Screening Rules for Convex Problems

We propose a new framework for deriving screening rules for convex optimization problems. Our approach covers a large class of constrained and penalized optimization formulations, and works in two steps. First, given any approximate point, the structure of the objective function and the duality gap is used to gather information on the optimal solution. In the second step, this information is used to produce screening rules, i.e. safely identifying unimportant weight variables of the optimal solution. Our general framework leads to a large variety of useful existing as well as new screening rules for many applications. For example, we provide new screening rules for general simplex and $L_1$-constrained problems, Elastic Net, squared-loss Support Vector Machines, minimum enclosing ball, as well as structured norm regularized problems, such as group lasso

Intelligent Word Embeddings of Free-Text Radiology Reports

Radiology reports are a rich resource for advancing deep learning applications in medicine by leveraging the large volume of data continuously being updated, integrated, and shared. However, there are significant challenges as well, largely due to the ambiguity and subtlety of natural language. We propose a hybrid strategy that combines semantic-dictionary mapping and word2vec modeling for creating dense vector embeddings of free-text radiology reports. Our method leverages the benefits of both semantic-dictionary mapping as well as unsupervised learning. Using the vector representation, we automatically classify the radiology reports into three classes denoting confidence in the diagnosis of intracranial hemorrhage by the interpreting radiologist. We performed experiments with varying hyperparameter settings of the word embeddings and a range of different classifiers. Best performance achieved was a weighted precision of 88% and weighted recall of 90%. Our work offers the potential to leverage unstructured electronic health record data by allowing direct analysis of narrative clinical notes.Comment: AMIA Annual Symposium 201

Explicit Learning Curves for Transduction and Application to Clustering and Compression Algorithms

Inductive learning is based on inferring a general rule from a finite data set and using it to label new data. In transduction one attempts to solve the problem of using a labeled training set to label a set of unlabeled points, which are given to the learner prior to learning. Although transduction seems at the outset to be an easier task than induction, there have not been many provably useful algorithms for transduction. Moreover, the precise relation between induction and transduction has not yet been determined. The main theoretical developments related to transduction were presented by Vapnik more than twenty years ago. One of Vapnik's basic results is a rather tight error bound for transductive classification based on an exact computation of the hypergeometric tail. While tight, this bound is given implicitly via a computational routine. Our first contribution is a somewhat looser but explicit characterization of a slightly extended PAC-Bayesian version of Vapnik's transductive bound. This characterization is obtained using concentration inequalities for the tail of sums of random variables obtained by sampling without replacement. We then derive error bounds for compression schemes such as (transductive) support vector machines and for transduction algorithms based on clustering. The main observation used for deriving these new error bounds and algorithms is that the unlabeled test points, which in the transductive setting are known in advance, can be used in order to construct useful data dependent prior distributions over the hypothesis space