The distance between the weights of the neural network is meaningful

基于Choquet积分的特征子集加权用于距离监督学习

Feature Subset Weighting for Distance-based Supervised Learning through Choquet Integration

本文提出基于Choquet积分的特征子集加权距离，用于监督学习，可捕捉非线性与特征交互，计算高效，并在KNN分类中优于马氏距离等方法。

A novel framework of the fuzzy c-means distances problem based weighted distance

Clustering is one of the major roles in data mining that is widely application in pattern recognition and image segmentation. Fuzzy C-means (FCM) is the most used clustering algorithm that proven efficient, fast and easy to implement, however, FCM uses the Euclidean distance that often leads to clustering errors, especially when handling multidimensional and noisy data. In the last few years, many distances metric have been proposed by researchers to improve the performance of the FCM algorithms, and the majority of researchers propose weighted distance. In this paper, we proposed Canberra Wei…

The Wasserstein-Fourier Distance for Stationary Time Series

We propose the Wasserstein-Fourier (WF) distance to measure the (dis)similarity between time series by quantifying the displacement of their energy across frequencies. The WF distance operates by calculating the Wasserstein distance between the (normalised) power spectral densities (NPSD) of time series. Yet this rationale has been considered in the past, we fill a gap in the open literature providing a formal introduction of this distance, together with its main properties from the joint perspective of Fourier analysis and optimal transport. As the main aim of this work is to validate WF as a…

Wasserstein GANs Work Because They Fail (to Approximate the Wasserstein Distance)

Wasserstein GANs are based on the idea of minimising the Wasserstein distance between a real and a generated distribution. We provide an in-depth mathematical analysis of differences between the theoretical setup and the reality of training Wasserstein GANs. In this work, we gather both theoretical and empirical evidence that the WGAN loss is not a meaningful approximation of the Wasserstein distance. Moreover, we argue that the Wasserstein distance is not even a desirable loss function for deep generative models, and conclude that the success of Wasserstein GANs can in truth be attributed to …

Wasserstein Distance Maximizing Intrinsic Control

This paper deals with the problem of learning a skill-conditioned policy that acts meaningfully in the absence of a reward signal. Mutual information based objectives have shown some success in learning skills that reach a diverse set of states in this setting. These objectives include a KL-divergence term, which is maximized by visiting distinct states even if those states are not far apart in the MDP. This paper presents an approach that rewards the agent for learning skills that maximize the Wasserstein distance of their state visitation from the start state of the skill. It shows that such…

Global optimization via inverse distance weighting and radial basis functions

Global optimization problems whose objective function is expensive to evaluate can be solved effectively by recursively fitting a surrogate function to function samples and minimizing an acquisition function to generate new samples. The acquisition step trades off between seeking for a new optimization vector where the surrogate is minimum (exploitation of the surrogate) and looking for regions of the feasible space that have not yet been visited and that may potentially contain better values of the objective function (exploration of the feasible space). This paper proposes a new global optimi…

从对数几率到Shapley值：加权朴素贝叶斯分类器的解释性几何

From Log-Odds to Shapley Values: An Explanatory Geometry for the Weighted Naive Bayes Classifier

本文构建加权朴素贝叶斯分类器的解释性空间，证明其诱导的距离与Shapley值向量的ℓ₁距离一致，还通过k近邻分类器实证比较相关监督距离，凸显监督距离、局部解释与预测行为的关联。

有向加权图的最优传输距离：以细胞间通信网络为例的案例研究

Optimal transport distances for directed, weighted graphs: a case study with cell-cell communication networks

针对有向图缺乏对称性导致最优传输距离难以应用的问题，提出基于Wasserstein和Gromov-Wasserstein变体的两种距离度量，并在模拟数据和真实单细胞RNA测序推断的细胞间通信图上评估了其性能。