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.
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Question: We introduce a novel training principle for generative probabilistic models that is an alternative to maximum likelihood. The proposed Generative Stochastic Networks (GSN) framework generalizes Denoising Auto-Encoders (DAE) and is based on learning the transition operator of a Markov chain whose stationary distribution estimates the data distribution. The transition distribution is a conditional distribution that generally involves a small move, so it has fewer dominant modes and is unimodal in the limit of small moves. This simplifies the learning problem, making it less like density estimation and more akin to supervised function approximation, with gradients that can be obtained by backprop. The theorems provided here provide a probabilistic interpretation for denoising autoencoders and generalize them; seen in the context of this framework, auto-encoders that learn with injected noise are a special case of GSNs and can be interpreted as generative models. The theorems also provide an interesting justification for dependency networks and generalized pseudolikelihood and define an appropriate joint distribution and sampling mechanism, even when the conditionals are not consistent. GSNs can be used with missing inputs and can be used to sample subsets of variables given the rest. Experiments validating these theoretical results are conducted on both synthetic datasets and image datasets. The experiments employ a particular architecture that mimics the Deep Boltzmann Machine Gibbs sampler but that allows training to proceed with backprop through a recurrent neural network with noise injected inside and without the need for layerwise pretraining.

Answer: GSNs: Generative Stochastic Networks


Question: 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.

Answer: DICTION INTERVAL ESTIMATION USING NOMINAL VARIABLES


Question: In this work we introduce a comprehensive algorithmic pipeline for multiple parametric model estimation. The proposed approach analyzes the information produced by a random sampling algorithm (e.g., RANSAC) from a machine learning/optimization perspective, using a parameterless biclustering algorithm based on L1 nonnegative matrix factorization (L1-NMF). The proposed framework exploits consistent patterns that naturally arise during the RANSAC execution, while explicitly avoiding spurious inconsistencies. Contrarily to the main trends in the literature, the proposed technique does not impose non-intersecting parametric models. A new accelerated algorithm to compute L1-NMFs allows to handle medium-sized problems faster while also extending the usability of the algorithm to much larger datasets. This accelerated algorithm has applications in any other context where an L1-NMF is needed, beyond the biclustering approach to parameter estimation here addressed. We accompany the algorithmic presentation with theoretical foundations and numerous and diverse examples.

Answer:
Fast L1-NMF for Multiple Parametric Model Estimation∗