Motivation: An important problem in systems biology is reconstructing complete networks of interactions between biological objects by extrapolating from a few known interactions as examples. While there are many computational techniques proposed for this network reconstruction task, their accuracy is consistently limited by the small number of high-confidence examples, and the uneven distribution of these examples across the potential interaction space, with some objects having many known interactions and others few. Results: To address this issue, we propose two computational methods based on the concept of training set expansion. They work particularly effectively in conjunction with kernel approaches, which are a popular class of approaches for fusing together many disparate types of features. Both our methods are based on semisupervised learning and involve augmenting the limited number of

This survey is an introduction to positive definite kernels and the set of methods they have inspired in the machine learning literature, namely kernel methods. We first discuss some properties of positive definite kernels as well as reproducing kernel Hibert spaces, the natural extension of the set of functions {k(x, ·), x ∈ X} associated with a kernel k defined on a space X. We discuss at length the construction of kernel functions that take advantage of well-known statistical models. We provide an overview of numerous data-analysis methods which take advantage of reproducing kernel Hilbert spaces and discuss the idea of combining several kernels to improve the performance on certain tasks. We also provide a short cookbook of different kernels which are particularly useful for certain datatypes such as images, graphs or speech segments. Remark: This report is a draft. Comments and suggestions will be highly appreciated. Summary We provide in this survey a short introduction to positive definite kernels and the set of methods they have inspired in machine learning, also known as kernel methods. The main idea behind kernel methods is the following. Most datainference tasks aim at defining an appropriate decision function f on a set of objects of interest X. When X is a vector space of dimension d, say R d, linear functions fa(x) = a T x are one of the easiest and better understood choices, notably for regression, classification or dimensionality reduction. Given a positive definite kernel k on X, that is a real-valued function on X × X which quantifies effectively how similar two points x and y are through the value k(x, y), kernel methods are algorithms which estimate functions f of the form f: x ∈ X → f(x) = ∑ αik(xi, x), (1) i∈I

Information diffusion and virus propagation are fundamental processes taking place in networks. While it is often possible to directly observe when nodes become infected with a virus or publish the information, observing individual transmissions (who infects whom, or who influences whom) is typically very difficult. Furthermore, in many applications, the underlying network over which the diffusions and propagations spread is actually unobserved. We tackle these challenges by developing a method for tracing paths of diffusion and influence through networks and inferring the networks over which contagions propagate. Given the times when nodes adopt pieces of information or become infected, we identify the optimal network that best explains the observed infection times. Since the optimization problem is NP-hard to solve exactly, we develop an efficient approximation algorithm that scales to large datasets and finds provably near-optimal networks. We demonstrate the effectiveness of our approach by tracing information diffusion in a set of 170 million blogs and news articles over a one year period to infer how information flows through the online media space. We find that the diffusion network of news for the top 1,000 media sites and blogs tends to have a core-periphery structure with a small set of core media sites that diffuse information to the rest of the Web. These sites tend to have stable circles of influence with more general news media sites acting as connectors between them.