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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.

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.

Sparse joint shift (SJS) was recently proposed as a tractable model for general dataset shift which may cause changes to the marginal distributions of features and labels as well as the posterior probabilities and the class-conditional feature distributions. Fitting SJS for a target dataset without label observations may produce valid predictions of labels and estimates of class prior probabilities. We present new results on the transmission of SJS from sets of features to larger sets of features, a conditional correction formula for the class posterior probabilities under the target distribution, identifiability of SJS, and the relationship between SJS and covariate shift. In addition, we point out inconsistencies in the algorithms which were proposed for estimating the characteristics of SJS, as they could hamper the search for optimal solutions, and suggest potential improvements.

Real-time Arbitrary Waveform Generation (AWG) is essential in various engineering and research applications, and often requires complex bespoke hardware and software. This paper introduces an AWG framework using an NVIDIA Graphics Processing Unit (GPU) and a commercially available high-speed Digital-to-Analog Converter (DAC) card, both running on a desktop personal computer (PC). The GPU accelerates the "embarrassingly" data parallel additive waveform synthesis framework for AWG, and the DAC reconstructs the generated waveform in the analog domain at high speed. The AWG framework is programmed using the developer-friendly Compute Unified Device Architecture (CUDA) runtime application programming interface from NVIDIA and is readily customizable, and scalable with additional parallel hardware. We present and characterize two different pathways for computing modulated radio-frequency (rf) waveforms: one pathway offers high-complexity simultaneous chirping of 1000 individual Nyquist-limited single-frequency tones for 35 ms at a sampling rate of 560 MB/s, and the other pathway allows simultaneous continuous chirping of 194 individual Nyquist-limited single-frequency tones at 100 MB/s, or 20 individual tones at 560 MB/s. This AWG framework is designed for fast on-the-fly rearrangement of a large stochastically-loaded optical tweezer array of single atoms or molecules into a defect-free array needed for quantum simulation and quantum computation applications.

We introduce a 2-dimensional stochastic dominance (2DSD) index to characterize both strict and almost stochastic dominance. Based on this index, we derive an estimator for the minimum violation ratio (MVR), also known as the critical parameter, of the almost stochastic ordering condition between two variables. We determine the asymptotic properties of the empirical 2DSD index and MVR for the most frequently used stochastic orders. We also provide conditions under which the bootstrap estimators of these quantities are strongly consistent. As an application, we develop consistent bootstrap testing procedures for almost stochastic dominance. The performance of the tests is checked via simulations and the analysis of real data.

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.

Electrohydrodynamics is a discipline that studies the interaction between fluid motion and electric field. Finite element method, finite difference method and other numerical simulations are effective numerical calculation methods for electrofluid dynamics models. In this paper, the finite element format of the electrofluid dynamics model is established, and the second-order convergence accuracy of the format is achieved through time filtering method. Finally, a numerical example is given to verify the convergence.

Existing statistical methods for the analysis of micro-randomized trials (MRTs) are designed to estimate causal excursion effects using data from a single MRT. In practice, however, researchers can often find previous MRTs that employ similar interventions. In this paper, we develop data integration methods that capitalize on this additional information, leading to statistical efficiency gains. To further increase efficiency, we demonstrate how to combine these approaches according to a generalization of multivariate precision weighting that allows for correlation between estimates, and we show that the resulting meta-estimator possesses an asymptotic optimality property. We illustrate our methods in simulation and in a case study involving two MRTs in the area of smoking cessation.