rather than the worst-case deviation in the considered class. The tail bound is established by introducing an initial "deflation" step to the standard generic chaining argument. The resulting tail bound is the sum of the complexity of the "deflated function class" in terms of a generalization of Talagrand's $\gamma$ functional, and the deviation of the function instance, both of which are formulated based on the natural seminorm induced by the corresponding Cram\'{e}r functions. We also provide certain approximations for the mentioned seminorm when the function class lies in a given (exponential type) Orlicz space, that can be used to make the complexity term and the deviation term more explicit.
This paper presents GeoFlood, a new open-source software package for solving shallow water equations (SWE) on a quadtree hierarchy of mapped, logically Cartesian grids managed by the parallel, adaptive library ForestClaw (Calhoun and Burstedde, 2017). The GeoFlood model is validated using standard benchmark tests from Neelz and Pender (2013) and against George (2011) results obtained from the GeoClaw software (Clawpack Development Team, 2020) for the historical Malpasset dam failure problem. The benchmark test results are compared against GeoClaw and software package HEC-RAS (Hydraulic Engineering Center - River Analysis System, Army Corp of Engineers) results (Brunner, 2018). This comparison demonstrates the capability of GeoFlood to accurately and efficiently predict flood wave propagation on complex terrain. The results from comparisons with the Malpasset dam break show good agreement with the GeoClaw results and are consistent with the historical records of the event.
In large-scale systems there are fundamental challenges when centralised techniques are used for task allocation. The number of interactions is limited by resource constraints such as on computation, storage, and network communication. We can increase scalability by implementing the system as a distributed task-allocation system, sharing tasks across many agents. However, this also increases the resource cost of communications and synchronisation, and is difficult to scale. In this paper we present four algorithms to solve these problems. The combination of these algorithms enable each agent to improve their task allocation strategy through reinforcement learning, while changing how much they explore the system in response to how optimal they believe their current strategy is, given their past experience. We focus on distributed agent systems where the agents' behaviours are constrained by resource usage limits, limiting agents to local rather than system-wide knowledge. We evaluate these algorithms in a simulated environment where agents are given a task composed of multiple subtasks that must be allocated to other agents with differing capabilities, to then carry out those tasks. We also simulate real-life system effects such as networking instability. Our solution is shown to solve the task allocation problem to 6.7% of the theoretical optimal within the system configurations considered. It provides 5x better performance recovery over no-knowledge retention approaches when system connectivity is impacted, and is tested against systems up to 100 agents with less than a 9% impact on the algorithms' performance.
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