We propose a general purpose confidence interval procedure (CIP) for statistical functionals constructed using data from a stationary time series. The procedures we propose are based on derived distribution-free analogues of the $\chi^2$ and Student's $t$ random variables for the statistical functional context, and hence apply in a wide variety of settings including quantile estimation, gradient estimation, M-estimation, CVAR-estimation, and arrival process rate estimation, apart from more traditional statistical settings. Like the method of subsampling, we use overlapping batches of time series data to estimate the underlying variance parameter; unlike subsampling and the bootstrap, however, we assume that the implied point estimator of the statistical functional obeys a central limit theorem (CLT) to help identify the weak asymptotics (called OB-x limits, x=I,II,III) of batched Studentized statistics. The OB-x limits, certain functionals of the Wiener process parameterized by the size of the batches and the extent of their overlap, form the essential machinery for characterizing dependence, and consequently the correctness of the proposed CIPs. The message from extensive numerical experimentation is that in settings where a functional CLT on the point estimator is in effect, using \emph{large overlapping batches} alongside OB-x critical values yields confidence intervals that are often of significantly higher quality than those obtained from more generic methods like subsampling or the bootstrap. We illustrate using examples from CVaR estimation, ARMA parameter estimation, and NHPP rate estimation; R and MATLAB code for OB-x critical values is available at~\texttt{web.ics.purdue.edu/~pasupath/}.
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We consider a specific graph learning task: reconstructing a symmetric matrix that represents an underlying graph using linear measurements. We present a sparsity characterization for distributions of random graphs (that are allowed to contain high-degree nodes), based on which we study fundamental trade-offs between the number of measurements, the complexity of the graph class, and the probability of error. We first derive a necessary condition on the number of measurements. Then, by considering a three-stage recovery scheme, we give a sufficient condition for recovery. Furthermore, assuming the measurements are Gaussian IID, we prove upper and lower bounds on the (worst-case) sample complexity for both noisy and noiseless recovery. In the special cases of the uniform distribution on trees with n nodes and the Erdos-Renyi (n,p) class, the fundamental trade-offs are tight up to multiplicative factors with noiseless measurements. In addition, for practical applications, we design and implement a polynomial-time (in n) algorithm based on the three-stage recovery scheme. Experiments show that the heuristic algorithm outperforms basis pursuit on star graphs. We apply the heuristic algorithm to learn admittance matrices in electric grids. Simulations for several canonical graph classes and IEEE power system test cases demonstrate the effectiveness and robustness of the proposed algorithm for parameter reconstruction.
Maximum mean discrepancy (MMD) refers to a general class of nonparametric two-sample tests that are based on maximizing the mean difference over samples from one distribution $P$ versus another $Q$, over all choices of data transformations $f$ living in some function space $\mathcal{F}$. Inspired by recent work that connects what are known as functions of $\textit{Radon bounded variation}$ (RBV) and neural networks (Parhi and Nowak, 2021, 2023), we study the MMD defined by taking $\mathcal{F}$ to be the unit ball in the RBV space of a given smoothness order $k \geq 0$. This test, which we refer to as the $\textit{Radon-Kolmogorov-Smirnov}$ (RKS) test, can be viewed as a generalization of the well-known and classical Kolmogorov-Smirnov (KS) test to multiple dimensions and higher orders of smoothness. It is also intimately connected to neural networks: we prove that the witness in the RKS test -- the function $f$ achieving the maximum mean difference -- is always a ridge spline of degree $k$, i.e., a single neuron in a neural network. This allows us to leverage the power of modern deep learning toolkits to (approximately) optimize the criterion that underlies the RKS test. We prove that the RKS test has asymptotically full power at distinguishing any distinct pair $P \not= Q$ of distributions, derive its asymptotic null distribution, and carry out extensive experiments to elucidate the strengths and weakenesses of the RKS test versus the more traditional kernel MMD test.
Many of the most commonly explored natural language processing (NLP) information extraction tasks can be thought of as evaluations of declarative knowledge, or fact-based information extraction. Procedural knowledge extraction, i.e., breaking down a described process into a series of steps, has received much less attention, perhaps in part due to the lack of structured datasets that capture the knowledge extraction process from end-to-end. To address this unmet need, we present FlaMB\'e (Flow annotations for Multiverse Biological entities), a collection of expert-curated datasets across a series of complementary tasks that capture procedural knowledge in biomedical texts. This dataset is inspired by the observation that one ubiquitous source of procedural knowledge that is described as unstructured text is within academic papers describing their methodology. The workflows annotated in FlaMB\'e are from texts in the burgeoning field of single cell research, a research area that has become notorious for the number of software tools and complexity of workflows used. Additionally, FlaMB\'e provides, to our knowledge, the largest manually curated named entity recognition (NER) and disambiguation (NED) datasets for tissue/cell type, a fundamental biological entity that is critical for knowledge extraction in the biomedical research domain. Beyond providing a valuable dataset to enable further development of NLP models for procedural knowledge extraction, automating the process of workflow mining also has important implications for advancing reproducibility in biomedical research.
Regression discontinuity design (RDD) is widely adopted for causal inference under intervention determined by a continuous variable. While one is interested in treatment effect heterogeneity by subgroups in many applications, RDD typically suffers from small subgroup-wise sample sizes, which makes the estimation results highly instable. To solve this issue, we introduce hierarchical RDD (HRDD), a hierarchical Bayes approach for pursuing treatment effect heterogeneity in RDD. A key feature of HRDD is to employ a pseudo-model based on a loss function to estimate subgroup-level parameters of treatment effects under RDD, and assign a hierarchical prior distribution to ``borrow strength" from other subgroups. The posterior computation can be easily done by a simple Gibbs sampling. We demonstrate the proposed HRDD through simulation and real data analysis, and show that HRDD provides much more stable point and interval estimation than separately applying the standard RDD method to each subgroup.
With the development of computational fluid dynamics, the requirements for the fluid simulation accuracy in industrial applications have also increased. The quality of the generated mesh directly affects the simulation accuracy. However, previous mesh quality metrics and models cannot evaluate meshes comprehensively and objectively. To this end, we propose MQENet, a structured mesh quality evaluation neural network based on dynamic graph attention. MQENet treats the mesh evaluation task as a graph classification task for classifying the quality of the input structured mesh. To make graphs generated from structured meshes more informative, MQENet introduces two novel structured mesh preprocessing algorithms. These two algorithms can also improve the conversion efficiency of structured mesh data. Experimental results on the benchmark structured mesh dataset NACA-Market show the effectiveness of MQENet in the mesh quality evaluation task.
Generative models, as an important family of statistical modeling, target learning the observed data distribution via generating new instances. Along with the rise of neural networks, deep generative models, such as variational autoencoders (VAEs) and generative adversarial network (GANs), have made tremendous progress in 2D image synthesis. Recently, researchers switch their attentions from the 2D space to the 3D space considering that 3D data better aligns with our physical world and hence enjoys great potential in practice. However, unlike a 2D image, which owns an efficient representation (i.e., pixel grid) by nature, representing 3D data could face far more challenges. Concretely, we would expect an ideal 3D representation to be capable enough to model shapes and appearances in details, and to be highly efficient so as to model high-resolution data with fast speed and low memory cost. However, existing 3D representations, such as point clouds, meshes, and recent neural fields, usually fail to meet the above requirements simultaneously. In this survey, we make a thorough review of the development of 3D generation, including 3D shape generation and 3D-aware image synthesis, from the perspectives of both algorithms and more importantly representations. We hope that our discussion could help the community track the evolution of this field and further spark some innovative ideas to advance this challenging task.
Designing and generating new data under targeted properties has been attracting various critical applications such as molecule design, image editing and speech synthesis. Traditional hand-crafted approaches heavily rely on expertise experience and intensive human efforts, yet still suffer from the insufficiency of scientific knowledge and low throughput to support effective and efficient data generation. Recently, the advancement of deep learning induces expressive methods that can learn the underlying representation and properties of data. Such capability provides new opportunities in figuring out the mutual relationship between the structural patterns and functional properties of the data and leveraging such relationship to generate structural data given the desired properties. This article provides a systematic review of this promising research area, commonly known as controllable deep data generation. Firstly, the potential challenges are raised and preliminaries are provided. Then the controllable deep data generation is formally defined, a taxonomy on various techniques is proposed and the evaluation metrics in this specific domain are summarized. After that, exciting applications of controllable deep data generation are introduced and existing works are experimentally analyzed and compared. Finally, the promising future directions of controllable deep data generation are highlighted and five potential challenges are identified.
The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.
Knowledge base question answering (KBQA) aims to answer a question over a knowledge base (KB). Recently, a large number of studies focus on semantically or syntactically complicated questions. In this paper, we elaborately summarize the typical challenges and solutions for complex KBQA. We begin with introducing the background about the KBQA task. Next, we present the two mainstream categories of methods for complex KBQA, namely semantic parsing-based (SP-based) methods and information retrieval-based (IR-based) methods. We then review the advanced methods comprehensively from the perspective of the two categories. Specifically, we explicate their solutions to the typical challenges. Finally, we conclude and discuss some promising directions for future research.
Few sample learning (FSL) is significant and challenging in the field of machine learning. The capability of learning and generalizing from very few samples successfully is a noticeable demarcation separating artificial intelligence and human intelligence since humans can readily establish their cognition to novelty from just a single or a handful of examples whereas machine learning algorithms typically entail hundreds or thousands of supervised samples to guarantee generalization ability. Despite the long history dated back to the early 2000s and the widespread attention in recent years with booming deep learning technologies, little surveys or reviews for FSL are available until now. In this context, we extensively review 200+ papers of FSL spanning from the 2000s to 2019 and provide a timely and comprehensive survey for FSL. In this survey, we review the evolution history as well as the current progress on FSL, categorize FSL approaches into the generative model based and discriminative model based kinds in principle, and emphasize particularly on the meta learning based FSL approaches. We also summarize several recently emerging extensional topics of FSL and review the latest advances on these topics. Furthermore, we highlight the important FSL applications covering many research hotspots in computer vision, natural language processing, audio and speech, reinforcement learning and robotic, data analysis, etc. Finally, we conclude the survey with a discussion on promising trends in the hope of providing guidance and insights to follow-up researches.
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