In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Example Input: Conditional probabilities are a core concept in machine learning. For ex-<lb>ample, optimal prediction of a label Y given an inputX corresponds to maximizing<lb>the conditional probability of Y given X . A common approach to inference tasks<lb>is learning a model of conditional probabilities. However, these models are often<lb>based on strong assumptions (e.g., log-linear models), and hence their estimate of<lb>conditional probabilities is not robust and is highly dependent on the validity of<lb>their assumptions.<lb>Here we propose a framework for reasoning about conditional probabilities without<lb>assuming anything about the underlying distributions, except knowledge of their<lb>second order marginals, which can be estimated from data. We show how this<lb>setting leads to guaranteed bounds on conditional probabilities, which can be calcu-<lb>lated efficiently in a variety of settings, including structured-prediction. Finally, we<lb>apply them to semi-supervised deep learning, obtaining results competitive with<lb>variational autoencoders.
Example Output: Robust Conditional Probabilities

Example Input: The study of social networks is a burgeoning research area. However, most existing work deals with networks that simply encode whether relationships exist or not. In contrast, relationships in signed networks can be positive (“like”, “trust”) or negative (“dislike”, “distrust”). The theory of social balance shows that signed networks tend to conform to some local patterns that, in turn, induce certain global characteristics. In this paper, we exploit both local as well as global aspects of social balance theory for two fundamental problems in the analysis of signed networks: sign prediction and clustering. Motivated by local patterns of social balance, we first propose two families of sign prediction methods: measures of social imbalance (MOIs), and supervised learning using high order cycles (HOCs). These methods predict signs of edges based on triangles and l-cycles for relatively small values of l. Interestingly, by examining measures of social imbalance, we show that the classic Katz measure, which is used widely in unsigned link prediction, actually has a balance theoretic interpretation when applied to signed networks. Furthermore, motivated by the global structure of balanced networks, we propose an effective low rank modeling approach for both sign prediction and clustering. For the low rank modeling approach, we provide theoretical performance guarantees via convex relaxations, scale it up to large problem sizes using a matrix factorization based algorithm, and provide extensive experimental validation including comparisons with local approaches. Our experimental results indicate that, by adopting a more global viewpoint of balance structure, we get significant performance and computational gains in prediction and clustering tasks on signed networks. Our work therefore highlights the usefulness of the global aspect of balance theory for the analysis of signed networks.
Example Output: Prediction and Clustering in Signed Networks: A Local to Global Perspective

Example Input: We investigate the problem of learning discrete, undirected graphical models in a differentially private way. We show that the approach of releasing noisy sufficient statistics using the Laplace mechanism achieves a good trade-off between privacy, utility, and practicality. A naive learning algorithm that uses the noisy sufficient statistics “as is” outperforms general-purpose differentially private learning algorithms. However, it has three limitations: it ignores knowledge about the data generating process, rests on uncertain theoretical foundations, and exhibits certain pathologies. We develop a more principled approach that applies the formalism of collective graphical models to perform inference over the true sufficient statistics within an expectationmaximization framework. We show that this learns better models than competing approaches on both synthetic data and on real human mobility data used as a case study.
Example Output:
Differentially Private Learning of Undirected Graphical Models Using Collective Graphical Models