arXiv subjects

Yao Xie

Publications and source records attributed to Yao Xie.

At least 109 records · Page 6Linked to original sources

arXiv2023

Conformal prediction for time series

We develop a general framework for constructing distribution-free prediction intervals for time series. Theoretically, we establish explicit bounds on conditional and marginal coverage gaps of estimated prediction intervals, which asymptotically converge to zero under additional assumptions. We obtain similar bounds on the size of set differences between oracle and estimated prediction intervals. Methodologically, we introduce a computationally efficient algorithm called \texttt{EnbPI} that wraps around ensemble predictors, which is closely related to conformal prediction (CP) but does not require data exchangeability. \texttt{EnbPI} avoids data-splitting and is computationally efficient by avoiding retraining and thus scalable to sequentially producing prediction intervals. We perform extensive simulation and real-data analyses to demonstrate its effectiveness compared with existing methods. We also discuss the extension of \texttt{EnbPI} on various other applications.

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arXiv2023

Causal Graph Discovery from Self and Mutually Exciting Time Series

We present a generalized linear structural causal model, coupled with a novel data-adaptive linear regularization, to recover causal directed acyclic graphs (DAGs) from time series. By leveraging a recently developed stochastic monotone Variational Inequality (VI) formulation, we cast the causal discovery problem as a general convex optimization. Furthermore, we develop a non-asymptotic recovery guarantee and quantifiable uncertainty by solving a linear program to establish confidence intervals for a wide range of non-linear monotone link functions. We validate our theoretical results and show the competitive performance of our method via extensive numerical experiments. Most importantly, we demonstrate the effectiveness of our approach in recovering highly interpretable causal DAGs over Sepsis Associated Derangements (SADs) while achieving comparable prediction performance to powerful ``black-box'' models such as XGBoost. Thus, the future adoption of our proposed method to conduct continuous surveillance of high-risk patients by clinicians is much more likely.

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arXiv2022

Online Score Statistics for Detecting Clustered Change in Network Point Processes

We consider online monitoring of the network event data to detect local changes in a cluster when the affected data stream distribution shifts from one point process to another with different parameters. Specifically, we are interested in detecting a change point that causes a shift of the underlying data distribution that follows a multivariate Hawkes process with exponential decay temporal kernel, whereby the Hawkes process is considered to account for spatio-temporal correlation between observations. The proposed detection procedure is based on scan score statistics. We derive the asymptotic distribution of the statistic, which enables the self-normalizing property and facilitates the approximation of the instantaneous false alarm probability and the average run length. When detecting a change in the Hawkes process with non-vanishing self-excitation, the procedure does not require estimating the post-change network parameter while assuming the temporal decay parameter, which enjoys computational efficiency. We further present an efficient procedure to accurately determine the false discovery rate via importance sampling, as validated by numerical examples. Using simulated and real stock exchange data, we show the effectiveness of the proposed method in detecting change while enjoying computational efficiency.

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arXiv2022

Tensor Kernel Recovery for Spatio-Temporal Hawkes Processes

We estimate the general influence functions for spatio-temporal Hawkes processes using a tensor recovery approach by formulating the location dependent influence function that captures the influence of historical events as a tensor kernel. We assume a low-rank structure for the tensor kernel and cast the estimation problem as a convex optimization problem using the Fourier transformed nuclear norm (TNN). We provide theoretical performance guarantees for our approach and present an algorithm to solve the optimization problem. Moreover, we demonstrate the efficiency of our estimation with numerical simulations.

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arXiv2022

Novelty Detection for Election Fraud: A Case Study with Agent-Based Simulation Data

In this paper, we propose a robust election simulation model and independently developed election anomaly detection algorithm that demonstrates the simulation's utility. The simulation generates artificial elections with similar properties and trends as elections from the real world, while giving users control and knowledge over all the important components of the elections. We generate a clean election results dataset without fraud as well as datasets with varying degrees of fraud. We then measure how well the algorithm is able to successfully detect the level of fraud present. The algorithm determines how similar actual election results are as compared to the predicted results from polling and a regression model of other regions that have similar demographics. We use k-means to partition electoral regions into clusters such that demographic homogeneity is maximized among clusters. We then use a novelty detection algorithm implemented as a one-class Support Vector Machine where the clean data is provided in the form of polling predictions and regression predictions. The regression predictions are built from the actual data in such a way that the data supervises itself. We show both the effectiveness of the simulation technique and the machine learning model in its success in identifying fraudulent regions.

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arXiv2022

Online Detection Of Supply Chain Network Disruptions Using Sequential Change-Point Detection for Hawkes Processes

In this paper, we attempt to detect an inflection or change-point resulting from the Covid-19 pandemic on supply chain data received from a large furniture company. To accomplish this, we utilize a modified CUSUM (Cumulative Sum) procedure on the company's spatial-temporal order data as well as a GLR (Generalized Likelihood Ratio) based method. We model the order data using the Hawkes Process Network, a multi-dimensional self and mutually exciting point process, by discretizing the spatial data and treating each order as an event that has a corresponding node and time. We apply the methodologies on the company's most ordered item on a national scale and perform a deep dive into a single state. Because the item was ordered infrequently in the state compared to the nation, this approach allows us to show efficacy upon different degrees of data sparsity. Furthermore, it showcases use potential across differing levels of spatial detail.

cs.LG↗

arXiv2022

Invertible Neural Networks for Graph Prediction

Graph prediction problems prevail in data analysis and machine learning. The inverse prediction problem, namely to infer input data from given output labels, is of emerging interest in various applications. In this work, we develop \textit{invertible graph neural network} (iGNN), a deep generative model to tackle the inverse prediction problem on graphs by casting it as a conditional generative task. The proposed model consists of an invertible sub-network that maps one-to-one from data to an intermediate encoded feature, which allows forward prediction by a linear classification sub-network as well as efficient generation from output labels via a parametric mixture model. The invertibility of the encoding sub-network is ensured by a Wasserstein-2 regularization which allows free-form layers in the residual blocks. The model is scalable to large graphs by a factorized parametric mixture model of the encoded feature and is computationally scalable by using GNN layers. The existence of invertible flow mapping is backed by theories of optimal transport and diffusion process, and we prove the expressiveness of graph convolution layers to approximate the theoretical flows of graph data. The proposed iGNN model is experimentally examined on synthetic data, including the example on large graphs, and the empirical advantage is also demonstrated on real-application datasets of solar ramping event data and traffic flow anomaly detection.

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arXiv2022

Spatio-temporal point processes with deep non-stationary kernels

Point process data are becoming ubiquitous in modern applications, such as social networks, health care, and finance. Despite the powerful expressiveness of the popular recurrent neural network (RNN) models for point process data, they may not successfully capture sophisticated non-stationary dependencies in the data due to their recurrent structures. Another popular type of deep model for point process data is based on representing the influence kernel (rather than the intensity function) by neural networks. We take the latter approach and develop a new deep non-stationary influence kernel that can model non-stationary spatio-temporal point processes. The main idea is to approximate the influence kernel with a novel and general low-rank decomposition, enabling efficient representation through deep neural networks and computational efficiency and better performance. We also take a new approach to maintain the non-negativity constraint of the conditional intensity by introducing a log-barrier penalty. We demonstrate our proposed method's good performance and computational efficiency compared with the state-of-the-art on simulated and real data.

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arXiv2022

Data-Adaptive Symmetric CUSUM for Sequential Change Detection

Detecting change points sequentially in a streaming setting, especially when both the mean and the variance of the signal can change, is often a challenging task. A key difficulty in this context often involves setting an appropriate detection threshold, which for many standard change statistics may need to be tuned depending on the pre-change and post-change distributions. This presents a challenge in a sequential change detection setting when a signal switches between multiple distributions. For example, consider a signal where change points are indicated by increases/decreases in the mean and variance of the signal. In this context, we would like to be able to compare our change statistic to a fixed threshold that will be symmetric to either increases or decreases in the mean and variance. Unfortunately, change point detection schemes that use the log-likelihood ratio, such as CUSUM and GLR, are quick to react to changes but are not symmetric when both the mean and the variance of the signal change. This makes it difficult to set a single threshold to detect multiple change points sequentially in a streaming setting. We propose a modified version of CUSUM that we call Data-Adaptive Symmetric CUSUM (DAS-CUSUM). The DAS-CUSUM change point detection procedure is symmetric for changes between distributions, making it suitable to set a single threshold to detect multiple change points sequentially in a streaming setting. We provide results that relate to the expected detection delay and average run length for our proposed procedure. Extensive simulations are used to validate these results. Experiments on real-world data further show the utility of using DAS-CUSUM over both CUSUM and GLR.

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arXiv2022

Online Critical-State Detection of Sepsis Among ICU Patients using Jensen-Shannon Divergence

Sepsis is a severe medical condition caused by a dysregulated host response to infection that has a high incidence and mortality rate. Even with such a high-level occurrence rate, the detection and diagnosis of sepsis continues to pose a challenge. There is a crucial need to accurately forecast the onset of sepsis promptly while also identifying the specific physiologic anomalies that contribute to this prediction in an interpretable fashion. This study proposes a novel approach to quantitatively measure the difference between patients and a reference group using non-parametric probability distribution estimates and highlight when abnormalities emerge using a Jensen-Shannon divergence-based single sample analysis approach. We show that we can quantitatively distinguish between these two groups and offer a measurement of divergence in real time while simultaneously identifying specific physiologic factors contributing to patient outcomes. We demonstrate our approach on a real-world dataset of patients admitted to Atlanta, Georgia's Grady Hospital.

stat.AP↗

arXiv2022

Solar Radiation Ramping Events Modeling Using Spatio-temporal Point Processes

Modeling and predicting solar events, particularly the solar ramping event, is critical for improving situational awareness for solar power generation systems. It has been acknowledged that weather conditions such as temperature, humidity, and cloud density can significantly impact the emergence and position of solar ramping events. As a result, modeling these events with complex spatio-temporal correlations is highly challenging. To tackle the question, we adopt a novel spatio-temporal categorical point process model, which intuitively and effectively addresses correlation and interaction among ramping events. We demonstrate the interpretability and predictive power of our model on extensive real-data experiments.

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arXiv2022

Conformal prediction set for time-series

When building either prediction intervals for regression (with real-valued response) or prediction sets for classification (with categorical responses), uncertainty quantification is essential to studying complex machine learning methods. In this paper, we develop Ensemble Regularized Adaptive Prediction Set (ERAPS) to construct prediction sets for time-series (with categorical responses), based on the prior work of [Xu and Xie, 2021]. In particular, we allow unknown dependencies to exist within features and responses that arrive in sequence. Method-wise, ERAPS is a distribution-free and ensemble-based framework that is applicable for arbitrary classifiers. Theoretically, we bound the coverage gap without assuming data exchangeability and show asymptotic set convergence. Empirically, we demonstrate valid marginal and conditional coverage by ERAPS, which also tends to yield smaller prediction sets than competing methods.

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arXiv2022

A Data-Driven Approach to Robust Hypothesis Testing Using Sinkhorn Uncertainty Sets

Hypothesis testing for small-sample scenarios is a practically important problem. In this paper, we investigate the robust hypothesis testing problem in a data-driven manner, where we seek the worst-case detector over distributional uncertainty sets centered around the empirical distribution from samples using Sinkhorn distance. Compared with the Wasserstein robust test, the corresponding least favorable distributions are supported beyond the training samples, which provides a more flexible detector. Various numerical experiments are conducted on both synthetic and real datasets to validate the competitive performances of our proposed method.

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arXiv2022

Bayesian Uncertainty Quantification for Low-Rank Matrix Completion

We consider the problem of uncertainty quantification for an unknown low-rank matrix $\mathbf{X}$, given a partial and noisy observation of its entries. This quantification of uncertainty is essential for many real-world problems, including image processing, satellite imaging, and seismology, providing a principled framework for validating scientific conclusions and guiding decision-making. However, existing literature has mainly focused on the completion (i.e., point estimation) of the matrix $\mathbf{X}$, with little work on investigating its uncertainty. To this end, we propose in this work a new Bayesian modeling framework, called BayeSMG, which parametrizes the unknown $\mathbf{X}$ via its underlying row and column subspaces. This Bayesian subspace parametrization enables efficient posterior inference on matrix subspaces, which represents interpretable phenomena in many applications. This can then be leveraged for improved matrix recovery. We demonstrate the effectiveness of BayeSMG over existing Bayesian matrix recovery methods in numerical experiments, image inpainting, and a seismic sensor network application.

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arXiv2022

PERCEPT: a new online change-point detection method using topological data analysis

Topological data analysis (TDA) provides a set of data analysis tools for extracting embedded topological structures from complex high-dimensional datasets. In recent years, TDA has been a rapidly growing field which has found success in a wide range of applications, including signal processing, neuroscience and network analysis. In these applications, the online detection of changes is of crucial importance, but this can be highly challenging since such changes often occur in a low-dimensional embedding within high-dimensional data streams. We thus propose a new method, called PERsistence diagram-based ChangE-PoinT detection (PERCEPT), which leverages the learned topological structure from TDA to sequentially detect changes. PERCEPT follows two key steps: it first learns the embedded topology as a point cloud via persistence diagrams, then applies a non-parametric monitoring approach for detecting changes in the resulting point cloud distributions. This yields a non-parametric, topology-aware framework which can efficiently detect online changes from high-dimensional data streams. We investigate the effectiveness of PERCEPT over existing methods in a suite of numerical experiments where the data streams have an embedded topological structure. We then demonstrate the usefulness of PERCEPT in two applications in solar flare monitoring and human gesture detection.

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arXiv2022

Sequential change-point detection for mutually exciting point processes over networks

We present a new CUSUM procedure for sequentially detecting change-point in the self and mutual exciting processes, a.k.a. Hawkes networks using discrete events data. Hawkes networks have become a popular model for statistics and machine learning due to their capability in modeling irregularly observed data where the timing between events carries a lot of information. The problem of detecting abrupt changes in Hawkes networks arises from various applications, including neuronal imaging, sensor network, and social network monitoring. Despite this, there has not been a computationally and memory-efficient online algorithm for detecting such changes from sequential data. We present an efficient online recursive implementation of the CUSUM statistic for Hawkes processes, both decentralized and memory-efficient, and establish the theoretical properties of this new CUSUM procedure. We then show that the proposed CUSUM method achieves better performance than existing methods, including the Shewhart procedure based on count data, the generalized likelihood ratio (GLR) in the existing literature, and the standard score statistic. We demonstrate this via a simulated example and an application to population code change-detection in neuronal networks.

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arXiv2022

Two-sample Test with Kernel Projected Wasserstein Distance

We develop a kernel projected Wasserstein distance for the two-sample test, an essential building block in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. This method operates by finding the nonlinear mapping in the data space which maximizes the distance between projected distributions. In contrast to existing works about projected Wasserstein distance, the proposed method circumvents the curse of dimensionality more efficiently. We present practical algorithms for computing this distance function together with the non-asymptotic uncertainty quantification of empirical estimates. Numerical examples validate our theoretical results and demonstrate good performance of the proposed method.

math.ST↗

arXiv2022

Distributionally Robust Weighted $k$-Nearest Neighbors

Learning a robust classifier from a few samples remains a key challenge in machine learning. A major thrust of research has been focused on developing $k$-nearest neighbor ($k$-NN) based algorithms combined with metric learning that captures similarities between samples. When the samples are limited, robustness is especially crucial to ensure the generalization capability of the classifier. In this paper, we study a minimax distributionally robust formulation of weighted $k$-nearest neighbors, which aims to find the optimal weighted $k$-NN classifiers that hedge against feature uncertainties. We develop an algorithm, \texttt{Dr.k-NN}, that efficiently solves this functional optimization problem and features in assigning minimax optimal weights to training samples when performing classification. These weights are class-dependent, and are determined by the similarities of sample features under the least favorable scenarios. When the size of the uncertainty set is properly tuned, the robust classifier has a smaller Lipschitz norm than the vanilla $k$-NN, and thus improves the generalization capability. We also couple our framework with neural-network-based feature embedding. We demonstrate the competitive performance of our algorithm compared to the state-of-the-art in the few-training-sample setting with various real-data experiments.

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