arXiv subjects

Yao Xie

Publications and source records attributed to Yao Xie.

At least 73 records · Page 4Linked to original sources

arXiv2024

Atlanta Gun Violence Modeling via Nonstationary Spatio-temporal Point Processes

Analysis of gun violence in the United States has utilized various models based on spatiotemporal point processes. Previous studies have identified a contagion effect in gun violence, characterized by bursts of diffusion across urban environments, which can be effectively represented using the self-excitatory spatiotemporal Hawkes process. The Hawkes process and its variants have been successful in modeling self-excitatory events, including earthquakes, disease outbreaks, financial market movements, neural activity, and the viral spread of memes on social networks. However, existing Hawkes models applied to gun violence often rely on simplistic stationary kernels, which fail to account for the complex, non-homogeneous spread of influence and impact over space and time. To address this limitation, we adopt a non-stationary spatiotemporal point process model that incorporates a neural network-based kernel to better represent the varied correlations among events of gun violence. Our study analyzes a comprehensive dataset of approximately 16,000 gunshot events in the Atlanta metropolitan area from 2021 to 2023. The cornerstone of our approach is the innovative non-stationary kernel, designed to enhance the model's expressiveness while preserving its interpretability. This approach not only demonstrates strong predictive performance but also provides insights into the spatiotemporal dynamics of gun violence and its propagation within urban settings.

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arXiv2024

Convergence of flow-based generative models via proximal gradient descent in Wasserstein space

Flow-based generative models enjoy certain advantages in computing the data generation and the likelihood, and have recently shown competitive empirical performance. Compared to the accumulating theoretical studies on related score-based diffusion models, analysis of flow-based models, which are deterministic in both forward (data-to-noise) and reverse (noise-to-data) directions, remain sparse. In this paper, we provide a theoretical guarantee of generating data distribution by a progressive flow model, the so-called JKO flow model, which implements the Jordan-Kinderleherer-Otto (JKO) scheme in a normalizing flow network. Leveraging the exponential convergence of the proximal gradient descent (GD) in Wasserstein space, we prove the Kullback-Leibler (KL) guarantee of data generation by a JKO flow model to be $O(\varepsilon^2)$ when using $N \lesssim \log (1/\varepsilon)$ many JKO steps ($N$ Residual Blocks in the flow) where $\varepsilon $ is the error in the per-step first-order condition. The assumption on data density is merely a finite second moment, and the theory extends to data distributions without density and when there are inversion errors in the reverse process where we obtain KL-$W_2$ mixed error guarantees. The non-asymptotic convergence rate of the JKO-type $W_2$-proximal GD is proved for a general class of convex objective functionals that includes the KL divergence as a special case, which can be of independent interest. The analysis framework can extend to other first-order Wasserstein optimization schemes applied to flow-based generative models.

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arXiv2024

Nonlinear time-series embedding by monotone variational inequality

In the wild, we often encounter collections of sequential data such as electrocardiograms, motion capture, genomes, and natural language, and sequences may be multichannel or symbolic with nonlinear dynamics. We introduce a new method to learn low-dimensional representations of nonlinear time series without supervision and can have provable recovery guarantees. The learned representation can be used for downstream machine-learning tasks such as clustering and classification. The method is based on the assumption that the observed sequences arise from a common domain, but each sequence obeys its own autoregressive models that are related to each other through low-rank regularization. We cast the problem as a computationally efficient convex matrix parameter recovery problem using monotone Variational Inequality and encode the common domain assumption via low-rank constraint across the learned representations, which can learn the geometry for the entire domain as well as faithful representations for the dynamics of each individual sequence using the domain information in totality. We show the competitive performance of our method on real-world time-series data with the baselines and demonstrate its effectiveness for symbolic text modeling and RNA sequence clustering.

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arXiv2024

Transformer Conformal Prediction for Time Series

We present a conformal prediction method for time series using the Transformer architecture to capture long-memory and long-range dependencies. Specifically, we use the Transformer decoder as a conditional quantile estimator to predict the quantiles of prediction residuals, which are used to estimate the prediction interval. We hypothesize that the Transformer decoder benefits the estimation of the prediction interval by learning temporal dependencies across past prediction residuals. Our comprehensive experiments using simulated and real data empirically demonstrate the superiority of the proposed method compared to the existing state-of-the-art conformal prediction methods.

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arXiv2024

Learning Cellular Network Connection Quality with Conformal

In this paper, we address the problem of uncertainty quantification for cellular network speed. It is a well-known fact that the actual internet speed experienced by a mobile phone can fluctuate significantly, even when remaining in a single location. This high degree of variability underscores that mere point estimation of network speed is insufficient. Rather, it is advantageous to establish a prediction interval that can encompass the expected range of speed variations. In order to build an accurate network estimation map, numerous mobile data need to be collected at different locations. Currently, public datasets rely on users to upload data through apps. Although massive data has been collected, the datasets suffer from significant noise due to the nature of cellular networks and various other factors. Additionally, the uneven distribution of population density affects the spatial consistency of data collection, leading to substantial uncertainty in the network quality maps derived from this data. We focus our analysis on large-scale internet-quality datasets provided by Ookla to construct an estimated map of connection quality. To improve the reliability of this map, we introduce a novel conformal prediction technique to build an uncertainty map. We identify regions with heightened uncertainty to prioritize targeted, manual data collection. In addition, the uncertainty map quantifies how reliable the prediction is in different areas. Our method also leads to a sampling strategy that guides researchers to selectively gather high-quality data that best complement the current dataset to improve the overall accuracy of the prediction model.

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arXiv2024

Conformal prediction for multi-dimensional time series by ellipsoidal sets

Conformal prediction (CP) has been a popular method for uncertainty quantification because it is distribution-free, model-agnostic, and theoretically sound. For forecasting problems in supervised learning, most CP methods focus on building prediction intervals for univariate responses. In this work, we develop a sequential CP method called $\texttt{MultiDimSPCI}$ that builds prediction $\textit{regions}$ for a multivariate response, especially in the context of multivariate time series, which are not exchangeable. Theoretically, we estimate $\textit{finite-sample}$ high-probability bounds on the conditional coverage gap. Empirically, we demonstrate that $\texttt{MultiDimSPCI}$ maintains valid coverage on a wide range of multivariate time series while producing smaller prediction regions than CP and non-CP baselines.

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arXiv2024

A Graph-Prediction-Based Approach for Debiasing Underreported Data

We present a novel Graph-based debiasing Algorithm for Underreported Data (GRAUD) aiming at an efficient joint estimation of event counts and discovery probabilities across spatial or graphical structures. This innovative method provides a solution to problems seen in fields such as policing data and COVID-$19$ data analysis. Our approach avoids the need for strong priors typically associated with Bayesian frameworks. By leveraging the graph structures on unknown variables $n$ and $p$, our method debiases the under-report data and estimates the discovery probability at the same time. We validate the effectiveness of our method through simulation experiments and illustrate its practicality in one real-world application: police 911 calls-to-service data.

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arXiv2024

Two-sample Test using Projected Wasserstein Distance

We develop a projected Wasserstein distance for the two-sample test, a fundamental problem in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. In particular, we aim to circumvent the curse of dimensionality in Wasserstein distance: when the dimension is high, it has diminishing testing power, which is inherently due to the slow concentration property of Wasserstein metrics in the high dimension space. A key contribution is to couple optimal projection to find the low dimensional linear mapping to maximize the Wasserstein distance between projected probability distributions. We characterize the theoretical property of the finite-sample convergence rate on IPMs and present practical algorithms for computing this metric. Numerical examples validate our theoretical results.

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arXiv2024

Generalizing to Unseen Domains with Wasserstein Distributional Robustness under Limited Source Knowledge

Domain generalization aims at learning a universal model that performs well on unseen target domains, incorporating knowledge from multiple source domains. In this research, we consider the scenario where different domain shifts occur among conditional distributions of different classes across domains. When labeled samples in the source domains are limited, existing approaches are not sufficiently robust. To address this problem, we propose a novel domain generalization framework called {Wasserstein Distributionally Robust Domain Generalization} (WDRDG), inspired by the concept of distributionally robust optimization. We encourage robustness over conditional distributions within class-specific Wasserstein uncertainty sets and optimize the worst-case performance of a classifier over these uncertainty sets. We further develop a test-time adaptation module leveraging optimal transport to quantify the relationship between the unseen target domain and source domains to make adaptive inference for target data. Experiments on the Rotated MNIST, PACS and the VLCS datasets demonstrate that our method could effectively balance the robustness and discriminability in challenging generalization scenarios.

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arXiv2024

Non-Convex Robust Hypothesis Testing using Sinkhorn Uncertainty Sets

We present a new framework to address the non-convex robust hypothesis testing problem, wherein the goal is to seek the optimal detector that minimizes the maximum of worst-case type-I and type-II risk functions. The distributional uncertainty sets are constructed to center around the empirical distribution derived from samples based on Sinkhorn discrepancy. Given that the objective involves non-convex, non-smooth probabilistic functions that are often intractable to optimize, existing methods resort to approximations rather than exact solutions. To tackle the challenge, we introduce an exact mixed-integer exponential conic reformulation of the problem, which can be solved into a global optimum with a moderate amount of input data. Subsequently, we propose a convex approximation, demonstrating its superiority over current state-of-the-art methodologies in literature. Furthermore, we establish connections between robust hypothesis testing and regularized formulations of non-robust risk functions, offering insightful interpretations. Our numerical study highlights the satisfactory testing performance and computational efficiency of the proposed framework.

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arXiv2024

An alternative approach to train neural networks using monotone variational inequality

We propose an alternative approach to neural network training using the monotone vector field, an idea inspired by the seminal work of Juditsky and Nemirovski [Juditsky & Nemirovsky, 2019] developed originally to solve parameter estimation problems for generalized linear models (GLM) by reducing the original non-convex problem to a convex problem of solving a monotone variational inequality (VI). Our approach leads to computationally efficient procedures that converge fast and offer guarantee in some special cases, such as training a single-layer neural network or fine-tuning the last layer of the pre-trained model. Our approach can be used for more efficient fine-tuning of a pre-trained model while freezing the bottom layers, an essential step for deploying many machine learning models such as large language models (LLM). We demonstrate its applicability in training fully-connected (FC) neural networks, graph neural networks (GNN), and convolutional neural networks (CNN) and show the competitive or better performance of our approach compared to stochastic gradient descent methods on both synthetic and real network data prediction tasks regarding various performance metrics.

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arXiv2024

Neural network-based CUSUM for online change-point detection

Change-point detection, detecting an abrupt change in the data distribution from sequential data, is a fundamental problem in statistics and machine learning. CUSUM is a popular statistical method for online change-point detection due to its efficiency from recursive computation and constant memory requirement, and it enjoys statistical optimality. CUSUM requires knowing the precise pre- and post-change distribution. However, post-change distribution is usually unknown a priori since it represents anomaly and novelty. Classic CUSUM can perform poorly when there is a model mismatch with actual data. While likelihood ratio-based methods encounter challenges facing high dimensional data, neural networks have become an emerging tool for change-point detection with computational efficiency and scalability. In this paper, we introduce a neural network CUSUM (NN-CUSUM) for online change-point detection. We also present a general theoretical condition when the trained neural networks can perform change-point detection and what losses can achieve our goal. We further extend our analysis by combining it with the Neural Tangent Kernel theory to establish learning guarantees for the standard performance metrics, including the average run length (ARL) and expected detection delay (EDD). The strong performance of NN-CUSUM is demonstrated in detecting change-point in high-dimensional data using both synthetic and real-world data.

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arXiv2024

Kernel Two-Sample Tests for Manifold Data

We present a study of a kernel-based two-sample test statistic related to the Maximum Mean Discrepancy (MMD) in the manifold data setting, assuming that high-dimensional observations are close to a low-dimensional manifold. We characterize the test level and power in relation to the kernel bandwidth, the number of samples, and the intrinsic dimensionality of the manifold. Specifically, when data densities $p$ and $q$ are supported on a $d$-dimensional sub-manifold ${M}$ embedded in an $m$-dimensional space and are Hölder with order $β$ (up to 2) on ${M}$, we prove a guarantee of the test power for finite sample size $n$ that exceeds a threshold depending on $d$, $β$, and $Δ_2$ the squared $L^2$-divergence between $p$ and $q$ on the manifold, and with a properly chosen kernel bandwidth $γ$. For small density departures, we show that with large $n$ they can be detected by the kernel test when $Δ_2$ is greater than $n^{- { 2 β/( d + 4 β) }}$ up to a certain constant and $γ$ scales as $n^{-1/(d+4β)}$. The analysis extends to cases where the manifold has a boundary and the data samples contain high-dimensional additive noise. Our results indicate that the kernel two-sample test has no curse-of-dimensionality when the data lie on or near a low-dimensional manifold. We validate our theory and the properties of the kernel test for manifold data through a series of numerical experiments.

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arXiv2024

Flow-based Distributionally Robust Optimization

We present a computationally efficient framework, called $\texttt{FlowDRO}$, for solving flow-based distributionally robust optimization (DRO) problems with Wasserstein uncertainty sets while aiming to find continuous worst-case distribution (also called the Least Favorable Distribution, LFD) and sample from it. The requirement for LFD to be continuous is so that the algorithm can be scalable to problems with larger sample sizes and achieve better generalization capability for the induced robust algorithms. To tackle the computationally challenging infinitely dimensional optimization problem, we leverage flow-based models and continuous-time invertible transport maps between the data distribution and the target distribution and develop a Wasserstein proximal gradient flow type algorithm. In theory, we establish the equivalence of the solution by optimal transport map to the original formulation, as well as the dual form of the problem through Wasserstein calculus and Brenier theorem. In practice, we parameterize the transport maps by a sequence of neural networks progressively trained in blocks by gradient descent. We demonstrate its usage in adversarial learning, distributionally robust hypothesis testing, and a new mechanism for data-driven distribution perturbation differential privacy, where the proposed method gives strong empirical performance on high-dimensional real data.

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arXiv2024

Normalizing flow neural networks by JKO scheme

Normalizing flow is a class of deep generative models for efficient sampling and likelihood estimation, which achieves attractive performance, particularly in high dimensions. The flow is often implemented using a sequence of invertible residual blocks. Existing works adopt special network architectures and regularization of flow trajectories. In this paper, we develop a neural ODE flow network called JKO-iFlow, inspired by the Jordan-Kinderleherer-Otto (JKO) scheme, which unfolds the discrete-time dynamic of the Wasserstein gradient flow. The proposed method stacks residual blocks one after another, allowing efficient block-wise training of the residual blocks, avoiding sampling SDE trajectories and score matching or variational learning, thus reducing the memory load and difficulty in end-to-end training. We also develop adaptive time reparameterization of the flow network with a progressive refinement of the induced trajectory in probability space to improve the model accuracy further. Experiments with synthetic and real data show that the proposed JKO-iFlow network achieves competitive performance compared with existing flow and diffusion models at a significantly reduced computational and memory cost.

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arXiv2024

Assessing Electricity Service Unfairness with Transfer Counterfactual Learning

Energy justice is a growing area of interest in interdisciplinary energy research. However, identifying systematic biases in the energy sector remains challenging due to confounding variables, intricate heterogeneity in counterfactual effects, and limited data availability. First, this paper demonstrates how one can evaluate counterfactual unfairness in a power system by analyzing the average causal effect of a specific protected attribute. Subsequently, we use subgroup analysis to handle model heterogeneity and introduce a novel method for estimating counterfactual unfairness based on transfer learning, which helps to alleviate the data scarcity in each subgroup. In our numerical analysis, we apply our method to a unique large-scale customer-level power outage data set and investigate the counterfactual effect of demographic factors, such as income and age of the population, on power outage durations. Our results indicate that low-income and elderly-populated areas consistently experience longer power outages under both daily and post-disaster operations, and such discrimination is exacerbated under severe conditions. These findings suggest a widespread, systematic issue of injustice in the power service systems and emphasize the necessity for focused interventions in disadvantaged communities.

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arXiv2024

Transfer Learning for Causal Effect Estimation

We present a Transfer Causal Learning (TCL) framework when target and source domains share the same covariate/feature spaces, aiming to improve causal effect estimation accuracy in limited data. Limited data is very common in medical applications, where some rare medical conditions, such as sepsis, are of interest. Our proposed method, named \texttt{$\ell_1$-TCL}, incorporates $\ell_1$ regularized TL for nuisance models (e.g., propensity score model); the TL estimator of the nuisance parameters is plugged into downstream average causal/treatment effect estimators (e.g., inverse probability weighted estimator). We establish non-asymptotic recovery guarantees for the \texttt{$\ell_1$-TCL} with generalized linear model (GLM) under the sparsity assumption in the high-dimensional setting, and demonstrate the empirical benefits of \texttt{$\ell_1$-TCL} through extensive numerical simulation for GLM and recent neural network nuisance models. Our method is subsequently extended to real data and generates meaningful insights consistent with medical literature, a case where all baseline methods fail.

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arXiv2023

Multi-resolution spatio-temporal prediction with application to wind power generation

Wind energy is becoming an increasingly crucial component of a sustainable grid, but its inherent variability and limited predictability present challenges for grid operators. The energy sector needs novel forecasting techniques that can precisely predict the generation of renewable power and offer precise quantification of prediction uncertainty. This will facilitate well-informed decision-making by operators who wish to integrate renewable energy into the power grid. This paper presents a novel approach to wind speed prediction with uncertainty quantification using a multi-resolution spatio-temporal Gaussian process. By leveraging information from multiple sources of predictions with varying accuracies and uncertainties, the joint framework provides a more accurate and robust prediction of wind speed while measuring the uncertainty in these predictions. We assess the effectiveness of our proposed framework using real-world wind data obtained from the Midwest region of the United States. Our results demonstrate that the framework enables predictors with varying data resolutions to learn from each other, leading to an enhancement in overall predictive performance. The proposed framework shows a superior performance compared to other state-of-the-art methods. The goal of this research is to improve grid operation and management by aiding system operators and policymakers in making better-informed decisions related to energy demand management, energy storage system deployment, and energy supply scheduling. This results in potentially further integration of renewable energy sources into the existing power systems.

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