Generative modeling using the sliced Wasserstein distance

Generative adversarial nets (GANs) are very successful at modeling distributions from given samples, even in the high-dimensional case. However, their formulation is also known to be hard to optimize and often unstable. While the aforementioned problems are particularly true for early GAN formulations, there has been significant empirically motivated and theoretically founded progress to improve stability, for instance, by using the Wasserstein distance rather than the Jenson-Shannon divergence. Here, we consider an alternative formulation for generative modeling based on random projections which, in its simplest form, results in a single objective rather than a saddlepoint formulation. By augmenting this approach with a discriminator we improve its accuracy. We found our approach to be significantly more stable compared to even the improved Wasserstein GAN. Further, unlike the traditional GAN loss, the loss formulated in our method is a good measure of the actual distance between the distributions and, for the first time for GAN training, we are able to show estimates for the same

Assembly and activation of DNA damage sensing kinase Mec1-Ddc2

This thesis comprises five chapters. Chapter 1 presents the introduction. It summarizes the role of checkpoint kinase Mec1-Ddc2 in the DNA damage response. In chapter 1, an extensive account of the literature on Mec1-Ddc2 recruitment and activation at DNA damage sites is provided which sets the foundation for chapter 2. Chapter 2 presents results that contribute the major finding of my thesis. This chapter focuses on how homodimers of Ddc2 are recruited to DNA damage sites via interaction with RPA. Based on structural, biochemical and in vivo data, the chapter presents a to-scale model of Mec1-Ddc2 bound to ssDNA-RPA complexes at DNA damage sites and shows that cell survival after UV-damage is dependent on Ddc2 homodimerization and recruitment to RPA. These results are published in Deshpande et al., Molecular Cell, 2017. Chapter 3 presents experimental results which show that an N-terminal region within the coiled-coil domain of human ATRIP is important for coiled-coil homodimerization. Chapter 4 presents results on the role of the MRX protein complex as a structural linchpin that holds sister chromatids together at DNA double-strand breaks. This function of MRX is apparently dependent on its interaction with a domain in RPA that also binds Ddc2. The results are published in Seeber et al., Molecular Cell, 2016. Chapter 5 summarizes the major conclusions of this thesis and discusses the future directions

Max-Sliced Wasserstein Distance and its use for GANs

Generative adversarial nets (GANs) and variational auto-encoders have significantly improved our distribution modeling capabilities, showing promise for dataset augmentation, image-to-image translation and feature learning. However, to model high-dimensional distributions, sequential training and stacked architectures are common, increasing the number of tunable hyper-parameters as well as the training time. Nonetheless, the sample complexity of the distance metrics remains one of the factors affecting GAN training. We first show that the recently proposed sliced Wasserstein distance has compelling sample complexity properties when compared to the Wasserstein distance. To further improve the sliced Wasserstein distance we then analyze its `projection complexity' and develop the max-sliced Wasserstein distance which enjoys compelling sample complexity while reducing projection complexity, albeit necessitating a max estimation. We finally illustrate that the proposed distance trains GANs on high-dimensional images up to a resolution of 256x256 easily.Comment: Accepted to CVPR 201

Fast exploration and learning of latent graphs with aliased observations

We consider the problem of recovering a latent graph where the observations at each node are \emph{aliased}, and transitions are stochastic. Observations are gathered by an agent traversing the graph. Aliasing means that multiple nodes emit the same observation, so the agent can not know in which node it is located. The agent needs to uncover the hidden topology as accurately as possible and in as few steps as possible. This is equivalent to efficient recovery of the transition probabilities of a partially observable Markov decision process (POMDP) in which the observation probabilities are known. An algorithm for efficiently exploring (and ultimately recovering) the latent graph is provided. Our approach is exponentially faster than naive exploration in a variety of challenging topologies with aliased observations while remaining competitive with existing baselines in the unaliased regime

Graph schemas as abstractions for transfer learning, inference, and planning

We propose schemas as a model for abstractions that can be used for rapid transfer learning, inference, and planning. Common structured representations of concepts and behaviors -- schemas -- have been proposed as a powerful way to encode abstractions. Latent graph learning is emerging as a new computational model of the hippocampus to explain map learning and transitive inference. We build on this work to show that learned latent graphs in these models have a slot structure -- schemas -- that allow for quick knowledge transfer across environments. In a new environment, an agent can rapidly learn new bindings between the sensory stream to multiple latent schemas and select the best fitting one to guide behavior. To evaluate these graph schemas, we use two previously published challenging tasks: the memory & planning game and one-shot StreetLearn, that are designed to test rapid task solving in novel environments. Graph schemas can be learned in far fewer episodes than previous baselines, and can model and plan in a few steps in novel variations of these tasks. We further demonstrate learning, matching, and reusing graph schemas in navigation tasks in more challenging environments with aliased observations and size variations, and show how different schemas can be composed to model larger 2D and 3D environments.Comment: 12 pages, 5 figures in main paper, 12 pages and 8 figures in appendi