instruction:
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.
question:
CUR matrix decomposition computes the low rank approximation of a given matrix by using the actual rows and columns of the matrix. It has been a very useful tool for handling large matrices. One limitation with the existing algorithms for CUR matrix decomposition is that they need an access to the full matrix, a requirement that can be difficult to fulfill in many real world applications. In this work, we alleviate this limitation by developing a CUR decomposition algorithm for partially observed matrices. In particular, the proposed algorithm computes the low rank approximation of the target matrix based on (i) the randomly sampled rows and columns, and (ii) a subset of observed entries that are randomly sampled from the matrix. Our analysis shows the relative error bound, measured by spectral norm, for the proposed algorithm when the target matrix is of full rank. We also show that only O(nr ln r) observed entries are needed by the proposed algorithm to perfectly recover a rank r matrix of size n n, which improves the sample complexity of the existing algorithms for matrix completion. Empirical studies on both synthetic and real-world datasets verify our theoretical claims and demonstrate the effectiveness of the proposed algorithm.
answer:
CUR Algorithm for Partially Observed Matrices

question:
Positive unlabeled (PU) learning is useful in various practical situations, where there is a need to learn a classifier for a class of interest from an unlabeled data set, which may contain anomalies as well as samples from unknown classes. The learning task can be formulated as an optimization problem under the framework of statistical learning theory. Recent studies have theoretically analyzed its properties and generalization performance, nevertheless, little effort has been made to consider the problem of scalability, especially when large sets of unlabeled data are available. In this work we propose a novel scalable PU learning algorithm that is theoretically proven to provide the optimal solution, while showing superior computational and memory performance. Experimental evaluation confirms the theoretical evidence and shows that the proposed method can be successfully applied to a large variety of real-world problems involving PU learning.
answer:
Efficient Training for Positive Unlabeled Learning

question:
This paper describes a new method for classifying a dataset that partitions elements into different categories. It has relations with neural networks but works in a different way, requiring only a single pass through the classifier to generate the weight sets. A grid structure is required and a novel idea of converting a row of real values into a 2-D or grid-like structure of value bands. Each cell in the band can then store a cell weight value and also a set of weights that represent its own importance to each of the output categories. For any input that needs to be categorised, all of the output weight lists for each relevant input cell can be retrieved and summed to produce a probability for what the correct output category is. So the relative importance of each input point to the output is distributed to each cell. The construction process itself can simply be the reinforcement of the weight values, without requiring an iterative adjustment process, making it potentially much faster.
answer:
A Single-Pass Classifier for Categorical Data