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.

Q: The downfall of many supervised learning algorithms, such as neural networks, is the inherent need for a large amount of training data (Benediktsson et al., 1993). Although there is a lot of buzz about big data, there is still the problem of doing classification from a small data-set. Other methods such as support vector machines, although capable of dealing with few samples, are inherently binary classifiers (Cortes and Vapnik, 1995), and are in need of learning strategies such as One vs All in the case of multi-classification. In the presence of a large number of classes this can become problematic. In this paper we present, a novel approach to supervised learning through the method of clustering. Unlike traditional methods such as K-Means (MacQueen, 1967), Gravitational Clustering does not require the initial number of clusters, and automatically builds the clusters, individual samples can be arbitrarily weighted and it requires only few samples while staying resilient to over-fitting. Keywords—Machine Learning, Classification, Clustering.

A: Introduction to Gravitational Clustering
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Q: Sampling from hierarchical Bayesian models is often difficult for MCMC methods, because of the strong correlations between the model parameters and the hyperparameters. Recent Riemannian manifold Hamiltonian Monte Carlo (RMHMC) methods have significant potential advantages in this setting, but are computationally expensive. We introduce a new RMHMC method, which we call semi-separable Hamiltonian Monte Carlo, which uses a specially designed mass matrix that allows the joint Hamiltonian over model parameters and hyperparameters to decompose into two simpler Hamiltonians. This structure is exploited by a new integrator which we call the alternating blockwise leapfrog algorithm. The resulting method can mix faster than simpler Gibbs sampling while being simpler and more efficient than previous instances of RMHMC.

A: Semi-Separable Hamiltonian Monte Carlo for Inference in Bayesian Hierarchical Models
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Q: Maximum Inner Product Search (MIPS) is an important task in many machine learning applications such as the prediction phase of a low-rank matrix factorization model for a recommender system. There have been some works on how to perform MIPS in sub-linear time recently. However, most of them do not have the flexibility to control the trade-off between search efficient and search quality. In this paper, we study the MIPS problem with a computational budget. By carefully studying the problem structure of MIPS, we develop a novel Greedy-MIPS algorithm, which can handle budgeted MIPS by design. While simple and intuitive, Greedy-MIPS yields surprisingly superior performance compared to state-of-the-art approaches. As a specific example, on a candidate set containing half a million vectors of dimension 200, Greedy-MIPS runs 200x faster than the naive approach while yielding search results with the top-5 precision greater than 75%.

A:
A Greedy Approach for Budgeted Maximum Inner Product Search
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