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.

Ex Input:
We present a practical and statistically consistent scheme for actively learning binary classifiers under general loss functions. Our algorithm uses importance weighting to correct sampling bias, and by controlling the variance, we are able to give rigorous label complexity bounds for the learning process. Experiments on passively labeled data show that this approach reduces the label complexity required to achieve good predictive performance on many learning problems.

Ex Output:
Importance Weighted Active Learning

Ex Input:
We extend the standard rough set-based approach to deal with huge amounts of numeric attributes versus small amount of available objects. Here, a novel approach of clustering along with dimensionality reduction; Hybrid Fuzzy C Means-Quick Reduct (FCMQR) algorithm is proposed for single gene selection. Gene selection is a process to select genes which are more informative. It is one of the important steps in knowledge discovery. The problem is that all genes are not important in gene expression data. Some of the genes may be redundant, and others may be irrelevant and noisy. In this study, the entire dataset is divided in proper grouping of similar genes by applying Fuzzy C Means (FCM) algorithm. A high class discriminated genes has been selected based on their degree of dependenc e by applying Quick Reduct algorithm based on Rough Set Theory to all the resultant clusters. Average Correlation Value (ACV) is calculated f or the high class discriminated genes. The clusters which have the ACV value a s 1 is determined as significant clusters, whose classification accuracy will be equal or high when comparing to the accuracy of the entire dataset. The proposed algorithm is evaluated using WEKA classifiers and compared. Finally, experimental results related to the leukemia cancer data confirm that our approach is quite promising, though it surely requires further research.

Ex Output:
A Novel Approach for Single Gene Selection Using Clustering and Dimensionality Reduction

Ex Input:
The use of M-estimators in generalized linear regression models in high dimensional settings requires risk minimization with hard L0 constraints. Of the known methods, the class of projected gradient descent (also known as iterative hard thresholding (IHT)) methods is known to offer the fastest and most scalable solutions. However, the current state-of-the-art is only able to analyze these methods in extremely restrictive settings which do not hold in high dimensional statistical models. In this work we bridge this gap by providing the first analysis for IHT-style methods in the high dimensional statistical setting. Our bounds are tight and match known minimax lower bounds. Our results rely on a general analysis framework that enables us to analyze several popular hard thresholding style algorithms (such as HTP, CoSaMP, SP) in the high dimensional regression setting. We also extend our analysis to a large family of "fully corrective methods" that includes two-stage and partial hard-thresholding algorithms. We show that our results hold for the problem of sparse regression, as well as low-rank matrix recovery.

Ex Output:
On Iterative Hard Thresholding Methods for High-dimensional M-Estimation