arXiv subjects

Zifeng Zhao

Publications and source records attributed to Zifeng Zhao.

28 records · Page 2Linked to original sources

arXiv2022

Change-point Detection for Sparse and Dense Functional Data in General Dimensions

We study the problem of change-point detection and localisation for functional data sequentially observed on a general d-dimensional space, where we allow the functional curves to be either sparsely or densely sampled. Data of this form naturally arise in a wide range of applications such as biology, neuroscience, climatology, and finance. To achieve such a task, we propose a kernel-based algorithm named functional seeded binary segmentation (FSBS). FSBS is computationally efficient, can handle discretely observed functional data, and is theoretically sound for heavy-tailed and temporally-dependent observations. Moreover, FSBS works for a general d-dimensional domain, which is the first in the literature of change-point estimation for functional data. We show the consistency of FSBS for multiple change-point estimations and further provide a sharp localisation error rate, which reveals an interesting phase transition phenomenon depending on the number of functional curves observed and the sampling frequency for each curve. Extensive numerical experiments illustrate the effectiveness of FSBS and its advantage over existing methods in the literature under various settings. A real data application is further conducted, where FSBS localises change-points of sea surface temperature patterns in the south Pacific attributed to El Nino.

stat.ME↗

arXiv2022

Speaker-Aware Mixture of Mixtures Training for Weakly Supervised Speaker Extraction

Dominant researches adopt supervised training for speaker extraction, while the scarcity of ideally clean corpus and channel mismatch problem are rarely considered. To this end, we propose speaker-aware mixture of mixtures training (SAMoM), utilizing the consistency of speaker identity among target source, enrollment utterance and target estimate to weakly supervise the training of a deep speaker extractor. In SAMoM, the input is constructed by mixing up different speaker-aware mixtures (SAMs), each contains multiple speakers with their identities known and enrollment utterances available. Informed by enrollment utterances, target speech is extracted from the input one by one, such that the estimated targets can approximate the original SAMs after a remix in accordance with the identity consistency. Moreover, using SAMoM in a semi-supervised setting with a certain amount of clean sources enables application in noisy scenarios. Extensive experiments on Libri2Mix show that the proposed method achieves promising results without access to any clean sources (11.06dB SI-SDRi). With a domain adaptation, our approach even outperformed supervised framework in a cross-domain evaluation on AISHELL-1.

eess.AS↗

arXiv2022

Target Confusion in End-to-end Speaker Extraction: Analysis and Approaches

Recently, end-to-end speaker extraction has attracted increasing attention and shown promising results. However, its performance is often inferior to that of a blind source separation (BSS) counterpart with a similar network architecture, due to the auxiliary speaker encoder may sometimes generate ambiguous speaker embeddings. Such ambiguous guidance information may confuse the separation network and hence lead to wrong extraction results, which deteriorates the overall performance. We refer to this as the target confusion problem. In this paper, we conduct an analysis of such an issue and solve it in two stages. In the training phase, we propose to integrate metric learning methods to improve the distinguishability of embeddings produced by the speaker encoder. While for inference, a novel post-filtering strategy is designed to revise the wrong results. Specifically, we first identify these confusion samples by measuring the similarities between output estimates and enrollment utterances, after which the true target sources are recovered by a subtraction operation. Experiments show that performance improvement of more than 1dB SI-SDRi can be brought, which validates the effectiveness of our methods and emphasizes the impact of the target confusion problem.

eess.AS↗

arXiv2021

Statistically and Computationally Efficient Change Point Localization in Regression Settings

Detecting when the underlying distribution changes for the observed time series is a fundamental problem arising in a broad spectrum of applications. In this paper, we study multiple change-point localization in the high-dimensional regression setting, which is particularly challenging as no direct observations of the parameter of interest is available. Specifically, we assume we observe $\{ x_t, y_t\}_{t=1}^n$ where $ \{ x_t\}_{t=1}^n $ are $p$-dimensional covariates, $\{y_t\}_{t=1}^n$ are the univariate responses satisfying $\mathbb{E}(y_t) = x_t^\top β_t^* \text{ for } 1\le t \le n $ and $\{β_t^*\}_{t=1}^n $ are the unobserved regression coefficients that change over time in a piecewise constant manner. We propose a novel projection-based algorithm, Variance Projected Wild Binary Segmentation~(VPWBS), which transforms the original (difficult) problem of change-point detection in $p$-dimensional regression to a simpler problem of change-point detection in mean of a one-dimensional time series. VPWBS is shown to achieve sharp localization rate $O_p(1/n)$ up to a log factor, a significant improvement from the best rate $O_p(1/\sqrt{n})$ known in the existing literature for multiple change-point localization in high-dimensional regression. Extensive numerical experiments are conducted to demonstrate the robust and favorable performance of VPWBS over two state-of-the-art algorithms, especially when the size of change in the regression coefficients $\{β_t^*\}_{t=1}^n $ is small.

math.ST↗

arXiv2021

Alternating Pruned Dynamic Programming for Multiple Epidemic Change-Point Estimation

In this paper, we study the problem of multiple change-point detection for a univariate sequence under the epidemic setting, where the behavior of the sequence alternates between a common normal state and different epidemic states. This is a non-trivial generalization of the classical (single) epidemic change-point testing problem. To explicitly incorporate the alternating structure of the problem, we propose a novel model selection based approach for simultaneous inference on both change-points and alternating states. Using the same spirit as profile likelihood, we develop a two-stage alternating pruned dynamic programming algorithm, which conducts efficient and exact optimization of the model selection criteria and has $O(n^2)$ as the worst case computational cost. As demonstrated by extensive numerical experiments, compared to classical general-purpose multiple change-point detection procedures, the proposed method improves accuracy for both change-point estimation and model parameter estimation. We further show promising applications of the proposed algorithm to multiple testing with locally clustered signals, and demonstrate its advantages over existing methods in large scale multiple testing, in DNA copy number variation detection, and in oceanographic study.

stat.ME↗

arXiv2020

Modeling Multivariate Time Series with Copula-linked Univariate D-vines

This paper proposes a novel multivariate time series model named Copula-linked univariate D-vines (CuDvine), which enables the simultaneous copula-based modeling of both temporal and cross-sectional dependence for multivariate time series. To construct CuDvine, we first build a semiparametric univariate D-vine time series model (uDvine) based on a D-vine. The uDvine generalizes the existing first-order copula-based Markov chain models to Markov chains of an arbitrary-order. Building upon uDvine, we construct CuDvine by linking multiple uDvines via a parametric copula. As a simple and tractable model, CuDvine provides flexible models for marginal behavior and temporal dependence of time series, and can also incorporate sophisticated cross-sectional dependence such as time-varying and spatio-temporal dependence for high-dimensional applications. Robust and computationally efficient procedures, including a sequential model selection method and a two-stage MLE, are proposed for model estimation and inference, and their statistical properties are investigated. Numerical experiments are conducted to demonstrate the flexibility of CuDvine, and to examine the performance of the sequential model selection procedure and the two-stage MLE. Real data applications on the Australian electricity price data demonstrate the superior performance of CuDvine to traditional multivariate time series models.

stat.ME↗

arXiv2020

Functional Autoregressive Processes in Reproducing Kernel Hilbert Spaces

We study the estimation and prediction of functional autoregressive~(FAR) processes, a statistical tool for modeling functional time series data. Due to the infinite-dimensional nature of FAR processes, the existing literature addresses its inference via dimension reduction and theoretical results therein require the (unrealistic) assumption of fully observed functional time series. We propose an alternative inference framework based on Reproducing Kernel Hilbert Spaces~(RKHS). Specifically, a nuclear norm regularization method is proposed for estimating the transition operators of the FAR process directly from discrete samples of the functional time series. We derive a representer theorem for the FAR process, which enables infinite-dimensional inference without dimension reduction. Sharp theoretical guarantees are established under the (more realistic) assumption that we only have finite discrete samples of the FAR process. Extensive numerical experiments and a real data application of energy consumption prediction are further conducted to illustrate the promising performance of the proposed approach compared to the state-of-the-art methods in the literature.

stat.ME↗

arXiv2020

Time Series Analysis of COVID-19 Infection Curve: A Change-Point Perspective

In this paper, we model the trajectory of the cumulative confirmed cases and deaths of COVID-19 (in log scale) via a piecewise linear trend model. The model naturally captures the phase transitions of the epidemic growth rate via change-points and further enjoys great interpretability due to its semiparametric nature. On the methodological front, we advance the nascent self-normalization (SN) technique (Shao, 2010) to testing and estimation of a single change-point in the linear trend of a nonstationary time series. We further combine the SN-based change-point test with the NOT algorithm (Baranowski et al., 2019) to achieve multiple change-point estimation. Using the proposed method, we analyze the trajectory of the cumulative COVID-19 cases and deaths for 30 major countries and discover interesting patterns with potentially relevant implications for effectiveness of the pandemic responses by different countries. Furthermore, based on the change-point detection algorithm and a flexible extrapolation function, we design a simple two-stage forecasting scheme for COVID-19 and demonstrate its promising performance in predicting cumulative deaths in the U.S.

econ.EM↗

arXiv2019

Regression for Copula-linked Compound Distributions with Applications in Modeling Aggregate Insurance Claims

In actuarial research, a task of particular interest and importance is to predict the loss cost for individual risks so that informative decisions are made in various insurance operations such as underwriting, ratemaking, and capital management. The loss cost is typically viewed to follow a compound distribution where the summation of the severity variables is stopped by the frequency variable. A challenging issue in modeling such outcome is to accommodate the potential dependence between the number of claims and the size of each individual claim. In this article, we introduce a novel regression framework for compound distributions that uses a copula to accommodate the association between the frequency and the severity variables, and thus allows for arbitrary dependence between the two components. We further show that the new model is very flexible and is easily modified to account for incomplete data due to censoring or truncation. The flexibility of the proposed model is illustrated using both simulated and real data sets. In the analysis of granular claims data from property insurance, we find substantive negative relationship between the number and the size of insurance claims. In addition, we demonstrate that ignoring the frequency-severity association could lead to biased decision-making in insurance operations.

stat.AP↗

arXiv2019

Change-point detection in dynamic networks via graphon estimation

We propose a general approach for change-point detection in dynamic networks. The proposed method is model-free and covers a wide range of dynamic networks. The key idea behind our approach is to effectively utilize the network structure in designing change-point detection algorithms. This is done via an initial step of graphon estimation, where we propose a modified neighborhood smoothing~(MNBS) algorithm for estimating the link probability matrices of a dynamic network. Based on the initial graphon estimation, we then develop a screening and thresholding algorithm for multiple change-point detection in dynamic networks. The convergence rate and consistency for the change-point detection procedure are derived as well as those for MNBS. When the number of nodes is large~(e.g., exceeds the number of temporal points), our approach yields a faster convergence rate in detecting change-points comparing with an algorithm that simply employs averaged information of the dynamic network across time. Numerical experiments demonstrate robust performance of the proposed algorithm for change-point detection under various types of dynamic networks, and superior performance over existing methods is observed. A real data example is provided to illustrate the effectiveness and practical impact of the procedure.

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