Learning bipartite Bayesian networks under monotonicity restrictions

ABSTRACT

Learning parameters of a probabilistic model is a necessary step in machine learning tasks. We present a method to improve learning from small datasets by using monotonicity conditions. Monotonicity simplifies the learning and it is often required by users. We present an algorithm for Bayesian Networks parameter learning. The algorithm and monotonicity conditions are described, and it is shown that with the monotonicity conditions we can better fit underlying data. Our algorithm is tested on artificial and empiric datasets. We use different methods satisfying monotonicity conditions: the proposed gradient descent, isotonic regression EM, and non-linear optimization. We also provide results of unrestricted EM and gradient descent methods. Learned models are compared with respect to their ability to fit data in terms of log-likelihood and their fit of parameters of the generating model. Our proposed method outperforms other methods for small sets, and provides better or comparable results for larger sets.     

An optimal linear time algorithm for quasi-monotonic segmentation1

Monotonicity is a simple yet significant qualitative characteristic. We consider the problem of segmenting a sequence in up to K segments. We want the segments to be as monotonic as possible and to alternate signs. We propose a quality metric for this problem using the l _∞ norm, and we present an optimal linear time algorithm based on a novel formalism. Moreover, given a precomputation in time O(n log n) consisting of a labelling of all extrema, we compute any optimal segmentation in constant time. We compare experimentally its performance to two piecewise linear segmentation heuristics (top-down and bottom-up). We show that our algorithm is faster and more accurate. Applications include pattern recognition and qualitative modelling.     

非概率可靠性中一维优化算法的改进及其在桥梁评估中应用

为了减少非概率可靠性指标的计算量,提出了改进的一维优化算法.将区间变量转换为标准化区间变量后,得到了关于失效面的极限状态方程.在扩展空间中,通过缩小区间变量的取值范围能方便的确定目标函数的单调性.进一步,为了显示求解非概率可靠性指标的计算过程,提出了非概率可靠性指标的改进一维优化算法的计算步骤.讨论了在役桥梁的非概率可...     

抛物线断面河渠收缩水深的直接计算公式

为便于工程设计应用,提出了一种抛物线形断面河渠收缩水深近似解直接计算公式.通过对收缩水深基本方程进行数学变换,将未知量与已知量分别用无量纲参数相对收缩水深λ和无量纲综合已知量参数β代替,用不动点迭代法建立迭代公式.在分析函数单调性和凹凸性以及方程的根的基础上,结合函数的几何图像,应用数值计算方法初步选取迭代初值,再以迭代次数最少且相对误差最小为目标对初值进行优化计算,最后得到了收缩水深直接计算公式,并进行相对误差分析和应用举例.结果表明直接计算公式形式较简单、适用范围广、结果精确,其最大误差小于0.43%.     

二型模糊集模糊推理方法的单调性

模糊推理是蓬勃发展中的模糊控制技术的数学核心,二型模糊集的模糊推理是研究二型模糊逻辑系统的基础。各种模糊推理方法都具有单调性,从而导致人们当使用这些模糊推理方法时,应首先判明所讨论问题领域的推理是否具有相应的性质,否则可能导致不恰当的推理结果。     

广义椭圆积分对参数的依赖性

给出了由广义椭圆积分κa(r)和εa(r)定义的某些函数依赖于参数a的分析性质.同时,揭示了广义椭圆积分与完全椭圆积分κ(r)和ε(r)的一些联系.     

关于广义椭圆积分的几个性质

揭示了由广义椭圆积分定义的一些函数的单调性,从而获得若干不等式。这些结果有助于对广义Grtzsch环函数和Ramanujan模方程及其解φak(r)、φk(r)的研究,这些函数在拟共形理论、数论、几何学等领域中具有非常广泛的应用;同时,从这些结果中可以得到关于完全椭圆积分的一些新的性质。     

构造函数证明不等式的方法

高等数学中存在大量的不等式证明,从函数增量法、幂级数法、凹函数法、线性函数法、极值法探讨了构造函数证明不等式的方法.     

Learning and classification of monotonic ordinal concepts

Ordinal reasoning plays a major role in human cognition. This paper identifies an important class of classification problems of patterns taken from ordinal domains and presents efficient, incremental algorithms for learning the classification rules from examples. We show that by adopting a monotonicity assumption of the output with respect to the input, inconsistencies among examples can be easily detected and the number of possible classification rules substantially reduced. By adopting a conservative classification criterion, the required number of rules further decreases. The monotonicity and conservatism of the classification also enable the resolution of conflicts among inconsistent examples and the graceful handling of don't knows and don't cares during the learning and classification phases. Two typical examples in which the suggested classification model works well are given. The first example is taken from the financial domain and the second from machining.     

LEARNING MONOTONIC-CONCAVE INTERVAL CONCEPTS USING THE BACK-PROPAGATION NEURAL NETWORKS

Monotonicity and concavity play important roles in human cognition, reasoning, and decision making. This paper shows that neural networks can learn monotonic-concave interval concepts based on real-world data, Traditionally, the training of neural networks has been based only on raw data. In cases where the training samples carry statistical fluctuations, the products of the training have often suffered. This paper suggests that global knowledge about monotonicity and concavity of a problem domain can be incorporated in neural network training. This paper proposes a learning scheme for the back-propagation layered neural networks in learning monotonic-concave interval concepts and provides an example to show its application.