Many biological data analysis processes like Cytometry or Next Generation Sequencing (NGS) produce massive amounts of data which needs to be processed in batches for down-stream analysis. Such datasets are prone to technical variations due to difference in handling the batches possibly at different times, by different experimenters or under other different conditions. This adds variation to the batches coming from the same source sample. These variations are known as Batch Effects. It is possible that these variations and natural variations due to biology confound but such situations can be avoided by performing experiments in a carefully planned manner. Batch effects can hamper down-stream analysis and may also cause results to be inconclusive. Thus, it is essential to correct for these effects. Some recent methods propose deep learning based solution to solve this problem. We demonstrate that this can be solved using a novel Generative Adversarial Networks (GANs) based framework. The advantage of using this framework over other prior approaches is that here we do not require to choose a reproducing kernel and define its parameters.We demonstrate results of our framework on a Mass Cytometry dataset.
Some of the recent deep learning based methods to solve this problem utilize residual networks to learn a near identity mapping from source to target by optimizing the Maximum Mean Discrepancy (MMD) between the transformed source and original target @cite_10 @cite_7 @cite_1 . MMD is one the several methods used to quantify the distance between two continuous distributions. It uses the distance measure between the means of distribution in some transformed space as a proxy to distance measure between distributions in original space. Let @math and @math be two distributions over set @math , let @math be a transformation from @math to reproducing kernel Hilbert space @math then MMD is defined as MMD depends upon the choice of reproducing kernel and hence one needs to devise a method to find the optimum kernel parameters. We propose a solution based on a Generative Adversarial Network (GAN) and report our results on a mass cytometry dataset which was used for a similar study before. Since our method does not involve reproducing kernel, we don't have to discover and specify kernel parameters explicitly.
@cite_1 @cite_10 @cite_7
2962892300 2962919088 2950863313 2592141621
Generative moment matching network (GMMN) is a deep generative model that differs from Generative Adversarial Network (GAN) by replacing the discriminator in GAN with a two-sample test based on kernel maximum mean discrepancy (MMD). Although some theoretical guarantees of MMD have been studied, the empirical performance of GMMN is still not as competitive as that of GAN on challenging and large benchmark datasets. The computational efficiency of GMMN is also less desirable in comparison with GAN, partially due to its requirement for a rather large batch size during the training. In this paper, we propose to improve both the model expressiveness of GMMN and its computational efficiency by introducing adversarial kernel learning techniques, as the replacement of a fixed Gaussian kernel in the original GMMN. The new approach combines the key ideas in both GMMN and GAN, hence we name it MMD-GAN. The new distance measure in MMD-GAN is a meaningful loss that enjoys the advantage of weak @math topology and can be optimized via gradient descent with relatively small batch sizes. In our evaluation on multiple benchmark datasets, including MNIST, CIFAR-10, CelebA and LSUN, the performance of MMD-GAN significantly outperforms GMMN, and is competitive with other representative GAN works. We investigate the training and performance of generative adversarial networks using the Maximum Mean Discrepancy (MMD) as critic, termed MMD GANs. As our main theoretical contribution, we clarify the situation with bias in GAN loss functions raised by recent work: we show that gradient estimators used in the optimization process for both MMD GANs and Wasserstein GANs are unbiased, but learning a discriminator based on samples leads to biased gradients for the generator parameters. We also discuss the issue of kernel choice for the MMD critic, and characterize the kernel corresponding to the energy distance used for the Cramer GAN critic. Being an integral probability metric, the MMD benefits from training strategies recently developed for Wasserstein GANs. In experiments, the MMD GAN is able to employ a smaller critic network than the Wasserstein GAN, resulting in a simpler and faster-training algorithm with matching performance. We also propose an improved measure of GAN convergence, the Kernel Inception Distance, and show how to use it to dynamically adapt learning rates during GAN training. We propose a method to optimize the representation and distinguishability of samples from two probability distributions, by maximizing the estimated power of a statistical test based on the maximum mean discrepancy (MMD). This optimized MMD is applied to the setting of unsupervised learning by generative adversarial networks (GAN), in which a model attempts to generate realistic samples, and a discriminator attempts to tell these apart from data samples. In this context, the MMD may be used in two roles: first, as a discriminator, either directly on the samples, or on features of the samples. Second, the MMD can be used to evaluate the performance of a generative model, by testing the model's samples against a reference data set. In the latter role, the optimized MMD is particularly helpful, as it gives an interpretable indication of how the model and data distributions differ, even in cases where individual model samples are not easily distinguished either by eye or by classifier. The learning of domain-invariant representations in the context of domain adaptation with neural networks is considered. We propose a new regularization method that minimizes the discrepancy between domain-specific latent feature representations directly in the hidden activation space. Although some standard distribution matching approaches exist that can be interpreted as the matching of weighted sums of moments, e.g. Maximum Mean Discrepancy (MMD), an explicit order-wise matching of higher order moments has not been considered before. We propose to match the higher order central moments of probability distributions by means of order-wise moment differences. Our model does not require computationally expensive distance and kernel matrix computations. We utilize the equivalent representation of probability distributions by moment sequences to define a new distance function, called Central Moment Discrepancy (CMD). We prove that CMD is a metric on the set of probability distributions on a compact interval. We further prove that convergence of probability distributions on compact intervals w.r.t. the new metric implies convergence in distribution of the respective random variables. We test our approach on two different benchmark data sets for object recognition (Office) and sentiment analysis of product reviews (Amazon reviews). CMD achieves a new state-of-the-art performance on most domain adaptation tasks of Office and outperforms networks trained with MMD, Variational Fair Autoencoders and Domain Adversarial Neural Networks on Amazon reviews. In addition, a post-hoc parameter sensitivity analysis shows that the new approach is stable w.r.t. parameter changes in a certain interval. The source code of the experiments is publicly available.