arXiv subjects

Li-Chun Zhang

Publications and source records attributed to Li-Chun Zhang.

At least 19 recordsLinked to original sources

arXiv2026

Conformal confidence intervals with an application to small area estimation

Conformal prediction inference yields intervals for out-of-sample random outcomes with designated coverage probabilities, given exchangeable or independent-and-identically distributed random variables. For regression analysis, valid coverage can be achieved given finite sample sizes, despite unavoidable misspecifications of the regression function. We propose a novel method of conformal inference, aimed to produce confidence intervals of the unknown expectations of the in-sample outcomes with the designated coverage probabilities conditional on the realised sample. These conformal confidence intervals fill a gap between classical regression and conformal inference. The proposed approach is applied to small area estimation problems.

stat.ME↗

arXiv2026

On design-unbiased algorithmic Machine Learning

Machine Learning (ML) algorithms, such as k-Nearest Neighbours (kNN) or random forest, eschew the ideal of true data models in favour of predictive performance. However, minimising the MSE or F-score cannot lead to unbiasedness directly, which is important in many situations such as official statistics. We study the conditions of algorithmic ML, other than the existence and knowledge of true data models, which lead to unbiased prediction or classification for a given finite population, including how the training data may be sampled from the population, how a trained prediction algorithm can be tuned to achieve unbiased prediction or classification for that population, and how the performance of out-of-sample prediction or classification can be assessed unbiasedly. The inference is based on the known probability design of samples and training sets, rather than any assumed distributions or models.

cs.LG↗

arXiv2024

On Admissibility in Bipartite Incidence Graph Sampling

In bipartite incidence graph sampling, the target study units may be formed as connected population elements, which are distinct to the units of sampling and there may exist generally more than one way by which a given study unit can be observed via sampling units. This generalizes finite-population element or multistage sampling, where each element can only be sampled directly or via a single primary sampling unit. We study the admissibility of estimators in bipartite incidence graph sampling and identify other admissible estimators than the classic Horvitz-Thompson estimator. Our admissibility results encompass those for finite-population sampling.

math.ST↗

arXiv2024

Schottky Anomaly of Reissner-Nordstr\"{o}m-de Sitter spacetime

In the extended thermodynamics of black holes, there exists a thermodynamical pressure whose dual thermodynamical quantity is volume. Extensive studies have been conducted on the phase structure of numerous black holes, which have demonstrated striking similarities to the phase structure of various ordinary matter systems. From the comparison of the thermodynamic properties between spherically symmetric AdS black holes and ordinary thermodynamic systems we known that the isovolumetric heat capacity of the former is zero, whereas that of the latter is non-zero. It is a subject of interest for the intrinsic reason for this discrepancy. For the Reissner-N\"{o}rdstrom-de Sitter (RN-dS) spacetime with the coexistence of the black hole and cosmological horizons the effective thermodynamic quantities as well as the interaction between two horizons are presented. The heat capacity in the Reissner-N\"{o}rdstrom-de Sitter (RN-dS) spacetime is then investigated, and it is demonstrated that the behavior of the heat capacity in the RN-dS spacetime is analogous to that of Schottky specific heat. Treating two horizons in the RN-dS spacetime as two distinct energy levels in a two-energy-level system we investigate the thermodynamic properties in the RN-dS spacetime with the method of studying the thermodynamic properties in an ordinary two-energy system, thereby elucidating the intrinsic reasons for the occurrence of Schottky specific heat in the RN-dS spacetime. The heat capacity observed in the RN-dS spacetime is not only consistent with that of the Schottky specific heat described by the effective thermodynamic quantities in the RN-dS spacetime, but also with that of an ordinary two-energy-level system. These results not only reveal the quantum properties of the RN-dS spacetime, but also provide a new avenue for further in-depth study of the quantum properties of black holes and dS spacetime.

hep-th↗

arXiv2023

Design-based individual prediction

A design-based individual prediction approach is developed based on the expected cross-validation results, given the sampling design and the sample-splitting design for cross-validation. Whether the predictor is selected from an ensemble of models or a weighted average of them, valid inference of the unobserved prediction errors is defined and obtained with respect to the sampling design, while outcomes and features are treated as constants.

stat.ML↗

arXiv2022

Graph sampling for node embedding

Node embedding is a central topic in graph representation learning. Computational efficiency and scalability can be challenging to any method that requires full-graph operations. We propose sampling approaches to node embedding, with or without explicit modelling of the feature vector, which aim to extract useful information from both the eigenvectors related to the graph Laplacien and the given values associated with the graph.

stat.ML↗

arXiv2022

Sampling for network function learning

Given a valued graph, where both the nodes and the edges of the graph are associated with one or several values, any network function for a given node must be defined in terms of that node and its connected nodes in the graph. Generally, applying the same definition to the whole graph or any given subgraph of it would result in systematically different network functions. In this paper we consider the feasibility of graph sampling approach to network function learning, as well as the corresponding learning methods based on the sample graphs. This can be useful either when the edges are unknown to start with or the graph is too large (or dynamic) to be processed entirely.

cs.SI↗

arXiv2022

Phase transition and entropic force in Reissner-Nordstr\"om-de Sitter spacetime

In this paper, thermodynamic properties of the Reissner-Nordstr\"om-de Sitter (RN-dS) black hole have been studied on the basis of the correlation between the black hole and cosmological horizons. It is found that the RN-dS black hole experiences a phase transition, when its state parameters satisfy certain conditions. From the analysis of the interaction between two horizons in RN-dS spacetime, we get the numerical solution of the interaction between two horizons. It makes us to realize the force between the black hole and cosmological horizons, which can be regarded as a candidate to explain our accelerating expansion universe. That provides a new window to explore the physical mechanism of the cosmic accelerating expansion.

hep-th↗

arXiv2022

Thermodynamics of the Reissner-Nordstr\"om-de Sitter Spacetime with Quintessence

For Anti-de Sitte (AdS) black holes, the isochoric heat capacity of system is vanished, while the isobaric heat capacity is not. However, this situation does not hold on for de Sitter (dS) black holes. In this work, by introducing the interaction between the black hole horizon and the cosmological horizon of the Reissner-Nordstr\"om-de Sitter (RNdS) spacetime with quintessence, we discuss the phase transition of this system. The results show that the spacetime not only has the similar phase transition behavior to that of Van der Waals (VdW) system, and the non-vanishing isochoric heat capacity fulfills the whole thermodynamics system. Through the discussion of the entropic force between two horizons, we find out the role of entropic force in the evolution of spacetime. In addition, we also study the influence of various parameters on the phase transition and entropic force, which will provide a new method for exploring the interaction among black hole molecules from a micro perspective.

hep-th↗

arXiv2022

Photon orbits and phase transition for Non-Linear charged Anti-de Sitter black holes

In this work, we investigate the relationship between the photon sphere radius and the first-order phase transition for the charged EPYM AdS black hole. Through the analysis, we find with a certain condition there exist the non-monotonic behaviors between the photon sphere radius, the impact parameter, the non-linear YM charge parameter, temperature, and pressure. And both the changes of photon sphere radius and impact parameter before and after phase transition can be regarded as the order parameter, their critical exponents near the critical point are equal to the same value $1/2$, just like the ordinary thermal systems. These indicate that there maybe exists a universal relationship of gravity nearby the critical point for a black hole thermodynamical system. Furthermore, the effect of impact parameter on the deflect angle is also investigated.

hep-th↗

arXiv2022

Graph spatial sampling

We develop lagged Metropolis-Hastings walk for sampling from simple undirected graphs according to given stationary sampling probabilities. We explain how to apply the technique together with designed graphs for sampling of units-in-space. We illustrate that the proposed graph spatial sampling approach can be more flexible for improving the design efficiency compared to the existing spatial sampling methods.

stat.ME↗

arXiv2021

Phase transition of non-linear charged Anti-de Sitter black holes

Understanding the thermodynamic phase transition of black holes can provide a deep insight into the fundamental properties of black hole gravity to establish the theory of quantum gravity. We investigate the condition and latent heat of phase transition for non-linear charged AdS black holes using the Maxwell's equal-area law, and analysis the boundary and curve of the two-phase coexistence area in the expanded phase space. We suggest that the phase transition of the non-linear charged AdS black hole with the fixed temperature ($T<T_c$) is related to the electric potential at the horizon, not only to the location of horizon. Recently, the molecular number density was introduced to study the phase transition and microstructure of black holes. On this basis, we discuss the continuous phase transition of a non-linear charged AdS black hole to reveal the potential microstructure of a black hole by introducing the order parameter and using the scalar curvature.

hep-th↗

arXiv2021

Dynamic Property of Phase Transition for Non-Linear Charged Anti-de Sitter black holes

Understanding the thermodynamic phase transition of black holes can provide the deep insight into the fundamental properties of black hole gravity to establish the quantum gravity. In this work, we investigate the phase transition and its dynamics for the charged EPYM AdS black hole. Through reconstructing the Maxwell's equal-area law, we find there exists the high-/low-potential black hole (HPBH/LPBL) phase transition, not only the pure large/small one. The Gibbs free energy landscape ($G_L$) is treated as a function of the black hole horizon, which is the order parameter of the phase transition due to the thermal fluctuation. From the view point of $G_L$, the stable HPBH/LPBL states are corresponding to two wells of $G_L$, which have the same depth. The unstable intermediate-potential black hole state corresponds to the local maximum of $G_L$. Then we focus on the probability evolution governed by the Fokker-Planck equation. Through solving the Fokker-Planck equating with different reflection/aborption boundary conditions and initial conditions, the dynamics of switching between the coexistent HPBH and LPBL phases is probed within the first passage time. Furthermore, the effect of temperature on the dynamic property of phase transition is also investigated.

hep-th↗

arXiv2021

On provision of UK neighbourhood population statistics beyond 2021

Census 2021 may well be the last of its kind in the UK. For provision of population statistics in the immediate years following 2021, the basic scheme currently envisaged is to supplement available administrate data with a continuous coverage survey, which amounts to a yearly sample size of about 0.5 million addresses, although the details of the methodology are yet to be determined. Meanwhile, the ONS is seeking alternative approaches, which can make greater use of the relevant administrative data. This report outlines the basic ideas of a rolling approach for provision of UK neighbourhood population statistics beyond 2021, set in the broad perspective of establishing a sustainable future for official statistical systems, which is faster in response, richer in detail and greater in return of long-term cost efficiency.

stat.AP↗

arXiv2021

Graph sampling by lagged random walk

We propose a family of lagged random walk sampling methods in simple undirected graphs, where transition to the next state (i.e. node) depends on both the current and previous states -- hence, lagged. The existing random walk sampling methods can be incorporated as special cases. We develop a novel approach to estimation based on lagged random walks at equilibrium, where the target parameter can be any function of values associated with finite-order subgraphs, such as edge, triangle, 4-cycle and others.

math.ST↗

arXiv2021

Hawking-Page Phase Transition of the four-dimensional de-Sitter Spacetime with non-linear source

The interplay between a dS black hole and cosmological horizons introduces distinctive thermodynamic behavior in a dS spacetime (for example the well-known upper bounds of mass and entropy in Class. Quant. Grav. 37 (2020) 5). Based on this point, we present the Hawking-Page (HP) phase transition of the four-dimensional dS spacetime with non-linear charge correction when the effective pressure is fixed, and analyze the effects of different effective pressures and non-linear charge corrections on HP phase transition. The evolution of this dS spacetime undergoing the HP phase transition is also investigated. We find that the existent curve of HP phase transition is a closed one with two different branches. That means there exist the upper bounds of the HP temperature and HP pressure, which is completely distinguished with that in AdS spacetime. And with the decreasing of the distance between two horizons, the dS spacetime at the coexistent curve of HP phase transition is going along with different branches. Furthermore we also explore the influence of charge and non-linear charge correction on the coexistent curve.

hep-th↗

arXiv2021

Continuous Phase Transition of the higher-dimensional topological de-Sitter Spacetime with the Non-linear Source

For the higher-dimensional dS spacetime embedded with black holes with non-linear charges, there are two horizons with different radiation temperatures. By introducing the interplay between two horizons this system can be regarded as an ordinary thermodynamic system in the thermodynamic equilibrium described by the thermodynamic quantities ($T_{eff},~P_{eff},~V,~S,~\Phi_{eff}$). In this work, our focus is on the thermodynamic properties of phase transition for the four-dimensional dS spacetime with different values of the charge correction $\bar\phi$. We find that with the increasing of the non-linear charge correction the two horizons get closer and closer, and the correction entropy is negative which indicates the interaction between the two horizons stronger and stronger. Furthermore, the heat capacity at constant pressure, isobaric expansion coefficient, and the isothermal compression coefficient have the schottky peak at the critical point. However, the heat capacity as constant volume for the dS spacetime is nonzero. Finally, the dynamical properties of phase transition for this system have investigated based on Gibbs free energy, where exists the different behavior with that for AdS black holes.

hep-th↗

arXiv2021

Thermodynamics of phase transition in Reissner-Nordstrom-de Sitter spacetime

The Reissner-Nordstrom-de Sitter (RN-dS) spacetime can be considered as a thermodynamic system. Its thermodynamic properties are discussed that the RN-dS spacetime has phase transitions and critical phenomena similar to that of the Van de Waals system or the charged AdS black hole. The continuous phase transition point of RN-dS spacetime depends on the position ratio of the black hole horizon and the cosmological horizon. We discuss the critical phenomenon of the continuous phase transition of RN-dS spacetime with Landau theory of continuous phase transition, that the critical exponent of spacetime is same as that of the Van de Waals system or the charged AdS black hole, which have universal physical meaning. We find that the order parameters are similar to those introduced in ferromagnetic systems. Our universe is an asymptotically dS spacetime, thermodynamic characteristics of RN-dS spacetime will help us understand the evolution of spacetime and provide a theoretical basis to explore the physical mechanism of accelerated expansion of the universe.

gr-qc↗