高斯混合物的平均值
Basheer Joudeh1, Boris Škorić1
1Department of Computer Science and Mathematics, Eindhoven University of Technology, 5612 AZ Eindhoven, The Netherlands.
Entropy (Basel, Switzerland)
|August 29, 2024
概括
本研究介绍了高斯混合物的平均微分的新型序列扩展. 这些发现为复杂的数据分布提供了准确的分析近似,具有错误极限.
科学领域:
- 信息理论 信息理论
- 可能性理论概率理论.
- 统计推理 统计推理
背景情况:
- 高斯混合模型被广泛用于密度估计.
- 计算混合物的微分是计算上具有挑战性的.
- 现有的方法缺乏精确的错误量化.
研究的目的:
- 为了获得高斯混合物的平均微分的分析近似值.
- 提供一种方法来计算近似中更高阶项的方法.
- 为了确定近似的可量化的误差界限.
主要方法:
- 对于微分的序列扩张的导数.
- 在Rn.中分析一个q成分高斯混合物.
- 在协差矩阵 (μ=s2/σ2) 的比率方面进行扩展.
主要成果:
- 获得了高达O(μ2) 的平均微分的分析近似值.
- 开发了一种系统的方法来计算更高阶的术语.
- 该近似包括一个可量化的错误大小.
结论:
- 衍生系列扩展与之前的文献相比,提供了显著的改进.
- 这项工作为分析高斯混合物的信息理论性质提供了有价值的工具.
- 该方法允许精确估计差异,并可控制误差.
更多相关视频
06:55Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
Published on: September 26, 2016
7.8K
09:12Optimization of Processing of Tiebangchui with Highland Barley Wine Based on the Box-Behnken Design Combined with the Entropy Method
Published on: May 19, 2023
600
相关概念视频
02:39Entropy
29.1K
Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
29.1K
02:38Third Law of Thermodynamics
18.5K
A pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K) may be described by a single microstate, as its purity, perfect crystallinity,and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (W = 1). According to the Boltzmann equation, the entropy of this system is zero.
18.5K
01:07Gauss's Law
7.2K
If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.
7.2K
01:20Entropy and the Second Law of Thermodynamics
2.8K
The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
The relation between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
The relation between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
2.8K
02:05Entropy and Solvation
7.0K
The process of surrounding a solute with solvent is called solvation. It involves evenly distributing the solute within the solvent. The rule of thumb for determining a solvent for a given compound is that like dissolves like. A good solvent has molecular characteristics similar to those of the compound to be dissolved. For example, polar solutions dissolve polar solutes, and apolar solvents dissolve apolar solutes. A polar solvent is a solvent that has a high dielectric constant (ϵ...
7.0K
03:00Standard Entropy Change for a Reaction
20.0K
Entropy is a state function, so the standard entropy change for a chemical reaction (ΔS°rxn) can be calculated from the difference in standard entropy between the products and the reactants.
20.0K