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Given that reliable cloud quantum computers are becoming closer to reality, the concept of delegation of quantum computations and its verifiability is of central interest. Many models have been proposed, each with specific strengths and weaknesses. Here, we put forth a new model where the client trusts only its classical processing, makes no computational assumptions, and interacts with a quantum server in a single round. In addition, during a set-up phase, the client specifies the size $n$ of the computation and receives an untrusted, off-the-shelf (OTS) quantum device that is used to report the outcome of a single measurement. We show how to delegate polynomial-time quantum computations in the OTS model. This also yields an interactive proof system for all of QMA, which, furthermore, we show can be accomplished in statistical zero-knowledge. This provides the first relativistic (one-round), two-prover zero-knowledge proof system for QMA. As a proof approach, we provide a new self-test for n EPR pairs using only constant-sized Pauli measurements, and show how it provides a new avenue for the use of simulatable codes for local Hamiltonian verification. Along the way, we also provide an enhanced version of a well-known stability result due to Gowers and Hatami and show how it completes a common argument used in self-testing.

This paper explores an iterative coupling approach to solve linear thermo-poroelasticity problems, with its application as a high-fidelity discretization utilizing finite elements during the training of projection-based reduced order models. One of the main challenges in addressing coupled multi-physics problems is the complexity and computational expenses involved. In this study, we introduce a decoupled iterative solution approach, integrated with reduced order modeling, aimed at augmenting the efficiency of the computational algorithm. The iterative coupling technique we employ builds upon the established fixed-stress splitting scheme that has been extensively investigated for Biot's poroelasticity. By leveraging solutions derived from this coupled iterative scheme, the reduced order model employs an additional Galerkin projection onto a reduced basis space formed by a small number of modes obtained through proper orthogonal decomposition. The effectiveness of the proposed algorithm is demonstrated through numerical experiments, showcasing its computational prowess.

Simulation-based inference (SBI) provides a powerful framework for inferring posterior distributions of stochastic simulators in a wide range of domains. In many settings, however, the posterior distribution is not the end goal itself -- rather, the derived parameter values and their uncertainties are used as a basis for deciding what actions to take. Unfortunately, because posterior distributions provided by SBI are (potentially crude) approximations of the true posterior, the resulting decisions can be suboptimal. Here, we address the question of how to perform Bayesian decision making on stochastic simulators, and how one can circumvent the need to compute an explicit approximation to the posterior. Our method trains a neural network on simulated data and can predict the expected cost given any data and action, and can, thus, be directly used to infer the action with lowest cost. We apply our method to several benchmark problems and demonstrate that it induces similar cost as the true posterior distribution. We then apply the method to infer optimal actions in a real-world simulator in the medical neurosciences, the Bayesian Virtual Epileptic Patient, and demonstrate that it allows to infer actions associated with low cost after few simulations.

We present a finite element approach for diffusion problems with thermal fluctuations based on a fluctuating hydrodynamics model. The governing transport equations are stochastic partial differential equations with a fluctuating forcing term. We propose a discrete formulation of the stochastic forcing term that has the correct covariance matrix up to a standard discretization error. Furthermore, to obtain a numerical solution with spatial correlations that converge to those of the continuum equation, we derive a linear mapping to transform the finite element solution into an equivalent discrete solution that is free from the artificial correlations introduced by the spatial discretization. The method is validated by applying it to two diffusion problems: a second-order diffusion equation and a fourth-order diffusion equation. The theoretical (continuum) solution to the first case presents spatially decorrelated fluctuations, while the second case presents fluctuations correlated over a finite length. In both cases, the numerical solution presents a structure factor that approximates well the continuum one.

This work introduces a novel framework for dynamic factor model-based data integration of multiple subjects time series data, called GRoup Integrative DYnamic factor (GRIDY) models. The framework identifies and characterizes inter-subject differences between two pre-labeled groups by considering a combination of group spatial information and individual temporal dependence. Furthermore, it enables the identification of intra-subject differences over time by employing different model configurations for each subject. Methodologically, the framework combines a novel principal angle-based rank selection algorithm and a non-iterative integrative analysis framework. Inspired by simultaneous component analysis, this approach also reconstructs identifiable latent factor series with flexible covariance structures. The performance of the GRIDY models is evaluated through simulations conducted under various scenarios. An application is also presented to compare resting-state functional MRI data collected from multiple subjects in the Autism Spectrum Disorder and control groups.

The solution to a stochastic optimal control problem can be determined by computing the value function from a discretisation of the associated Hamilton-Jacobi-Bellman equation. Alternatively, the problem can be reformulated in terms of a pair of forward-backward SDEs, which makes Monte-Carlo techniques applicable. More recently, the problem has also been viewed from the perspective of forward and reverse time SDEs and their associated Fokker-Planck equations. This approach is closely related to techniques used in score generative models. Forward and reverse time formulations express the value function as the ratio of two probability density functions; one stemming from a forward McKean-Vlasov SDE and another one from a reverse McKean-Vlasov SDE. In this note, we extend this approach to a more general class of stochastic optimal control problems and combine it with ensemble Kalman filter type and diffusion map approximation techniques in order to obtain efficient and robust particle-based algorithms.

We develop an NLP-based procedure for detecting systematic nonmeritorious consumer complaints, simply called systematic anomalies, among complaint narratives. While classification algorithms are used to detect pronounced anomalies, in the case of smaller and frequent systematic anomalies, the algorithms may falter due to a variety of reasons, including technical ones as well as natural limitations of human analysts. Therefore, as the next step after classification, we convert the complaint narratives into quantitative data, which are then analyzed using an algorithm for detecting systematic anomalies. We illustrate the entire procedure using complaint narratives from the Consumer Complaint Database of the Consumer Financial Protection Bureau.

The neural architectures of language models are becoming increasingly complex, especially that of Transformers, based on the attention mechanism. Although their application to numerous natural language processing tasks has proven to be very fruitful, they continue to be models with little or no interpretability and explainability. One of the tasks for which they are best suited is the encoding of the contextual sense of words using contextualized embeddings. In this paper we propose a transparent, interpretable, and linguistically motivated strategy for encoding the contextual sense of words by modeling semantic compositionality. Particular attention is given to dependency relations and semantic notions such as selection preferences and paradigmatic classes. A partial implementation of the proposed model is carried out and compared with Transformer-based architectures for a given semantic task, namely the similarity calculation of word senses in context. The results obtained show that it is possible to be competitive with linguistically motivated models instead of using the black boxes underlying complex neural architectures.

We propose an innovative and generic methodology to analyse individual and collective behaviour through individual trajectory data. The work is motivated by the analysis of GPS trajectories of fishing vessels collected from regulatory tracking data in the context of marine biodiversity conservation and ecosystem-based fisheries management. We build a low-dimensional latent representation of trajectories using convolutional neural networks as non-linear mapping. This is done by training a conditional variational auto-encoder taking into account covariates. The posterior distributions of the latent representations can be linked to the characteristics of the actual trajectories. The latent distributions of the trajectories are compared with the Bhattacharyya coefficient, which is well-suited for comparing distributions. Using this coefficient, we analyse the variation of the individual behaviour of each vessel during time. For collective behaviour analysis, we build proximity graphs and use an extension of the stochastic block model for multiple networks. This model results in a clustering of the individuals based on their set of trajectories. The application to French fishing vessels enables us to obtain groups of vessels whose individual and collective behaviours exhibit spatio-temporal patterns over the period 2014-2018.

Most state-of-the-art machine learning techniques revolve around the optimisation of loss functions. Defining appropriate loss functions is therefore critical to successfully solving problems in this field. We present a survey of the most commonly used loss functions for a wide range of different applications, divided into classification, regression, ranking, sample generation and energy based modelling. Overall, we introduce 33 different loss functions and we organise them into an intuitive taxonomy. Each loss function is given a theoretical backing and we describe where it is best used. This survey aims to provide a reference of the most essential loss functions for both beginner and advanced machine learning practitioners.