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For a sequence of Boolean functions $f_n : \{-1,1\}^{V_n} \longrightarrow \{-1,1\}$, defined on increasing configuration spaces of random inputs, we say that there is sparse reconstruction if there is a sequence of subsets $U_n \subseteq V_n$ of the coordinates satisfying $|U_n| = o(|V_n|)$ such that knowing the coordinates in $U_n$ gives us a non-vanishing amount of information about the value of $f_n$. We first show that, if the underlying measure is a product measure, then no sparse reconstruction is possible for any sequence of transitive functions. We discuss the question in different frameworks, measuring information content in $L^2$ and with entropy. We also highlight some interesting connections with cooperative game theory. Beyond transitive functions, we show that the left-right crossing event for critical planar percolation on the square lattice does not admit sparse reconstruction either. Some of these results answer questions posed by Itai Benjamini.

Deep learning has revolutionized the field of artificial intelligence. Based on the statistical correlations uncovered by deep learning-based methods, computer vision has contributed to tremendous growth in areas like autonomous driving and robotics. Despite being the basis of deep learning, such correlation is not stable and is susceptible to uncontrolled factors. In the absence of the guidance of prior knowledge, statistical correlations can easily turn into spurious correlations and cause confounders. As a result, researchers are now trying to enhance deep learning methods with causal theory. Causal theory models the intrinsic causal structure unaffected by data bias and is effective in avoiding spurious correlations. This paper aims to comprehensively review the existing causal methods in typical vision and vision-language tasks such as semantic segmentation, object detection, and image captioning. The advantages of causality and the approaches for building causal paradigms will be summarized. Future roadmaps are also proposed, including facilitating the development of causal theory and its application in other complex scenes and systems.

For exchangeable data, mixture models are an extremely useful tool for density estimation due to their attractive balance between smoothness and flexibility. When additional covariate information is present, mixture models can be extended for flexible regression by modeling the mixture parameters, namely the weights and atoms, as functions of the covariates. These types of models are interpretable and highly flexible, allowing non only the mean but the whole density of the response to change with the covariates, which is also known as density regression. This article reviews Bayesian covariate-dependent mixture models and highlights which data types can be accommodated by the different models along with the methodological and applied areas where they have been used. In addition to being highly flexible, these models are also numerous; we focus on nonparametric constructions and broadly organize them into three categories: 1) joint models of the responses and covariates, 2) conditional models with single-weights and covariate-dependent atoms, and 3) conditional models with covariate-dependent weights. The diversity and variety of the available models in the literature raises the question of how to choose among them for the application at hand. We attempt to shed light on this question through a careful analysis of the predictive equations for the conditional mean and density function as well as predictive comparisons in three simulated data examples.

A new method of representing graph projections in computer memory is proposed, which is more informative than matrix and list data structures based on elementary relations of vertices adjacency or edge incidences. The class of graphs considered in this study is expanded to include mixed graphs containing both undirected and directed edges (arcs). A new method for searching the shortest routes based on this approach is also proposed. The results of the general and special (for compact graphs) analysis of the asymptotic complexity of this method in solving typical SPP problems (Shortest Path Problem) show that the developed method is highly efficient and will find its application not only in information networks, where there are particularly high requirements for the topology of computing systems and the efficiency of finding shortest routes, but also in other scientific, technical, transport and economic fields.

The recent trend in deep learning methods for 3D point cloud understanding is to propose increasingly sophisticated architectures either to better capture 3D geometries or by introducing possibly undesired inductive biases. Moreover, prior works introducing novel architectures compared their performance on the same domain, devoting less attention to their generalization to other domains. We argue that the ability of a model to transfer the learnt knowledge to different domains is an important feature that should be evaluated to exhaustively assess the quality of a deep network architecture. In this work we propose PatchMixer, a simple yet effective architecture that extends the ideas behind the recent MLP-Mixer paper to 3D point clouds. The novelties of our approach are the processing of local patches instead of the whole shape to promote robustness to partial point clouds, and the aggregation of patch-wise features using an MLP as a simpler alternative to the graph convolutions or the attention mechanisms that are used in prior works. We evaluated our method on the shape classification and part segmentation tasks, achieving superior generalization performance compared to a selection of the most relevant deep architectures.

The crossed random-effects model is widely used in applied statistics, finding applications in various fields such as longitudinal studies, e-commerce, and recommender systems, among others. However, these models encounter scalability challenges, as the computational time grows disproportionately with the number of data points, typically following a cubic root relationship $(N^{(3/2)}$ or worse) with $N$. Our inspiration for addressing this issue comes from observing the recommender system employed by an online clothing retailer. Our dataset comprises over 700,000 clients, 5,000 items, and 5,000,000 measurements. When applying the maximum likelihood approach to fit crossed random effects, computational inefficiency becomes a significant concern, limiting the applicability of this approach in large-scale settings. To tackle the scalability issues, previous research by Ghosh et al. (2022a) and Ghosh et al. (2022b) has explored linear and logistic regression models utilizing fixed-effect features based on client and item variables, while incorporating random intercept terms for clients and items. In this study, we present a more generalized version of the problem, allowing random effect sizes/slopes. This extension enables us to capture the variability in effect size among both clients and items. Importantly, we have developed a scalable solution to address the aforementioned problem and have empirically demonstrated the consistency of our estimates. Specifically, as the number of data points increases, our estimates converge towards the true parameters. To validate our approach, we implement the proposed algorithm using Stitch Fix data.

State-of-the-art visual localization methods mostly rely on complex procedures to match local descriptors and 3D point clouds. However, these procedures can incur significant cost in terms of inference, storage, and updates over time. In this study, we propose a direct learning-based approach that utilizes a simple network named D2S to represent local descriptors and their scene coordinates. Our method is characterized by its simplicity and cost-effectiveness. It solely leverages a single RGB image for localization during the testing phase and only requires a lightweight model to encode a complex sparse scene. The proposed D2S employs a combination of a simple loss function and graph attention to selectively focus on robust descriptors while disregarding areas such as clouds, trees, and several dynamic objects. This selective attention enables D2S to effectively perform a binary-semantic classification for sparse descriptors. Additionally, we propose a new outdoor dataset to evaluate the capabilities of visual localization methods in terms of scene generalization and self-updating from unlabeled observations. Our approach outperforms the state-of-the-art CNN-based methods in scene coordinate regression in indoor and outdoor environments. It demonstrates the ability to generalize beyond training data, including scenarios involving transitions from day to night and adapting to domain shifts, even in the absence of the labeled data sources. The source code, trained models, dataset, and demo videos are available at the following link: //thpjp.github.io/d2s

Recommender systems, a pivotal tool to alleviate the information overload problem, aim to predict user's preferred items from millions of candidates by analyzing observed user-item relations. As for tackling the sparsity and cold start problems encountered by recommender systems, uncovering hidden (indirect) user-item relations by employing side information and knowledge to enrich observed information for the recommendation has been proven promising recently; and its performance is largely determined by the scalability of recommendation models in the face of the high complexity and large scale of side information and knowledge. Making great strides towards efficiently utilizing complex and large-scale data, research into graph embedding techniques is a major topic. Equipping recommender systems with graph embedding techniques contributes to outperforming the conventional recommendation implementing directly based on graph topology analysis and has been widely studied these years. This article systematically retrospects graph embedding-based recommendation from embedding techniques for bipartite graphs, general graphs, and knowledge graphs, and proposes a general design pipeline of that. In addition, comparing several representative graph embedding-based recommendation models with the most common-used conventional recommendation models, on simulations, manifests that the conventional models overall outperform the graph embedding-based ones in predicting implicit user-item interactions, revealing the relative weakness of graph embedding-based recommendation in these tasks. To foster future research, this article proposes constructive suggestions on making a trade-off between graph embedding-based recommendation and the conventional recommendation in different tasks as well as some open questions.

Time Series Classification (TSC) is an important and challenging problem in data mining. With the increase of time series data availability, hundreds of TSC algorithms have been proposed. Among these methods, only a few have considered Deep Neural Networks (DNNs) to perform this task. This is surprising as deep learning has seen very successful applications in the last years. DNNs have indeed revolutionized the field of computer vision especially with the advent of novel deeper architectures such as Residual and Convolutional Neural Networks. Apart from images, sequential data such as text and audio can also be processed with DNNs to reach state-of-the-art performance for document classification and speech recognition. In this article, we study the current state-of-the-art performance of deep learning algorithms for TSC by presenting an empirical study of the most recent DNN architectures for TSC. We give an overview of the most successful deep learning applications in various time series domains under a unified taxonomy of DNNs for TSC. We also provide an open source deep learning framework to the TSC community where we implemented each of the compared approaches and evaluated them on a univariate TSC benchmark (the UCR/UEA archive) and 12 multivariate time series datasets. By training 8,730 deep learning models on 97 time series datasets, we propose the most exhaustive study of DNNs for TSC to date.

Deep learning constitutes a recent, modern technique for image processing and data analysis, with promising results and large potential. As deep learning has been successfully applied in various domains, it has recently entered also the domain of agriculture. In this paper, we perform a survey of 40 research efforts that employ deep learning techniques, applied to various agricultural and food production challenges. We examine the particular agricultural problems under study, the specific models and frameworks employed, the sources, nature and pre-processing of data used, and the overall performance achieved according to the metrics used at each work under study. Moreover, we study comparisons of deep learning with other existing popular techniques, in respect to differences in classification or regression performance. Our findings indicate that deep learning provides high accuracy, outperforming existing commonly used image processing techniques.