This paper concerns about the limiting distributions of change point estimators, in a high-dimensional linear regression time series context, where a regression object $(y_t, X_t) \in \mathbb{R} \times \mathbb{R}^p$ is observed at every time point $t \in \{1, \ldots, n\}$. At unknown time points, called change points, the regression coefficients change, with the jump sizes measured in $\ell_2$-norm. We provide limiting distributions of the change point estimators in the regimes where the minimal jump size vanishes and where it remains a constant. We allow for both the covariate and noise sequences to be temporally dependent, in the functional dependence framework, which is the first time seen in the change point inference literature. We show that a block-type long-run variance estimator is consistent under the functional dependence, which facilitates the practical implementation of our derived limiting distributions. We also present a few important byproducts of our analysis, which are of their own interest. These include a novel variant of the dynamic programming algorithm to boost the computational efficiency, consistent change point localisation rates under temporal dependence and a new Bernstein inequality for data possessing functional dependence. Extensive numerical results are provided to support our theoretical results. The proposed methods are implemented in the R package \texttt{changepoints} \citep{changepoints_R}.
相關內容
Complex and nonlinear dynamical systems often involve parameters that change with time, accurate tracking of which is essential to tasks such as state estimation, prediction, and control. Existing machine-learning methods require full state observation of the underlying system and tacitly assume adiabatic changes in the parameter. Formulating an inverse problem and exploiting reservoir computing, we develop a model-free and fully data-driven framework to accurately track time-varying parameters from partial state observation in real time. In particular, with training data from a subset of the dynamical variables of the system for a small number of known parameter values, the framework is able to accurately predict the parameter variations in time. Low- and high-dimensional, Markovian and non-Markovian nonlinear dynamical systems are used to demonstrate the power of the machine-learning based parameter-tracking framework. Pertinent issues affecting the tracking performance are addressed.
Generalized linear models (GLMs) are popular for data-analysis in almost all quantitative sciences, but the choice of likelihood family and link function is often difficult. This motivates the search for likelihoods and links that minimize the impact of potential misspecification. We perform a large-scale simulation study on double-bounded and lower-bounded response data where we systematically vary both true and assumed likelihoods and links. In contrast to previous studies, we also study posterior calibration and uncertainty metrics in addition to point-estimate accuracy. Our results indicate that certain likelihoods and links can be remarkably robust to misspecification, performing almost on par with their respective true counterparts. Additionally, normal likelihood models with identity link (i.e., linear regression) often achieve calibration comparable to the more structurally faithful alternatives, at least in the studied scenarios. On the basis of our findings, we provide practical suggestions for robust likelihood and link choices in GLMs.
Measurements of systems taken along a continuous functional dimension, such as time or space, are ubiquitous in many fields, from the physical and biological sciences to economics and engineering.Such measurements can be viewed as realisations of an underlying smooth process sampled over the continuum. However, traditional methods for independence testing and causal learning are not directly applicable to such data, as they do not take into account the dependence along the functional dimension. By using specifically designed kernels, we introduce statistical tests for bivariate, joint, and conditional independence for functional variables. Our method not only extends the applicability to functional data of the HSIC and its d-variate version (d-HSIC), but also allows us to introduce a test for conditional independence by defining a novel statistic for the CPT based on the HSCIC, with optimised regularisation strength estimated through an evaluation rejection rate. Our empirical results of the size and power of these tests on synthetic functional data show good performance, and we then exemplify their application to several constraint- and regression-based causal structure learning problems, including both synthetic examples and real socio-economic data.
The maximum likelihood estimator (MLE) is pivotal in statistical inference, yet its application is often hindered by the absence of closed-form solutions for many models. This poses challenges in real-time computation scenarios, particularly within embedded systems technology, where numerical methods are impractical. This study introduces a generalized form of the MLE that yields closed-form estimators under certain conditions. We derive the asymptotic properties of the proposed estimator and demonstrate that our approach retains key properties such as invariance under one-to-one transformations, strong consistency, and an asymptotic normal distribution. The effectiveness of the generalized MLE is exemplified through its application to the Gamma, Nakagami, and Beta distributions, showcasing improvements over the traditional MLE. Additionally, we extend this methodology to a bivariate gamma distribution, successfully deriving closed-form estimators. This advancement presents significant implications for real-time statistical analysis across various applications.
Selection models are ubiquitous in statistics. In recent years, they have regained considerable popularity as the working inferential models in many selective inference problems. In this paper, we derive an asymptotic expansion of the local likelihood ratios of selection models. We show that under mild regularity conditions, they are asymptotically equivalent to a sequence of Gaussian selection models. This generalizes the Local Asymptotic Normality framework of Le Cam (1960). Furthermore, we derive the asymptotic shape of Bayesian posterior distributions constructed from selection models, and show that they can be significantly miscalibrated in a frequentist sense.
This paper presents a novel centralized, variational data assimilation approach for calibrating transient dynamic models in electrical power systems, focusing on load model parameters. With the increasing importance of inverter-based resources, assessing power systems' dynamic performance under disturbances has become challenging, necessitating robust model calibration methods. The proposed approach expands on previous Bayesian frameworks by establishing a posterior distribution of parameters using an approximation around the maximum a posteriori value. We illustrate the efficacy of our method by generating events of varying intensity, highlighting its ability to capture the systems' evolution accurately and with associated uncertainty estimates. This research improves the precision of dynamic performance assessments in modern power systems, with potential applications in managing uncertainties and optimizing system operations.
Over the recent past data-driven algorithms for solving stochastic optimal control problems in face of model uncertainty have become an increasingly active area of research. However, for singular controls and underlying diffusion dynamics the analysis has so far been restricted to the scalar case. In this paper we fill this gap by studying a multivariate singular control problem for reversible diffusions with controls of reflection type. Our contributions are threefold. We first explicitly determine the long-run average costs as a domain-dependent functional, showing that the control problem can be equivalently characterized as a shape optimization problem. For given diffusion dynamics, assuming the optimal domain to be strongly star-shaped, we then propose a gradient descent algorithm based on polytope approximations to numerically determine a cost-minimizing domain. Finally, we investigate data-driven solutions when the diffusion dynamics are unknown to the controller. Using techniques from nonparametric statistics for stochastic processes, we construct an optimal domain estimator, whose static regret is bounded by the minimax optimal estimation rate of the unreflected process' invariant density. In the most challenging situation, when the dynamics must be learned simultaneously to controlling the process, we develop an episodic learning algorithm to overcome the emerging exploration-exploitation dilemma and show that given the static regret as a baseline, the loss in its sublinear regret per time unit is of natural order compared to the one-dimensional case.
For the differential privacy under the sub-Gamma noise, we derive the asymptotic properties of a class of network models with binary values with a general link function. In this paper, we release the degree sequences of the binary networks under a general noisy mechanism with the discrete Laplace mechanism as a special case. We establish the asymptotic result including both consistency and asymptotically normality of the parameter estimator when the number of parameters goes to infinity in a class of network models. Simulations and a real data example are provided to illustrate asymptotic results.
It is common to conduct causal inference in matched observational studies by proceeding as though treatment assignments within matched sets are assigned uniformly at random and using this distribution as the basis for inference. This approach ignores observed discrepancies in matched sets that may be consequential for the distribution of treatment, which are succinctly captured by within-set differences in the propensity score. We address this problem via covariate-adaptive randomization inference, which modifies the permutation probabilities to vary with estimated propensity score discrepancies and avoids requirements to exclude matched pairs or model an outcome variable. We show that the test achieves type I error control arbitrarily close to the nominal level when large samples are available for propensity score estimation. We characterize the large-sample behavior of the new randomization test for a difference-in-means estimator of a constant additive effect. We also show that existing methods of sensitivity analysis generalize effectively to covariate-adaptive randomization inference. Finally, we evaluate the empirical value of covariate-adaptive randomization procedures via comparisons to traditional uniform inference in matched designs with and without propensity score calipers and regression adjustment using simulations and analyses of genetic damage among welders and right-heart catheterization in surgical patients.
Knowledge graphs (KGs) of real-world facts about entities and their relationships are useful resources for a variety of natural language processing tasks. However, because knowledge graphs are typically incomplete, it is useful to perform knowledge graph completion or link prediction, i.e. predict whether a relationship not in the knowledge graph is likely to be true. This paper serves as a comprehensive survey of embedding models of entities and relationships for knowledge graph completion, summarizing up-to-date experimental results on standard benchmark datasets and pointing out potential future research directions.
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