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This paper proposes a flexible framework for inferring large-scale time-varying and time-lagged correlation networks from multivariate or high-dimensional non-stationary time series with piecewise smooth trends. Built on a novel and unified multiple-testing procedure of time-lagged cross-correlation functions with a fixed or diverging number of lags, our method can accurately disclose flexible time-varying network structures associated with complex functional structures at all time points. We broaden the applicability of our method to the structure breaks by developing difference-based nonparametric estimators of cross-correlations, achieve accurate family-wise error control via a bootstrap-assisted procedure adaptive to the complex temporal dynamics, and enhance the probability of recovering the time-varying network structures using a new uniform variance reduction technique. We prove the asymptotic validity of the proposed method and demonstrate its effectiveness in finite samples through simulation studies and empirical applications.

In this letter, a novel method for change detection is proposed using neighborhood structure correlation. Because structure features are insensitive to the intensity differences between bi-temporal images, we perform the correlation analysis on structure features rather than intensity information. First, we extract the structure feature maps by using multi-orientated gradient information. Then, the structure feature maps are used to obtain the Neighborhood Structural Correlation Image (NSCI), which can represent the context structure information. In addition, we introduce a measure named matching error which can be used to improve neighborhood information. Subsequently, a change detection model based on the random forest is constructed. The NSCI feature and matching error are used as the model inputs for training and prediction. Finally, the decision tree voting is used to produce the change detection result. To evaluate the performance of the proposed method, it was compared with three state-of-the-art change detection methods. The experimental results on two datasets demonstrated the effectiveness and robustness of the proposed method.

When deploying modern machine learning-enabled robotic systems in high-stakes applications, detecting distribution shift is critical. However, most existing methods for detecting distribution shift are not well-suited to robotics settings, where data often arrives in a streaming fashion and may be very high-dimensional. In this work, we present an online method for detecting distribution shift with guarantees on the false positive rate - i.e., when there is no distribution shift, our system is very unlikely (with probability $< \epsilon$) to falsely issue an alert; any alerts that are issued should therefore be heeded. Our method is specifically designed for efficient detection even with high dimensional data, and it empirically achieves up to 11x faster detection on realistic robotics settings compared to prior work while maintaining a low false negative rate in practice (whenever there is a distribution shift in our experiments, our method indeed emits an alert).

We introduce a high-order spline geometric approach for the initial boundary value problem for Maxwell's equations. The method is geometric in the sense that it discretizes in structure preserving fashion the two de Rham sequences of differential forms involved in the formulation of the continuous system. Both the Ampere--Maxwell and the Faraday equations are required to hold strongly, while to make the system solvable two discrete Hodge star operators are used. By exploiting the properties of the chosen spline spaces and concepts from exterior calculus, a non-standard explicit in time formulation is introduced, based on the solution of linear systems with matrices presenting Kronecker product structure, rather than mass matrices as in the standard literature. These matrices arise from the application of the exterior (wedge) product in the discrete setting, and they present Kronecker product structure independently of the geometry of the domain or the material parameters. The resulting scheme preserves the desirable energy conservation properties of the known approaches. The computational advantages of the newly proposed scheme are studied both through a complexity analysis and through numerical experiments in three dimensions.

Online changepoint detection algorithms that are based on likelihood-ratio tests have been shown to have excellent statistical properties. However, a simple online implementation is computationally infeasible as, at time $T$, it involves considering $O(T)$ possible locations for the change. Recently, the FOCuS algorithm has been introduced for detecting changes in mean in Gaussian data that decreases the per-iteration cost to $O(\log T)$. This is possible by using pruning ideas, which reduce the set of changepoint locations that need to be considered at time $T$ to approximately $\log T$. We show that if one wishes to perform the likelihood ratio test for a different one-parameter exponential family model, then exactly the same pruning rule can be used, and again one need only consider approximately $\log T$ locations at iteration $T$. Furthermore, we show how we can adaptively perform the maximisation step of the algorithm so that we need only maximise the test statistic over a small subset of these possible locations. Empirical results show that the resulting online algorithm, which can detect changes under a wide range of models, has a constant-per-iteration cost on average.

The majority of Americans fail to achieve recommended levels of physical activity, which leads to numerous preventable health problems such as diabetes, hypertension, and heart diseases. This has generated substantial interest in monitoring human activity to gear interventions toward environmental features that may relate to higher physical activity. Wearable devices, such as wrist-worn sensors that monitor gross motor activity (actigraph units) continuously record the activity levels of a subject, producing massive amounts of high-resolution measurements. Analyzing actigraph data needs to account for spatial and temporal information on trajectories or paths traversed by subjects wearing such devices. Inferential objectives include estimating a subject's physical activity levels along a given trajectory; identifying trajectories that are more likely to produce higher levels of physical activity for a given subject; and predicting expected levels of physical activity in any proposed new trajectory for a given set of health attributes. Here, we devise a Bayesian hierarchical modeling framework for spatial-temporal actigraphy data to deliver fully model-based inference on trajectories while accounting for subject-level health attributes and spatial-temporal dependencies. We undertake a comprehensive analysis of an original dataset from the Physical Activity through Sustainable Transport Approaches in Los Angeles (PASTA-LA) study to ascertain spatial zones and trajectories exhibiting significantly higher levels of physical activity while accounting for various sources of heterogeneity.

We consider the idealized setting of gradient flow on the population risk for infinitely wide two-layer ReLU neural networks (without bias), and study the effect of symmetries on the learned parameters and predictors. We first describe a general class of symmetries which, when satisfied by the target function $f^*$ and the input distribution, are preserved by the dynamics. We then study more specific cases. When $f^*$ is odd, we show that the dynamics of the predictor reduces to that of a (non-linearly parameterized) linear predictor, and its exponential convergence can be guaranteed. When $f^*$ has a low-dimensional structure, we prove that the gradient flow PDE reduces to a lower-dimensional PDE. Furthermore, we present informal and numerical arguments that suggest that the input neurons align with the lower-dimensional structure of the problem.

Motivated by the increasing need for fast processing of large-scale graphs, we study a number of fundamental graph problems in a message-passing model for distributed computing, called $k$-machine model, where we have $k$ machines that jointly perform computations on $n$-node graphs. The graph is assumed to be partitioned in a balanced fashion among the $k$ machines, a common implementation in many real-world systems. Communication is point-to-point via bandwidth-constrained links, and the goal is to minimize the round complexity, i.e., the number of communication rounds required to finish a computation. We present a generic methodology that allows to obtain efficient algorithms in the $k$-machine model using distributed algorithms for the classical CONGEST model of distributed computing. Using this methodology, we obtain algorithms for various fundamental graph problems such as connectivity, minimum spanning trees, shortest paths, maximal independent sets, and finding subgraphs, showing that many of these problems can be solved in $\tilde{O}(n/k)$ rounds; this shows that one can achieve speedup nearly linear in $k$. To complement our upper bounds, we present lower bounds on the round complexity that quantify the fundamental limitations of solving graph problems distributively. We first show a lower bound of $\Omega(n/k)$ rounds for computing a spanning tree of the input graph. This result implies the same bound for other fundamental problems such as computing a minimum spanning tree, breadth-first tree, or shortest paths tree. We also show a $\tilde \Omega(n/k^2)$ lower bound for connectivity, spanning tree verification and other related problems. The latter lower bounds follow from the development and application of novel results in a random-partition variant of the classical communication complexity model.

Parallel-in-time integration has been the focus of intensive research efforts over the past two decades due to the advent of massively parallel computer architectures and the scaling limits of purely spatial parallelization. Various iterative parallel-in-time (PinT) algorithms have been proposed, like Parareal, PFASST, MGRIT, and Space-Time Multi-Grid (STMG). These methods have been described using different notations, and the convergence estimates that are available are difficult to compare. We describe Parareal, PFASST, MGRIT and STMG for the Dahlquist model problem using a common notation and give precise convergence estimates using generating functions. This allows us, for the first time, to directly compare their convergence. We prove that all four methods eventually converge super-linearly, and also compare them numerically. The generating function framework provides further opportunities to explore and analyze existing and new methods.

Salient object detection is a problem that has been considered in detail and many solutions proposed. In this paper, we argue that work to date has addressed a problem that is relatively ill-posed. Specifically, there is not universal agreement about what constitutes a salient object when multiple observers are queried. This implies that some objects are more likely to be judged salient than others, and implies a relative rank exists on salient objects. The solution presented in this paper solves this more general problem that considers relative rank, and we propose data and metrics suitable to measuring success in a relative objects saliency landscape. A novel deep learning solution is proposed based on a hierarchical representation of relative saliency and stage-wise refinement. We also show that the problem of salient object subitizing can be addressed with the same network, and our approach exceeds performance of any prior work across all metrics considered (both traditional and newly proposed).