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Register a new userGenerating Data using Monte Carlo Dropout
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For many analytical problems the challenge is to handle huge amounts of available data. However, there are data science application areas where collecting information is difficult and costly, e.g., in the study of geological phenomena, rare diseases, faults in complex systems, insurance frauds, etc. In many such cases, generators of synthetic data with the same statistical and predictive properties as the actual data allow efficient simulations and development of tools and applications. In this work, we propose the incorporation of Monte Carlo Dropout method within Autoencoder (MCD-AE) and Variational Autoencoder (MCD-VAE) as efficient generators of synthetic data sets. As the Variational Autoencoder (VAE) is one of the most popular generator techniques, we explore its similarities and differences to the proposed methods. We compare the generated data sets with the original data based on statistical properties, structural similarity, and predictive similarity. The results obtained show a strong similarity between the results of VAE, MCD-VAE and MCD-AE; however, the proposed methods are faster and can generate values similar to specific selected initial instances.
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Due to complex experimental settings, missing values are common in biomedical data. To handle this issue, many methods have been proposed, from ignoring incomplete instances to various data imputation approaches. With the recent rise of deep neural networks, the field of missing data imputation has oriented towards modelling of the data distribution. This paper presents an approach based on Monte Carlo dropout within (Variational) Autoencoders which offers not only very good adaptation to the distribution of the data but also allows generation of new data, adapted to each specific instance. The evaluation shows that the imputation error and predictive similarity can be improved with the proposed approach.
Markov chain Monte Carlo (MCMC) is a popular and successful general-purpose tool for Bayesian inference. However, MCMC cannot be practically applied to large data sets because of the prohibitive cost of evaluating every likelihood term at every iteration. Here we present Firefly Monte Carlo (FlyMC) an auxiliary variable MCMC algorithm that only queries the likelihoods of a potentially small subset of the data at each iteration yet simulates from the exact posterior distribution, in contrast to recent proposals that are approximate even in the asymptotic limit. FlyMC is compatible with a wide variety of modern MCMC algorithms, and only requires a lower bound on the per-datum likelihood factors. In experiments, we find that FlyMC generates samples from the posterior more than an order of magnitude faster than regular MCMC, opening up MCMC methods to larger datasets than were previously considered feasible.
Computational color constancy is a preprocessing step used in many camera systems. The main aim is to discount the effect of the illumination on the colors in the scene and restore the original colors of the objects. Recently, several deep learning-based approaches have been proposed to solve this problem and they often led to state-of-the-art performance in terms of average errors. However, for extreme samples, these methods fail and lead to high errors. In this paper, we address this limitation by proposing to aggregate different deep learning methods according to their output uncertainty. We estimate the relative uncertainty of each approach using Monte Carlo dropout and the final illumination estimate is obtained as the sum of the different model estimates weighted by the log-inverse of their corresponding uncertainties. The proposed framework leads to state-of-the-art performance on INTEL-TAU dataset.
Deep Gaussian Processes (DGPs) are hierarchical generalizations of Gaussian Processes that combine well calibrated uncertainty estimates with the high flexibility of multilayer models. One of the biggest challenges with these models is that exact inference is intractable. The current state-of-the-art inference method, Variational Inference (VI), employs a Gaussian approximation to the posterior distribution. This can be a potentially poor unimodal approximation of the generally multimodal posterior. In this work, we provide evidence for the non-Gaussian nature of the posterior and we apply the Stochastic Gradient Hamiltonian Monte Carlo method to generate samples. To efficiently optimize the hyperparameters, we introduce the Moving Window MCEM algorithm. This results in significantly better predictions at a lower computational cost than its VI counterpart. Thus our method establishes a new state-of-the-art for inference in DGPs.
The classical Langevin Monte Carlo method looks for samples from a target distribution by descending the samples along the gradient of the target distribution. The method enjoys a fast convergence rate. However, the numerical cost is sometimes high because each iteration requires the computation of a gradient. One approach to eliminate the gradient computation is to employ the concept of ensemble. A large number of particles are evolved together so the neighboring particles provide gradient information to each other. In this article, we discuss two algorithms that integrate the ensemble feature into LMC and the associated properties. In particular, we find that if one directly surrogates the gradient using the ensemble approximation, the algorithm, termed Ensemble Langevin Monte Carlo, is unstable due to a high variance term. If the gradients are replaced by the ensemble approximations only in a constrained manner, to protect from the unstable points, the algorithm, termed Constrained Ensemble Langevin Monte Carlo, resembles the classical LMC up to an ensemble error but removes most of the gradient computation.
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