arXiv subjects

Yao Xie

Publications and source records attributed to Yao Xie.

At least 145 records · Page 8Linked to original sources

arXiv2021

Sequential Change Detection by Optimal Weighted $\ell_2$ Divergence

We present a new non-parametric statistic, called the weighed $\ell_2$ divergence, based on empirical distributions for sequential change detection. We start by constructing the weighed $\ell_2$ divergence as a fundamental building block for two-sample tests and change detection. The proposed statistic is proved to attain the optimal sample complexity in the offline setting. We then study the sequential change detection using the weighed $\ell_2$ divergence and characterize the fundamental performance metrics, including the average run length (ARL) and the expected detection delay (EDD). We also present practical algorithms to find the optimal projection to handle high-dimensional data and the optimal weights, which is critical to quick detection since, in such settings, there are not many post-change samples. Simulation results and real data examples are provided to validate the good performance of the proposed method.

math.ST↗

arXiv2021

Deep Fourier Kernel for Self-Attentive Point Processes

We present a novel attention-based model for discrete event data to capture complex non-linear temporal dependence structures. We borrow the idea from the attention mechanism and incorporate it into the point processes' conditional intensity function. We further introduce a novel score function using Fourier kernel embedding, whose spectrum is represented using neural networks, which drastically differs from the traditional dot-product kernel and can capture a more complex similarity structure. We establish our approach's theoretical properties and demonstrate our approach's competitive performance compared to the state-of-the-art for synthetic and real data.

stat.ML↗

arXiv2021

Goodness-of-Fit Test for Mismatched Self-Exciting Processes

Recently there have been many research efforts in developing generative models for self-exciting point processes, partly due to their broad applicability for real-world applications. However, rarely can we quantify how well the generative model captures the nature or ground-truth since it is usually unknown. The challenge typically lies in the fact that the generative models typically provide, at most, good approximations to the ground-truth (e.g., through the rich representative power of neural networks), but they cannot be precisely the ground-truth. We thus cannot use the classic goodness-of-fit (GOF) test framework to evaluate their performance. In this paper, we develop a GOF test for generative models of self-exciting processes by making a new connection to this problem with the classical statistical theory of Quasi-maximum-likelihood estimator (QMLE). We present a non-parametric self-normalizing statistic for the GOF test: the Generalized Score (GS) statistics, and explicitly capture the model misspecification when establishing the asymptotic distribution of the GS statistic. Numerical simulation and real-data experiments validate our theory and demonstrate the proposed GS test's good performance.

math.ST↗

arXiv2021

Optimality of Graph Scanning Statistic for Online Community Detection

Sequential change-point detection for graphs is a fundamental problem for streaming network data types and has wide applications in social networks and power systems. Given fixed vertices and a sequence of random graphs, the objective is to detect the change-point where the underlying distribution of the random graph changes. In particular, we focus on the local change that only affects a subgraph. We adopt the classical Erdos-Renyi model and revisit the generalized likelihood ratio (GLR) detection procedure. The scan statistic is computed by sequentially estimating the most-likely subgraph where the change happens. We provide theoretical analysis for the asymptotic optimality of the proposed procedure based on the GLR framework. We demonstrate the efficiency of our detection algorithm using simulations.

math.ST↗

arXiv2021

Balanced Districting on Grid Graphs with Provable Compactness and Contiguity

Given a graph $G = (V,E)$ with vertex weights $w(v)$ and a desired number of parts $k$, the goal in graph partitioning problems is to partition the vertex set V into parts $V_1,\ldots,V_k$. Metrics for compactness, contiguity, and balance of the parts $V_i$ are frequent objectives, with much existing literature focusing on compactness and balance. Revisiting an old method known as striping, we give the first polynomial-time algorithms with guaranteed contiguity and provable bicriteria approximations for compactness and balance for planar grid graphs. We consider several types of graph partitioning, including when vertex weights vary smoothly or are stochastic, reflecting concerns in various real-world instances. We show significant improvements in experiments for balancing workloads for the fire department and reducing over-policing using 911 call data from South Fulton, GA.

cs.DS↗

arXiv2021

Online detection of cascading change-points

We propose an online detection procedure for cascading failures in the network from sequential data, which can be modeled as multiple correlated change-points happening during a short period. We consider a temporal diffusion network model to capture the temporal dynamic structure of multiple change-points and develop a sequential Shewhart procedure based on the generalized likelihood ratio statistics based on the diffusion network model assuming unknown post-change distribution parameters. We also tackle the computational complexity posed by the unknown propagation. Numerical experiments demonstrate the good performance for detecting cascade failures.

stat.OT↗

arXiv2021

Inferring serial correlation with dynamic backgrounds

Sequential data with serial correlation and an unknown, unstructured, and dynamic background is ubiquitous in neuroscience, psychology, and econometrics. Inferring serial correlation for such data is a fundamental challenge in statistics. We propose a total variation constrained least square estimator coupled with hypothesis tests to infer the serial correlation in the presence of unknown and unstructured dynamic background. The total variation constraint on the dynamic background encourages a piece-wise constant structure, which can approximate a wide range of dynamic backgrounds. The tuning parameter is selected via the Ljung-Box test to control the bias-variance trade-off. We establish a non-asymptotic upper bound for the estimation error through variational inequalities. We also derive a lower error bound via Fano's method and show the proposed method is near-optimal. Numerical simulation and a real study in psychology demonstrate the excellent performance of our proposed method compared with the state-of-the-art.

math.ST↗

arXiv2021

Testing Rank of Incomplete Unimodal Matrices

Several statistics-based detectors, based on unimodal matrix models, for determining the number of sources in a field are designed. A new variance ratio statistic is proposed, and its asymptotic distribution is analyzed. The variance ratio detector is shown to outperform the alternatives. It is shown that further improvements are achievable via optimally selected rotations. Numerical experiments demonstrate the performance gains of our detection methods over the baseline approach.

stat.AP↗

arXiv2021

Imitation Learning of Neural Spatio-Temporal Point Processes

We present a novel Neural Embedding Spatio-Temporal (NEST) point process model for spatio-temporal discrete event data and develop an efficient imitation learning (a type of reinforcement learning) based approach for model fitting. Despite the rapid development of one-dimensional temporal point processes for discrete event data, the study of spatial-temporal aspects of such data is relatively scarce. Our model captures complex spatio-temporal dependence between discrete events by carefully design a mixture of heterogeneous Gaussian diffusion kernels, whose parameters are parameterized by neural networks. This new kernel is the key that our model can capture intricate spatial dependence patterns and yet still lead to interpretable results as we examine maps of Gaussian diffusion kernel parameters. The imitation learning model fitting for the NEST is more robust than the maximum likelihood estimate. It directly measures the divergence between the empirical distributions between the training data and the model-generated data. Moreover, our imitation learning-based approach enjoys computational efficiency due to the explicit characterization of the reward function related to the likelihood function; furthermore, the likelihood function under our model enjoys tractable expression due to Gaussian kernel parameterization. Experiments based on real data show our method's good performance relative to the state-of-the-art and the good interpretability of NEST's result.

cs.LG↗

arXiv2020

Learning Temporal Point Processes via Reinforcement Learning

Social goods, such as healthcare, smart city, and information networks, often produce ordered event data in continuous time. The generative processes of these event data can be very complex, requiring flexible models to capture their dynamics. Temporal point processes offer an elegant framework for modeling event data without discretizing the time. However, the existing maximum-likelihood-estimation (MLE) learning paradigm requires hand-crafting the intensity function beforehand and cannot directly monitor the goodness-of-fit of the estimated model in the process of training. To alleviate the risk of model-misspecification in MLE, we propose to generate samples from the generative model and monitor the quality of the samples in the process of training until the samples and the real data are indistinguishable. We take inspiration from reinforcement learning (RL) and treat the generation of each event as the action taken by a stochastic policy. We parameterize the policy as a flexible recurrent neural network and gradually improve the policy to mimic the observed event distribution. Since the reward function is unknown in this setting, we uncover an analytic and nonparametric form of the reward function using an inverse reinforcement learning formulation. This new RL framework allows us to derive an efficient policy gradient algorithm for learning flexible point process models, and we show that it performs well in both synthetic and real data.

cs.LG↗

arXiv2020

Convex Parameter Recovery for Interacting Marked Processes

We introduce a new general modeling approach for multivariate discrete event data with categorical interacting marks, which we refer to as marked Bernoulli processes. In the proposed model, the probability of an event of a specific category to occur in a location may be influenced by past events at this and other locations. We do not restrict interactions to be positive or decaying over time as it is commonly adopted, allowing us to capture an arbitrary shape of influence from historical events, locations, and events of different categories. In our modeling, prior knowledge is incorporated by allowing general convex constraints on model parameters. We develop two parameter estimation procedures utilizing the constrained Least Squares (LS) and Maximum Likelihood (ML) estimation, which are solved using variational inequalities with monotone operators. We discuss different applications of our approach and illustrate the performance of proposed recovery routines on synthetic examples and a real-world police dataset.

math.ST↗

arXiv2020

On characteristic rank for matrix and tensor completion

In this lecture note, we discuss a fundamental concept, referred to as the {\it characteristic rank}, which suggests a general framework for characterizing the basic properties of various low-dimensional models used in signal processing. Below, we illustrate this framework using two examples: matrix and three-way tensor completion problems, and consider basic properties include identifiability of a matrix or tensor, given partial observations. In this note, we consider cases without observation noise to illustrate the principle.

math.ST↗

arXiv2020

Goodness-of-fit tests on manifolds

We develop a general theory for the goodness-of-fit test to non-linear models. In particular, we assume that the observations are noisy samples of a submanifold defined by a \yao{sufficiently smooth non-linear map}. The observation noise is additive Gaussian. Our main result shows that the "residual" of the model fit, by solving a non-linear least-square problem, follows a (possibly noncentral) $χ^2$ distribution. The parameters of the $χ^2$ distribution are related to the model order and dimension of the problem. We further present a method to select the model orders sequentially. We demonstrate the broad application of the general theory in machine learning and signal processing, including determining the rank of low-rank (possibly complex-valued) matrices and tensors from noisy, partial, or indirect observations, determining the number of sources in signal demixing, and potential applications in determining the number of hidden nodes in neural networks.

stat.ML↗

arXiv2020

Uncertainty Quantification for Inferring Hawkes Networks

Multivariate Hawkes processes are commonly used to model streaming networked event data in a wide variety of applications. However, it remains a challenge to extract reliable inference from complex datasets with uncertainty quantification. Aiming towards this, we develop a statistical inference framework to learn causal relationships between nodes from networked data, where the underlying directed graph implies Granger causality. We provide uncertainty quantification for the maximum likelihood estimate of the network multivariate Hawkes process by providing a non-asymptotic confidence set. The main technique is based on the concentration inequalities of continuous-time martingales. We compare our method to the previously-derived asymptotic Hawkes process confidence interval, and demonstrate the strengths of our method in an application to neuronal connectivity reconstruction.

stat.ML↗

arXiv2020

CheXplain: Enabling Physicians to Explore and UnderstandData-Driven, AI-Enabled Medical Imaging Analysis

The recent development of data-driven AI promises to automate medical diagnosis; however, most AI functions as 'black boxes' to physicians with limited computational knowledge. Using medical imaging as a point of departure, we conducted three iterations of design activities to formulate CheXplain---a system that enables physicians to explore and understand AI-enabled chest X-ray analysis: (1) a paired survey between referring physicians and radiologists reveals whether, when, and what kinds of explanations are needed; (2) a low-fidelity prototype co-designed with three physicians formulates eight key features; and (3) a high-fidelity prototype evaluated by another six physicians provides detailed summative insights on how each feature enables the exploration and understanding of AI. We summarize by discussing recommendations for future work to design and implement explainable medical AI systems that encompass four recurring themes: motivation, constraint, explanation, and justification.

cs.HC↗

arXiv2019

Learning Transformation Synchronization

Reconstructing the 3D model of a physical object typically requires us to align the depth scans obtained from different camera poses into the same coordinate system. Solutions to this global alignment problem usually proceed in two steps. The first step estimates relative transformations between pairs of scans using an off-the-shelf technique. Due to limited information presented between pairs of scans, the resulting relative transformations are generally noisy. The second step then jointly optimizes the relative transformations among all input depth scans. A natural constraint used in this step is the cycle-consistency constraint, which allows us to prune incorrect relative transformations by detecting inconsistent cycles. The performance of such approaches, however, heavily relies on the quality of the input relative transformations. Instead of merely using the relative transformations as the input to perform transformation synchronization, we propose to use a neural network to learn the weights associated with each relative transformation. Our approach alternates between transformation synchronization using weighted relative transformations and predicting new weights of the input relative transformations using a neural network. We demonstrate the usefulness of this approach across a wide range of datasets.

cs.CV↗

arXiv2019

An Approximation Algorithm for training One-Node ReLU Neural Network

Training a one-node neural network with ReLU activation function (One-Node-ReLU) is a fundamental optimization problem in deep learning. In this paper, we begin with proving the NP-hardness of training One-Node-ReLU. We then present an approximation algorithm to solve One-Node-ReLU whose running time is $\mathcal{O}(n^k)$ where $n$ is the number of samples, $k$ is a predefined integral constant. Except $k$, this algorithm does not require pre-processing or tuning of parameters. We analyze the performance of this algorithm under various regimes. First, given any arbitrary set of training sample data set, we show that the algorithm guarantees a $\frac{n}{k}$-approximation for training One-Node-ReLU problem. As a consequence, in the realizable case (i.e. when the training error is zero), this approximation algorithm achieves the global optimal solution for the One-Node-ReLU problem. Second, we assume that the training sample data is obtained from an underlying one-node neural network with ReLU activation function, where the output is perturbed by a Gaussian noise. In this regime, we show that the same approximation algorithm guarantees a much better asymptotic approximation ratio which is independent of the number of samples $n$. Finally, we conduct extensive empirical studies and arrive at two conclusions. One, the approximation algorithm together with some heuristic performs better than gradient descent algorithm. Two, the solution of the approximation algorithm can be used as starting point for gradient descent -- a combination that works significantly better than gradient descent.

math.OC↗

arXiv2019

Deep Zero-Shot Learning for Scene Sketch

We introduce a novel problem of scene sketch zero-shot learning (SSZSL), which is a challenging task, since (i) different from photo, the gap between common semantic domain (e.g., word vector) and sketch is too huge to exploit common semantic knowledge as the bridge for knowledge transfer, and (ii) compared with single-object sketch, more expressive feature representation for scene sketch is required to accommodate its high-level of abstraction and complexity. To overcome these challenges, we propose a deep embedding model for scene sketch zero-shot learning. In particular, we propose the augmented semantic vector to conduct domain alignment by fusing multi-modal semantic knowledge (e.g., cartoon image, natural image, text description), and adopt attention-based network for scene sketch feature learning. Moreover, we propose a novel distance metric to improve the similarity measure during testing. Extensive experiments and ablation studies demonstrate the benefit of our sketch-specific design.

cs.CV↗