TASK DEFINITION: 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.
PROBLEM: Proposed methods for prediction interval estimation so far focus on cases where input variables are numerical. In datasets with solely nominal input variables, we observe records with the exact same input x, but different real valued outputs due to the inherent noise in the system. Existing prediction interval estimation methods do not use representations that can accurately model such inherent noise in the case of nominal inputs. We propose a new prediction interval estimation method tailored for this type of data, which is prevalent in biology and medicine. We call this method Distribution Adaptive Prediction Interval Estimation given Nominal inputs (DAPIEN) and has four main phases. First, we select a distribution function that can best represent the inherent noise of the system for all unique inputs. Then we infer the parameters θi (e.g. θi = [meani, variancei]) of the selected distribution function for all unique input vectors xi and generate a new corresponding training set using pairs of xi , θi. III). Then, we train a model to predict θ given a new xu. Finally, we calculate the prediction interval for a new sample using the inverse of the cumulative distribution function once the parameters θ is predicted by the trained model. We compared DAPIEN to the commonly used Bootstrap method on three synthetic datasets. Our results show that DAPIEN provides tighter prediction intervals while preserving the requested coverage when compared to Bootstrap. This work can facilitate broader usage of regression methods in medicine and biology where it is necessary to provide tight prediction intervals while preserving coverage when input variables are nominal.

SOLUTION: DICTION INTERVAL ESTIMATION USING NOMINAL VARIABLES

PROBLEM: The Frank-Wolfe method (a.k.a. conditional gradient algorithm) for smooth optimization has regained much interest in recent years in the context of large scale optimization and machine learning. A key advantage of the method is that it avoids projections the computational bottleneck in many applications replacing it by a linear optimization step. Despite this advantage, the known convergence rates of the FW method fall behind standard first order methods for most settings of interest. It is an active line of research to derive faster linear optimization-based algorithms for various settings of convex optimization. In this paper we consider the special case of optimization over strongly convex sets, for which we prove that the vanila FW method converges at a rate of 1 t2 . This gives a quadratic improvement in convergence rate compared to the general case, in which convergence is of the order 1t , and known to be tight. We show that various balls induced by `p norms, Schatten norms and group norms are strongly convex on one hand and on the other hand, linear optimization over these sets is straightforward and admits a closed-form solution. We further show how several previous fastrate results for the FW method follow easily from our analysis.

SOLUTION: Faster Rates for the Frank-Wolfe Method over Strongly-Convex Sets

PROBLEM: Person knowledge extraction is the foundation of the Tibetan knowledge graph construction, which provides support for Tibetan question answering system, information retrieval, information extraction and other researches, and promotes national unity and social stability. This paper proposes a SVM and template based approach to Tibetan person knowledge extraction. Through constructing the training corpus, we build the templates based the shallow parsing analysis of Tibetan syntactic, semantic features and verbs. Using the training corpus, we design a hierarchical SVM classifier to realize the entity knowledge extraction. Finally, experimental results prove the method has greater improvement in Tibetan person knowledge extraction.

SOLUTION:
Method of Tibetan Person Knowledge Extraction