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Kernel techniques are among the most influential approaches in data science and statistics. Under mild conditions, the reproducing kernel Hilbert space associated to a kernel is capable of encoding the independence of $M\ge 2$ random variables. Probably the most widespread independence measure relying on kernels is the so-called Hilbert-Schmidt independence criterion (HSIC; also referred to as distance covariance in the statistics literature). Despite various existing HSIC estimators designed since its introduction close to two decades ago, the fundamental question of the rate at which HSIC can be estimated is still open. In this work, we prove that the minimax optimal rate of HSIC estimation on $\mathbb R^d$ for Borel measures containing the Gaussians with continuous bounded translation-invariant characteristic kernels is $\mathcal O\!\left(n^{-1/2}\right)$. Specifically, our result implies the optimality in the minimax sense of many of the most-frequently used estimators (including the U-statistic, the V-statistic, and the Nystr\"om-based one) on $\mathbb R^d$.

Spatiotemporal datasets, which consist of spatially-referenced time series, are ubiquitous in many scientific and business-intelligence applications, such as air pollution monitoring, disease tracking, and cloud-demand forecasting. As modern datasets continue to increase in size and complexity, there is a growing need for new statistical methods that are flexible enough to capture complex spatiotemporal dynamics and scalable enough to handle large prediction problems. This work presents the Bayesian Neural Field (BayesNF), a domain-general statistical model for inferring rich probability distributions over a spatiotemporal domain, which can be used for data-analysis tasks including forecasting, interpolation, and variography. BayesNF integrates a novel deep neural network architecture for high-capacity function estimation with hierarchical Bayesian inference for robust uncertainty quantification. By defining the prior through a sequence of smooth differentiable transforms, posterior inference is conducted on large-scale data using variationally learned surrogates trained via stochastic gradient descent. We evaluate BayesNF against prominent statistical and machine-learning baselines, showing considerable improvements on diverse prediction problems from climate and public health datasets that contain tens to hundreds of thousands of measurements. The paper is accompanied with an open-source software package (//github.com/google/bayesnf) that is easy-to-use and compatible with modern GPU and TPU accelerators on the JAX machine learning platform.

In the realm of personalization, integrating diverse information sources such as consumption signals and content-based representations is becoming increasingly critical to build state-of-the-art solutions. In this regard, two of the biggest trends in research around this subject are Graph Neural Networks (GNNs) and Foundation Models (FMs). While GNNs emerged as a popular solution in industry for powering personalization at scale, FMs have only recently caught attention for their promising performance in personalization tasks like ranking and retrieval. In this paper, we present a graph-based foundation modeling approach tailored to personalization. Central to this approach is a Heterogeneous GNN (HGNN) designed to capture multi-hop content and consumption relationships across a range of recommendable item types. To ensure the generality required from a Foundation Model, we employ a Large Language Model (LLM) text-based featurization of nodes that accommodates all item types, and construct the graph using co-interaction signals, which inherently transcend content specificity. To facilitate practical generalization, we further couple the HGNN with an adaptation mechanism based on a two-tower (2T) architecture, which also operates agnostically to content type. This multi-stage approach ensures high scalability; while the HGNN produces general purpose embeddings, the 2T component models in a continuous space the sheer size of user-item interaction data. Our comprehensive approach has been rigorously tested and proven effective in delivering recommendations across a diverse array of products within a real-world, industrial audio streaming platform.

Image restoration problems are typically ill-posed in the sense that each degraded image can be restored in infinitely many valid ways. To accommodate this, many works generate a diverse set of outputs by attempting to randomly sample from the posterior distribution of natural images given the degraded input. Here we argue that this strategy is commonly of limited practical value because of the heavy tail of the posterior distribution. Consider for example inpainting a missing region of the sky in an image. Since there is a high probability that the missing region contains no object but clouds, any set of samples from the posterior would be entirely dominated by (practically identical) completions of sky. However, arguably, presenting users with only one clear sky completion, along with several alternative solutions such as airships, birds, and balloons, would better outline the set of possibilities. In this paper, we initiate the study of meaningfully diverse image restoration. We explore several post-processing approaches that can be combined with any diverse image restoration method to yield semantically meaningful diversity. Moreover, we propose a practical approach for allowing diffusion based image restoration methods to generate meaningfully diverse outputs, while incurring only negligent computational overhead. We conduct extensive user studies to analyze the proposed techniques, and find the strategy of reducing similarity between outputs to be significantly favorable over posterior sampling. Code and examples are available at //noa-cohen.github.io/MeaningfulDiversityInIR.

We propose a new method for cloth digitalization. Deviating from existing methods which learn from data captured under relatively casual settings, we propose to learn from data captured in strictly tested measuring protocols, and find plausible physical parameters of the cloths. However, such data is currently absent, so we first propose a new dataset with accurate cloth measurements. Further, the data size is considerably smaller than the ones in current deep learning, due to the nature of the data capture process. To learn from small data, we propose a new Bayesian differentiable cloth model to estimate the complex material heterogeneity of real cloths. It can provide highly accurate digitalization from very limited data samples. Through exhaustive evaluation and comparison, we show our method is accurate in cloth digitalization, efficient in learning from limited data samples, and general in capturing material variations. Code and data are available //github.com/realcrane/Bayesian-Differentiable-Physics-for-Cloth-Digitalization

We consider the planar dynamic convex hull problem. In the literature, solutions exist supporting the insertion and deletion of points in poly-logarithmic time and various queries on the convex hull of the current set of points in logarithmic time. If arbitrary insertion and deletion of points are allowed, constant time updates and fast queries are known to be impossible. This paper considers two restricted cases where worst-case constant time updates and logarithmic time queries are possible. We assume all updates are performed on a deque (double-ended queue) of points. The first case considers the monotonic path case, where all points are sorted in a given direction, say horizontally left-to-right, and only the leftmost and rightmost points can be inserted and deleted. The second case assumes that the points in the deque constitute a simple path. Note that the monotone case is a special case of the simple path case. For both cases, we present solutions supporting deque insertions and deletions in worst-case constant time and standard queries on the convex hull of the points in $O(\log n)$ time, where $n$ is the number of points in the current point set. The convex hull of the current point set can be reported in $O(h+\log n)$ time, where $h$ is the number of edges of the convex hull. For the 1-sided monotone path case, where updates are only allowed on one side, the reporting time can be reduced to $O(h)$, and queries on the convex hull are supported in $O(\log h)$ time. All our time bounds are worst case. In addition, we prove lower bounds that match these time bounds, and thus our results are optimal. For a quick comparison, the previous best update bounds for the simple path problem were amortized $O(\log n)$ time by Friedman, Hershberger, and Snoeyink [SoCG 1989].

Changes in the timescales at which complex systems evolve are essential to predicting critical transitions and catastrophic failures. Disentangling the timescales of the dynamics governing complex systems remains a key challenge. With this study, we introduce an integrated Bayesian framework based on temporal network models to address this challenge. We focus on two methodologies: change point detection for identifying shifts in system dynamics, and a spectrum analysis for inferring the distribution of timescales. Applied to synthetic and empirical datasets, these methologies robustly identify critical transitions and comprehensively map the dominant and subsidiaries timescales in complex systems. This dual approach offers a powerful tool for analyzing temporal networks, significantly enhancing our understanding of dynamic behaviors in complex systems.

We consider the problem of explaining the predictions of graph neural networks (GNNs), which otherwise are considered as black boxes. Existing methods invariably focus on explaining the importance of graph nodes or edges but ignore the substructures of graphs, which are more intuitive and human-intelligible. In this work, we propose a novel method, known as SubgraphX, to explain GNNs by identifying important subgraphs. Given a trained GNN model and an input graph, our SubgraphX explains its predictions by efficiently exploring different subgraphs with Monte Carlo tree search. To make the tree search more effective, we propose to use Shapley values as a measure of subgraph importance, which can also capture the interactions among different subgraphs. To expedite computations, we propose efficient approximation schemes to compute Shapley values for graph data. Our work represents the first attempt to explain GNNs via identifying subgraphs explicitly and directly. Experimental results show that our SubgraphX achieves significantly improved explanations, while keeping computations at a reasonable level.

A community reveals the features and connections of its members that are different from those in other communities in a network. Detecting communities is of great significance in network analysis. Despite the classical spectral clustering and statistical inference methods, we notice a significant development of deep learning techniques for community detection in recent years with their advantages in handling high dimensional network data. Hence, a comprehensive overview of community detection's latest progress through deep learning is timely to both academics and practitioners. This survey devises and proposes a new taxonomy covering different categories of the state-of-the-art methods, including deep learning-based models upon deep neural networks, deep nonnegative matrix factorization and deep sparse filtering. The main category, i.e., deep neural networks, is further divided into convolutional networks, graph attention networks, generative adversarial networks and autoencoders. The survey also summarizes the popular benchmark data sets, model evaluation metrics, and open-source implementations to address experimentation settings. We then discuss the practical applications of community detection in various domains and point to implementation scenarios. Finally, we outline future directions by suggesting challenging topics in this fast-growing deep learning field.

While it is nearly effortless for humans to quickly assess the perceptual similarity between two images, the underlying processes are thought to be quite complex. Despite this, the most widely used perceptual metrics today, such as PSNR and SSIM, are simple, shallow functions, and fail to account for many nuances of human perception. Recently, the deep learning community has found that features of the VGG network trained on the ImageNet classification task has been remarkably useful as a training loss for image synthesis. But how perceptual are these so-called "perceptual losses"? What elements are critical for their success? To answer these questions, we introduce a new Full Reference Image Quality Assessment (FR-IQA) dataset of perceptual human judgments, orders of magnitude larger than previous datasets. We systematically evaluate deep features across different architectures and tasks and compare them with classic metrics. We find that deep features outperform all previous metrics by huge margins. More surprisingly, this result is not restricted to ImageNet-trained VGG features, but holds across different deep architectures and levels of supervision (supervised, self-supervised, or even unsupervised). Our results suggest that perceptual similarity is an emergent property shared across deep visual representations.