Information-Corrected Estimation: A Generalization Error Reducing Parameter Estimation Method

Modern computational models in supervised machine learning are often highly parameterized universal approximators. As such, the value of the parameters is unimportant, and only the out of sample performance is considered. On the other hand much of the literature on model estimation assumes that the parameters themselves have intrinsic value, and thus is concerned with bias and variance of parameter estimates, which may not have any simple relationship to out of sample model performance. Therefore, within supervised machine learning, heavy use is made of ridge regression (i.e., L2 regularization), which requires the the estimation of hyperparameters and can be rendered ineffective by certain model parameterizations. We introduce an objective function which we refer to as Information-Corrected Estimation (ICE) that reduces KL divergence based generalization error for supervised machine learning. ICE attempts to directly maximize a corrected likelihood function as an estimator of the KL divergence. Such an approach is proven, theoretically, to be effective for a wide class of models, with only mild regularity restrictions. Under finite sample sizes, this corrected estimation procedure is shown experimentally to lead to significant reduction in generalization error compared to maximum likelihood estimation and L2 regularization.     

静态像点高斯灰度扩散模型参数估计方法

为了实现星敏感器高斯灰度扩散模型的参数估计,设计了平行光管成像标定实验及相关算法。基于高斯规律建立并求解了以高斯扩散半径和像点质心坐标偏差为变量的方程组,进一步求得灰度能量系数;在3个不同平行光源方位拍摄图像,利用图像灰度数据计算模型参数的系列测量值,分别取均值作为其估计值;建立实验验证方法,将3个估计参数代入模型模拟静态星像点,将模拟图像与存在噪声的实拍图像做相似度比较,3pixel×3pixel窗口内相似度高于0.97,5pixel×5pixel窗口内高于0.98,7pixel×7pixel窗口内高于0.98。结果表明,方程组求解得到的高斯扩散半径、像点质心偏差的值可信,推导公式正确。     

空间光学成像系统波像差的位相差异估计方法

针对传统光学设计和校正手段无法有效消除空间光学成像系统在轨工作时受各种因素影响使像质变差的问题,提出把均匀设计的思想引入位相差异波前传感技术,对系统在轨工作时的波前畸变进行估计.从而实现了对系统波像差的全局优化估计,放宽了波像差的估计范围,易于实现并行化.通过仿真实验发现,该方法正确估计率高,抗噪声能力强,是进行空间光学成像系统波像差估计的有效方法.     

空间光学成像系统波像差的位相差异估计方法

针对传统光学设计和校正手段无法有效消除空间光学成像系统在轨工作时受各种因素影响使像质变差的问题,提出把均匀设计的思想引入位相差异波前传感技术,对系统在轨工作时的波前畸变进行估计.从而实现了对系统波像差的全局优化估计,放宽了波像差的估计范围,易于实现并行化.通过仿真实验发现,该方法正确估计率高,抗噪声能力强,是进行空间光学成像系统波像差估计的有效方法.     

Nonequilibrium Effects on the Precision of Parameter Estimation

The impact of nonequilibrium environment effects on the accuracy of quantum parameter estimation is investigated, and it is found that these effects can significantly affect estimation accuracy. Using an individual estimation strategy reveals that the nonequilibrium effects consistently enhance accuracy, regardless of the coupling strength between the probe and its environment. In contrast, weak memory effects undermine estimation accuracy. When employing a multi-parameter simultaneous estimation strategy, it is observed that the nonequilibrium effects consistently improve the advantages of simultaneous estimation, as analyzed by the ratio of total variances between the two estimation scenarios. However, the memory effects on these advantages depend on the coupling strength between the qubit and the environment. These findings suggest that appropriate parameters of a nonequilibrium environment can increase the quantum Fisher information (QFI), thereby enhancing the accuracy of quantum parameter estimation. These significant results are essential for improving parameter estimation accuracy in quantum systems interacting with nonequilibrium environments.     

双波段成像光学系统调焦过程的成像误差分析

双波段成像光学系统要达到像素级图像融合,两幅待融合图像间的空间差异要保证在一个像元范围内,因此必须从光机结构设计的层面上保证两个成像光学系统的光轴平行性达到所要求的精度。而由于制造、安装等误差的存在,光学系统在调焦过程中不可避免地会导致其光轴发生偏移。运用Zemax对调焦过程中影响光轴平行性的因素进行了仿真分析,并对光学系统进行了建模、成像误差分析与计算,最后得到了红外系统中可调焦镜片和可见光系统的最大容许安装误差,对于实际光学系统的装调具有一定的指导意义。     

Error Estimation in the Histogram Monte Carlo Method

We examine the sources of error in the histogram reweighting method for Monte Carlo data analysis. We demonstrate that, in addition to the standard statistical error which has been studied elsewhere, there are two other sources of error, one arising through correlations in the reweighted samples, and one arising from the finite range of energies sampled by a simulation of finite length. We demonstrate that while the former correction is usually negligible by comparison with statistical fluctuations, the latter may not be, and give criteria for judging the range of validity of histogram extrapolations based on the size of this latter correction.     

水下对空成像中的波面估计

水下相机向上对海洋表面场景成像时会形成扭曲的图像,为了矫正图像并重构场景,提出了一种基于水下对空成像的波面计算方法,通过分析光线在空一水交界面的传输特性,建立了前向散射和消光边界模型,并在消光边界处估计出表面的径向斜率。从而为海浪高度的计算奠定了基础。     

An Estimation for the Power-Law Distribution Parameter Based on Entropy

A new estimation based on the Shannon entropy for the power-law distribution parameter is presented, The maximum likelihood estimation （MLE） of the parameter is discussed and the relation between the MLE and the moment estimation of the parameter is given out. It is shown that the minimum Shannon entropy estimation is equivalent to the MLE giving the log expectation.     

Enhancing the Precision of Parameter Estimation in Band Gap

Recently, the dynamics of quantum Fisher information(QFI) in various environment are investigated and many kinds of schemes to overcome the drawback of decoherence are designed. Here we propose the pseudomode method to enhance the phase parameter precision of optimal quantum estimation of a qubit coupled to a non-Markovian structured environment. We find that the QFI can be enhanced in the weak-coupling regime with non-perfect band gap and can be trapped permanently with a large value in the perfect band gap. The effects of qubit-pseudomode detuning and the spectrum of reservoir are discussed, a reasonable physical explanation is given, too.     

无线传感器网络的分布扩散时钟自同步协议研究

针对大规模无线传感器网络同步协议的精度较低、可扩展性差的问题,提出一种分布式扩散时钟自同步协议(DDCSS);DDCSS是一个局部、并行执行的协议,基于分布式扩散的思想,以节点能量、分布和平均传输时延为依据,每轮动态地选取执行局部扩散的一组主节点和扩散节点,把主节点域内的节点平均时钟扩散有限的跳数,周围节点以接收的所有主节点域平均时钟取平均更新本地时钟,采用互扩散的方法使节点时钟近似同步到网络节点的平均时钟上,从而实现全网的时间同步;与RBS、TPSN协议相比较,该协议收敛速度较快,另外消除了误差累积,同步误差较低,扩展性较好。     

核磁共振扩散测量和q-空间成像进展(英文)

在过去的近半个世纪, NMR扩散测量在理论和实践方面都不断取得进展,使得测量更加可靠和准确,并能获取越来越多的信息.随着扩散测量技术的发展,其科学应用范围也不断增加,覆盖从物理化学到临床医学等各个领域. NMR扩散测量不仅能提供分子的平移运动动力学信息,而且也可以提供影响平移运动的局部几何结构的信息,后一种应用通常称为q-空间成像.该综述聚焦于过去10年中的NMR扩散研究方面一些重大的进展.     

Multi-Bits Transfer Based on the Quantum Three-Stage Protocol with Quantum Error Correction Codes

International Journal of Theoretical Physics - This paper presents a multi-bits transfer quantum protocol based on the three-stage quantum cryptography in which both parties use their own secret...     

多边形单元平均值插值的误差估计及应用

对多边形单元上平均值插值的误差进行分析,利用平均值插值形函数的性质和二元函数的Taylor展开式,证明平均值插值的误差估计不等式.给出平均值插值应用于凸域温度分布插值近似的算例,数值算例表明平均值插值能够表现出区域温度分布的特征.     

Inverse Filter of Chaos with Applications on Parameter Estimation

Linear filter may hide simple nonlinearity of chaotic dynamics, which would decrease the accuracy of parameter estimation, and reduce the effect of signal processing. Based on theoretical and experimental analysis, this paper provides a method to recover the dynamics. An example of radar data proves that the dynamics hidden in observed data can be found by inverse filter of chaos. It is also pointed out that inverse filter of chaos can be applied to mine inner regulation of some time series and estimate parameters of nonlinear models in data processing for radar. And the method is significant to clutter modeling.     

Shortcut-to-Adiabaticity-Like Techniques for Parameter Estimation in Quantum Metrology

Quantum metrology makes use of quantum mechanics to improve precision measurements and measurement sensitivities. It is usually formulated for time-independent Hamiltonians, but time-dependent Hamiltonians may offer advantages, such as a T4 time dependence of the Fisher information which cannot be reached with a time-independent Hamiltonian. In Optimal adaptive control for quantum metrology with time-dependent Hamiltonians (Nature Communications 8, 2017), Shengshi Pang and Andrew N. Jordan put forward a Shortcut-to-adiabaticity (STA)-like method, specifically an approach formally similar to the “counterdiabatic approach”, adding a control term to the original Hamiltonian to reach the upper bound of the Fisher information. We revisit this work from the point of view of STA to set the relations and differences between STA-like methods in metrology and ordinary STA. This analysis paves the way for the application of other STA-like techniques in parameter estimation. In particular we explore the use of physical unitary transformations to propose alternative time-dependent Hamiltonians which may be easier to implement in the laboratory.     

Parameter Estimation as a Problem in Statistical Thermodynamics

In this work, we explore the connections between parameter fitting and statistical thermodynamics using the maxent principle of Jaynes as a starting point. In particular, we show how signal averaging may be described by a suitable one particle partition function, modified for the case of a variable number of particles. These modifications lead to an entropy that is extensive in the number of measurements in the average. Systematic error may be interpreted as a departure from ideal gas behavior. In addition, we show how to combine measurements from different experiments in an unbiased way in order to maximize the entropy of simultaneous parameter fitting. We suggest that fit parameters may be interpreted as generalized coordinates and the forces conjugate to them may be derived from the system partition function. From this perspective, the parameter fitting problem may be interpreted as a process where the system (spectrum) does work against internal stresses (non-optimum model parameters) to achieve a state of minimum free energy/maximum entropy. Finally, we show how the distribution function allows us to define a geometry on parameter space, building on previous work[1, 2]. This geometry has implications for error estimation and we outline a program for incorporating these geometrical insights into an automated parameter fitting algorithm.     

简易高斯灰度扩散模型的误差分析及适用性研究

为了验证简易高斯灰度扩散模型的适用性,与传统高斯灰度扩散模型进行了对比分析。将两种高斯模型做归一化处理,设定检验像素,分析检验像元灰度的归一化值的相对误差;进行星图模拟,得到4个不同高斯半径(σ)下灰度赋值相对误差与像点映射位置偏离值的关系曲线,整体上误差随σ的增大而减小;对星图模拟得到的系列星像点采用灰度重心法提取质心,质心误差随σ增大而减小,传统模型模拟像点的质心提取精度比简易模型高约2个数量级。无噪声条件下σ=0.671时,简易模型模拟像点最大质心误差仅为0.033pixel。仿真结果表明:单就像点外形仿真而言,当σ较小时,简易模型不再适用;但针对像点的质心定位及后续算法,简易模型带来质心误差量级可以忽略,运算量更小,适于应用。     

Magnetic Resonance Imaging of Diffusion in the Presence of Background Gradients and Imaging of Background Gradients

The measurement of the self-diffusion coefficient D by an NMR technique that uses an applied gradient G_A can be corrupted by systems that have a background magnetic field gradient G₀ and also by imaging gradients G₁, when used in an imaging mode. In a nonimaging mode, the corrupting cross term G_A · G₀can be eliminated in the diffusion measurement by use of an alternating-pulse-field-gradient (APFG) sequence that allows an accurate and uncorrupted measurement of D. A Carr-Purcell echo train enables the measurement of the expectation value, 〈DG²₀〉; assuming D and G₀ to be uncorrelated will allow 〈G²₀〉 to be determined. An image of D or of 〈DG²₀〉 may be obtained without the corrupting G_A · G₀ and G_A · G_I terms by appending a standard imaging sequence to an APFG sequence or a Carr-Purcell sequence, respectively; assuming D and G₀ to be uncorrelated will allow (〈G²₀〉 to be determined within each pixel. Measurements of D and 〈G²₀〉 and their images are made in apple flesh in which minute air bubbles are shown to produce the large 〈G²₀〉. Their values in an 81 g Golden Delicious apple at a measuring frequency of 100 MHz were D = 1.42 × 10⁻⁵ cm²/s and [formula] = 8.9 G/cm.