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We propose an implementable, feedforward neural network-based structure preserving probabilistic numerical approximation for a generalized obstacle problem describing the value of a zero-sum differential game of optimal stopping with asymmetric information. The target solution depends on three variables: the time, the spatial (or state) variable, and a variable from a standard $(I-1)$-simplex which represents the probabilities with which the $I$ possible configurations of the game are played. The proposed numerical approximation preserves the convexity of the continuous solution as well as the lower and upper obstacle bounds. We show convergence of the fully-discrete scheme to the unique viscosity solution of the continuous problem and present a range of numerical studies to demonstrate its applicability.

In recent years, the amount of data available on the internet and the number of users who utilize the Internet have increased at an unparalleled pace. The exponential development in the quantity of digital information accessible and the number of Internet users has created the possibility for information overload, impeding fast access to items of interest on the Internet. Information retrieval systems like as Google, DevilFinder, and Altavista have partly overcome this challenge, but prioritizing and customization of information (where a system maps accessible material to a user's interests and preferences) were lacking. This has resulted in a higher-than-ever need for recommender systems. Recommender systems are information filtering systems that address the issue of information overload by filtering important information fragments from a huge volume of dynamically produced data based on the user's interests, favorite things, preferences and ratings on the desired item. Recommender systems can figure out if a person would like an item or not based on their profile.

In applications such as remote estimation and monitoring, update packets are transmitted by power-constrained devices using short-packet codes over wireless networks. Therefore, networks need to be end-to-end optimized using information freshness metrics such as age of information under transmit power and reliability constraints to ensure support for such applications. For short-packet coding, modelling and understanding the effect of block codeword length on transmit power and other performance metrics is important. To understand the above optimization for short-packet coding, we consider the optimal tradeoff problem between age of information and transmit power under reliability constraints for short packet point-to-point communication model with an exogenous packet generation process. In contrast to prior work, we consider scheduling policies that can possibly adapt the block-length or transmission time of short packet codes in order to achieve the optimal tradeoff. We characterize the tradeoff using a semi-Markov decision process formulation. We also obtain analytical upper bounds as well as numerical, analytical, and asymptotic lower bounds on the optimal tradeoff. We show that in certain regimes, such as high reliability and high packet generation rate, non-adaptive scheduling policies (fixed transmission time policies) are close-to-optimal. Furthermore, in a high-power or in a low-power regime, non-adaptive as well as state-independent randomized scheduling policies are order-optimal. These results are corroborated by numerical and simulation experiments. The tradeoff is then characterized for a wireless point-to-point channel with block fading as well as for other packet generation models (including an age-dependent packet generation model).

The Horvitz-Thompson (H-T) estimator is widely used for estimating various types of average treatment effects under network interference. We systematically investigate the optimality properties of H-T estimator under network interference, by embedding it in the class of all linear estimators. In particular, we show that in presence of any kind of network interference, H-T estimator is in-admissible in the class of all linear estimators when using a completely randomized and a Bernoulli design. We also show that the H-T estimator becomes admissible under certain restricted randomization schemes termed as ``fixed exposure designs''. We give examples of such fixed exposure designs. It is well known that the H-T estimator is unbiased when correct weights are specified. Here, we derive the weights for unbiased estimation of various causal effects, and illustrate how they depend not only on the design, but more importantly, on the assumed form of interference (which in many real world situations is unknown at design stage), and the causal effect of interest.

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.

In the field of medical imaging, the scarcity of large-scale datasets due to privacy restrictions stands as a significant barrier to develop large models for medical. To address this issue, we introduce SynFundus-1M, a high-quality synthetic dataset with over 1 million retinal fundus images and extensive disease and pathologies annotations, which is generated by a Denoising Diffusion Probabilistic Model. The SynFundus-Generator and SynFundus-1M achieve superior Frechet Inception Distance (FID) scores compared to existing methods on main-stream public real datasets. Furthermore, the ophthalmologists evaluation validate the difficulty in discerning these synthetic images from real ones, confirming the SynFundus-1M's authenticity. Through extensive experiments, we demonstrate that both CNN and ViT can benifit from SynFundus-1M by pretraining or training directly. Compared to datasets like ImageNet or EyePACS, models train on SynFundus-1M not only achieve better performance but also faster convergence on various downstream tasks.

The trace plot is seldom used in meta-analysis, yet it is a very informative plot. In this article we define and illustrate what the trace plot is, and discuss why it is important. The Bayesian version of the plot combines the posterior density of tau, the between-study standard deviation, and the shrunken estimates of the study effects as a function of tau. With a small or moderate number of studies, tau is not estimated with much precision, and parameter estimates and shrunken study effect estimates can vary widely depending on the correct value of tau. The trace plot allows visualization of the sensitivity to tau along with a plot that shows which values of tau are plausible and which are implausible. A comparable frequentist or empirical Bayes version provides similar results. The concepts are illustrated using examples in meta-analysis and meta-regression; implementaton in R is facilitated in a Bayesian or frequentist framework using the bayesmeta and metafor packages, respectively.

Many approaches have been proposed to use diffusion models to augment training datasets for downstream tasks, such as classification. However, diffusion models are themselves trained on large datasets, often with noisy annotations, and it remains an open question to which extent these models contribute to downstream classification performance. In particular, it remains unclear if they generalize enough to improve over directly using the additional data of their pre-training process for augmentation. We systematically evaluate a range of existing methods to generate images from diffusion models and study new extensions to assess their benefit for data augmentation. Personalizing diffusion models towards the target data outperforms simpler prompting strategies. However, using the pre-training data of the diffusion model alone, via a simple nearest-neighbor retrieval procedure, leads to even stronger downstream performance. Our study explores the potential of diffusion models in generating new training data, and surprisingly finds that these sophisticated models are not yet able to beat a simple and strong image retrieval baseline on simple downstream vision tasks.

Collaboration between human and robot requires effective modes of communication to assign robot tasks and coordinate activities. As communication can utilize different modalities, a multi-modal approach can be more expressive than single modal models alone. In this work we propose a co-speech gesture model that can assign robot tasks for human-robot collaboration. Human gestures and speech, detected by computer vision and speech recognition, can thus refer to objects in the scene and apply robot actions to them. We present an experimental evaluation of the multi-modal co-speech model with a real-world industrial use case. Results demonstrate that multi-modal communication is easy to achieve and can provide benefits for collaboration with respect to single modal tools.

High-dimensional, higher-order tensor data are gaining prominence in a variety of fields, including but not limited to computer vision and network analysis. Tensor factor models, induced from noisy versions of tensor decomposition or factorization, are natural potent instruments to study a collection of tensor-variate objects that may be dependent or independent. However, it is still in the early stage of developing statistical inferential theories for estimation of various low-rank structures, which are customary to play the role of signals of tensor factor models. In this paper, starting from tensor matricization, we aim to ``decode" estimation of a higher-order tensor factor model in the sense that, we recast it into mode-wise traditional high-dimensional vector/fiber factor models so as to deploy the conventional estimation of principle components analysis (PCA). Demonstrated by the Tucker tensor factor model (TuTFaM), which is induced from most popular Tucker decomposition, we summarize that estimations on signal components are essentially mode-wise PCA techniques, and the involvement of projection and iteration will enhance the signal-to-noise ratio to various extend. We establish the inferential theory of the proposed estimations and conduct rich simulation experiments under TuTFaM, and illustrate how the proposed estimations can work in tensor reconstruction, clustering for video and economic datasets, respectively.