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About 2,876 papers for “conditional probability density”

Conditional probability density functional theory

Ryan Pederson, Jielun Chen, Steven R. White et al. · Physical review. B./Physical review. B · 2022

Conditional probability density functional theory (CP-DFT) determines the ground-state energy of a many-electron system by finding the conditional probability density from a parallelizable series of Kohn-Sham DFT calculations. By directly calculating conditional probability densities, the authors bypass the need for an approximate exchange-correlation (XC) energy functional. CP-DFT is formally exact, but approximate potentials are used in practice. We explore a suitable approximation that satisfies many presented exact constraints and even properly dissociates neutral hydrogen chains.

Cited by 8Open access

Joint Conditional Probability and Bound Quantum Density

Ruggeri, Francesco R. · Zenodo (CERN European Organization for Nuclear Research) · 2020

<strong> In a number of previous notes, we have argued that the bound state quantum problem may be considered in terms of a conditional probability P(p/x) i.e. Sum over p p*p/2m P(p/x) + V(x) = E with P(p/x)= a(p)f(p,x)/ W(x) (where W(x), a normalization constant, is identical to the wavefunction). In other words, one considers a momentum distribution at x (with the different times pulled out). This momentum distribution may be thought of as being created by a stochastic potential which on average is V(x). Thus, within a little region delta x, in which one potential hit occurs, a particle has a joint conditional probability to move from momentum p1 to p2. Because the potential is stochastic, it is not clear where in the region delta x this occurs. Thus, we suggest a joint conditional probability of Sum on p1, p2 f(p1,x)f(p2,x). This is equivalent to W(x)W(x) the quantum density or P(x). From this, one may calculate P(p)= Sum over x P(p/x) P(x) leading to the idea that f(p,x) is an orthonormal basis. Thus, one moves from probability to linear algebra. We suggest that the stochastic force may be given by: -Sum over k k Vk(x), where -d/dx Vk(x) =-k Vk(x) or at least Vk(x)=Vk(kx). If one considers the bound state Schrodinger equation: Sum over p P(p/x) p*p/2m + V(x) W(x) = E W(x) then V(x)W(x)= Sum over p Vk(x) a(p-k)f(p-k,x). Vk(x), however, is associated with a hit of momentum=k, so one would expect that Vk(x)f(p-k,x) = f(p,x). This together with Vk(x)=Vk(kx) may lead to V(p,x) = b(p) f(p,x) where f(p,x)=exp(ipx). </strong>

Cited by 0Open access

Density Ratio Estimation with Conditional Probability Paths

Hanlin Yu, Arto Klami, Aapo Hyvärinen et al. · ArXiv.org · 2025

Density ratio estimation in high dimensions can be reframed as integrating a certain quantity, the time score, over probability paths which interpolate between the two densities. In practice, the time score has to be estimated based on samples from the two densities. However, existing methods for this problem remain computationally expensive and can yield inaccurate estimates. Inspired by recent advances in generative modeling, we introduce a novel framework for time score estimation, based on a conditioning variable. Choosing the conditioning variable judiciously enables a closed-form objective function. We demonstrate that, compared to previous approaches, our approach results in faster learning of the time score and competitive or better estimation accuracies of the density ratio on challenging tasks. Furthermore, we establish theoretical guarantees on the error of the estimated density ratio.

Cited by 0Open access

Conditional probability density function estimation with sigmoidal neural networks

A. Sarajedini, Robert Hecht-Nielsen, P.M. Chau · IEEE Transactions on Neural Networks · 1999

Real-world problems can often be couched in terms of conditional probability density function estimation. In particular, pattern recognition, signal detection, and financial prediction are among the multitude of applications requiring conditional density estimation. Previous developments in this direction have used neural nets to estimate statistics of the distribution or the marginal or joint distributions of the input-output variables. We have modified the joint distribution estimating sigmoidal neural network to estimate the conditional distribution. Thus, the probability density of the output conditioned on the inputs is estimated using a neural network. We have derived and implemented the learning laws to train the network. We show that this network has computational advantages over a brute force ratio of joint and marginal distributions. We also compare its performance to a kernel conditional density estimator in a larger scale (higher dimensional) problem simulating more realistic conditions.

Cited by 21

Rao-Blackwellised approximate conditional mean probability hypothesis density filtering

N. Nandakumaran, S. Sutharsan, Ratnasingham Tharmarasa et al. · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2009

In this paper, a new state estimation algorithm for estimating the states of targets that are separable into linear and nonlinear subsets with non-Gaussian observation noise distributed according to a mixture of Gaussian functions is proposed. The approach involves modeling the collection of targets and measurements as random finite sets and applying a new Rao-Blackwellised Approximate Conditional Mean Probability Hypothesis Density (RB-ACM-PHD) recursion to propagate the posterior density. The RB-ACM-PHD filter jointly estimates the time-varying number of targets and the observation sets in the presence of data association uncertainty, detection uncertainty, noise and false alarms. The proposed algorithm approximates a mixture Gaussian distribution with a moment-matched Gaussian in the weight update phase of the filtering recursion. A two dimensional maneuvering target tracking example is used to evaluate the merits of the proposed algorithm. The RB-ACM-PHD filter results in a significant reduction in computation time while maintaining filter accuracies similar to the standard sequential Monte Carlo PHD implementation.

Cited by 0

Function applicability to class conditional probability density of hourly rainfall

Tieyuan Shen, Xiang Yiheng, Yishan Liao et al. · Journal of Lake Sciences · 2023

暴雨强度公式在水文、气象、工程设计等各领域都是非常关注的问题,而常用降雨概率分布函数的适用性欠缺,理论分布函数一直处于争鸣之中。从逐时降雨概率密度函数的适用性分析入手,有利于发现普适且恰当的理论密度函数。本文从我国暴雨洪涝灾害易发区中沿30°N选取4个经纬度长方形区域(雅安附近、鄂西南、江汉平原南部、杭州湾西),并在其南、北各选一对比分区(海南岛、郑州),对6个分区内降雨资料直接采用全样本,统计逐时降雨的三类概率密度经验函数,对照这些函数的特性,从理论上分析了众多分布函数的适用性,筛选适用函数并进行拟合试验,优选出理论密度函数。研究结果表明:三参广义伽玛函数拟合误差最小,而两参广义正态函数更恰当、被首推为理论密度函数;拟合参数寻优时的目标函数综合了乘性与加性误差模型,能使拟合曲线兼顾头尾;本研究有别于极值降雨概率分布中仅采用极少部分样本的方法,采用降雨概率密度方法替代传统的年极值法,使重现期计算更准确有效,能提高暴雨强度公式的科学性,拟合的高精度与函数的普适性有望解决降雨概率分布模型统一的问题。

Cited by 1Open access

Deep-Based Conditional Probability Density Function Forecasting of Residential Loads

Mousa Afrasiabi, Mohammad Mohammadi, Mohammad Rastegar et al. · IEEE Transactions on Smart Grid · 2020

This paper proposes a direct model for conditional probability density forecasting of residential loads, based on a deep mixture network. Probabilistic residential load forecasting can provide comprehensive information about future uncertainties in demand. An end-to-end composite model comprising convolution neural networks (CNNs) and gated recurrent unit (GRU) is designed for probabilistic residential load forecasting. Then, the designed deep model is merged into a mixture density network (MDN) to directly predict probability density functions (PDFs). In addition, several techniques, including adversarial training, are presented to formulate a new loss function in the direct probabilistic residential load forecasting (PRLF) model. Several state-of-the-art deep and shallow forecasting models are also presented in order to compare the results. Furthermore, the effectiveness of the proposed deep mixture model in characterizing predicted PDFs is demonstrated through comparison with kernel density estimation, Monte Carlo dropout, a combined probabilistic load forecasting method and the proposed MDN without adversarial training.

Cited by 148

Conditional Averages and Probability Density Functions in the Passive Scalar Field

Takahashi, Naoya, Kambe, Tsutomu, Nakano, Tohru et al. · arXiv (Cornell University) · 1997

Two conditional averages for the increment Delta(x,x+r) = T(x)-T(x+r) of the scalar field are estimated for DNS data: H(Delta)= and G(Delta)=. The probability density function P(Delta) for Delta(x,x+r) is also calculated. If Delta, P(Delta), H(Delta), and G(Delta) are expressed as theta, P(theta), h(theta), and g(theta) in a dimensionless form, the data analysis has revealed interesting simple relationships between them. These relations may be helpful to construct a turbulence model.

Cited by 0Open access