We introduce a notion of distance between supervised learning problems, which we call the Risk distance. This optimal-transport-inspired distance facilitates stability results; one can quantify how seriously issues like sampling bias, noise, limited data, and approximations might change a given problem by bounding how much these modifications can move the problem under the Risk distance. With the distance established, we explore the geometry of the resulting space of supervised learning problems, providing explicit geodesics and proving that the set of classification problems is dense in a larger class of problems. We also provide two variants of the Risk distance: one that incorporates specified weights on a problem's predictors, and one that is more sensitive to the contours of a problem's risk landscape.

As a classical problem in the field of complex networks, link prediction has attracted much attention from researchers, which is of great significance to help us understand the evolution and dynamic development mechanisms of networks. Although various network type-specific algorithms have been proposed to tackle the link prediction problem, most of them suppose that the network structure is dominated by the Triadic Closure Principle. We still lack an adaptive and comprehensive understanding of network formation patterns for predicting potential links. In addition, it is valuable to investigate how network local information can be better utilized. To this end, we proposed a novel method named Link prediction using Multiple Order Local Information (MOLI) that exploits the local information from the neighbors of different distances, with parameters that can be a prior-driven based on prior knowledge, or data-driven by solving an optimization problem on observed networks. MOLI defined a local network diffusion process via random walks on the graph, resulting in better use of network information. We show that MOLI outperforms the other 11 widely used link prediction algorithms on 11 different types of simulated and real-world networks. We also conclude that there are different patterns of local information utilization for different networks, including social networks, communication networks, biological networks, etc. In particular, the classical common neighbor-based algorithm is not as adaptable to all social networks as it is perceived to be; instead, some of the social networks obey the Quadrilateral Closure Principle which preferentially connects paths of length three.

Researchers have generated a diverse repository of 838,644 histopathologic images and used them to optimize and discretize learned representations into 512-dimensional feature vectors. They show that individual machine-engineered features correlate with salient human-derived morphologic constructs and ontological relationships. Dynamic and reversible RNA modifications such as N6-methyladenosine (m6A) can play important roles in regulating messenger RNA (mRNA) splicing, export, stability and translation. Researchers developed RNAmod (https://bioinformatics.sc.cn/RNAmod), an interactive, one-stop, web-based platform for the automated analysis, annotation, and visualization of mRNA modifications in 21 species. MOLI, a multi-omics late integration method based on deep neural networks, takes somatic mutation, copy number aberration and gene expression data as input, and integrates them for drug response prediction.