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.

Input: Consider Input: 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 i (e.g. i = [meani, variancei]) of the selected distribution function for all unique input vectors xi and generate a new corresponding training set using pairs of xi , i. III). Then, we train a model to predict 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 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.

Output: DICTION INTERVAL ESTIMATION USING NOMINAL VARIABLES

Input: Consider Input: An approach to incorporate deep learning within an iterative image reconstruction framework to reconstruct images from severely incomplete measurement data is presented. Specifically, we utilize a convolutional neural network (CNN) as a quasi-projection operator within a least squares minimization procedure. The CNN is trained to encode high level information about the class of images being imaged; this information is utilized to mitigate artifacts in intermediate images produced by use of an iterative method. The structure of the method was inspired by the proximal gradient descent method, where the proximal operator is replaced by a deep CNN and the gradient descent step is generalized by use of a linear reconstruction operator. It is demonstrated that this approach improves image quality for several cases of limited-view image reconstruction and that using a CNN in an iterative method increases performance compared to conventional image reconstruction approaches. We test our method on several limited-view image reconstruction problems. Qualitative and quantitative results demonstrate state-of-the-art performance.

Output: Deep Learning-Guided Image Reconstruction from Incomplete Data

Input: Consider Input: We propose a method to construct finite-state reactive controllers for systems whose interactions with their adversarial environment are modeled by infinite-duration twoplayer games over (possibly) infinite graphs. The proposed method targets safety games with infinitely many states or with such a large number of states that it would be impractical if not impossiblefor conventional synthesis techniques that work on the entire state space. We resort to constructing finitestate controllers for such systems through an automata learning approach, utilizing a symbolic representation of the underlying game that is based on finite automata. Throughout the learning process, the learner maintains an approximation of the winning region (represented as a finite automaton) and refines it using different types of counterexamples provided by the teacher until a satisfactory controller can be derived (if one exists). We present a symbolic representation of safety games (inspired by regular model checking), propose implementations of the learner and teacher, and evaluate their performance on examples motivated by robotic motion planning in dynamic environments.
Output: An Automaton Learning Approach to Solving Safety Games over Infinite Graphs