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: Mean-field variational inference is a method for approximate Bayesian posterior inference. It approximates a full posterior distribution with a factorized set of distributions by maximizing a lower bound on the marginal likelihood. This requires the ability to integrate a sum of terms in the log joint likelihood using this factorized distribution. Often not all integrals are in closed form, which is typically handled by using a lower bound. We present an alternative algorithm based on stochastic optimization that allows for direct optimization of the variational lower bound. This method uses control variates to reduce the variance of the stochastic search gradient, in which existing lower bounds can play an important role. We demonstrate the approach on two non-conjugate models: logistic regression and an approximation to the HDP.

Answer: Variational Bayesian Inference with Stochastic Search


Question: CUR matrix decomposition computes the low rank approximation of a given matrix by using the actual rows and columns of the matrix. It has been a very useful tool for handling large matrices. One limitation with the existing algorithms for CUR matrix decomposition is that they need an access to the full matrix, a requirement that can be difficult to fulfill in many real world applications. In this work, we alleviate this limitation by developing a CUR decomposition algorithm for partially observed matrices. In particular, the proposed algorithm computes the low rank approximation of the target matrix based on (i) the randomly sampled rows and columns, and (ii) a subset of observed entries that are randomly sampled from the matrix. Our analysis shows the relative error bound, measured by spectral norm, for the proposed algorithm when the target matrix is of full rank. We also show that only O(nr ln r) observed entries are needed by the proposed algorithm to perfectly recover a rank r matrix of size n × n, which improves the sample complexity of the existing algorithms for matrix completion. Empirical studies on both synthetic and real-world datasets verify our theoretical claims and demonstrate the effectiveness of the proposed algorithm.

Answer: CUR Algorithm for Partially Observed Matrices


Question: Sleep stages pattern provides important clues in diagnosing the presence of sleep disorder. By analyzing sleep stages pattern and extracting its features from EEG, EOG, and EMG signals, we can classify sleep stages. This study presents a novel classification model for predicting sleep stages with a high accuracy. The main idea is to combine the generative capability of Deep Belief Network (DBN) with a discriminative ability and sequence pattern recognizing capability of Long Short-term Memory (LSTM). We use DBN that is treated as an automatic higher level features generator. The input to DBN is 28 ”handcrafted” features as used in previous sleep stages studies. We compared our method with other techniques which combined DBN with Hidden Markov Model (HMM).In this study, we exploit the sequence or time series characteristics of sleep dataset. To the best of our knowledge, most of the present sleep analysis from polysomnogram relies only on single instanced label (nonsequence) for classification. In this study, we used two datasets: an open data set that is treated as a benchmark; the other dataset is our sleep stages dataset (available for download) to verify the results further. Our experiments showed that the combination of DBN with LSTM gives better overall accuracy 98.75% (Fscore=0.9875) for benchmark dataset and 98.94% (Fscore=0.9894) for MKG dataset. This result is better than the state of the art of sleep stages classification that was 91.31%i. Keywords— sleep stages classification, long short term memory, deep belief network, deep learning

Answer:
Combining Generative and Discriminative Neural Networks for Sleep Stages Classification