The optimal transport barycenter (a.k.a. Wasserstein barycenter) is a fundamental notion of averaging that extends from the Euclidean space to the Wasserstein space of probability distributions. Computation of the unregularized barycenter for discretized probability distributions on point clouds is a challenging task when the domain dimension $d > 1$. Most practical algorithms for approximating the barycenter problem are based on entropic regularization. In this paper, we introduce a nearly linear time $O(m \log{m})$ and linear space complexity $O(m)$ primal-dual algorithm, the Wasserstein-Descent $\dot{\mathbb{H}}^1$-Ascent (WDHA) algorithm, for computing the exact barycenter when the input probability density functions are discretized on an $m$-point grid. The key success of the WDHA algorithm hinges on alternating between two different yet closely related Wasserstein and Sobolev optimization geometries for the primal barycenter and dual Kantorovich potential subproblems. Under reasonable assumptions, we establish the convergence rate and iteration complexity of WDHA to its stationary point when the step size is appropriately chosen. Superior computational efficacy, scalability, and accuracy over the existing Sinkhorn-type algorithms are demonstrated on high-resolution (e.g., $1024 \times 1024$ images) 2D synthetic and real data.

This paper introduces a novel theoretical simplification of the Diffusion Schr\"odinger Bridge (DSB) that facilitates its unification with Score-based Generative Models (SGMs), addressing the limitations of DSB in complex data generation and enabling faster convergence and enhanced performance. By employing SGMs as an initial solution for DSB, our approach capitalizes on the strengths of both frameworks, ensuring a more efficient training process and improving the performance of SGM. We also propose a reparameterization technique that, despite theoretical approximations, practically improves the network's fitting capabilities. Our extensive experimental evaluations confirm the effectiveness of the simplified DSB, demonstrating its significant improvements. We believe the contributions of this work pave the way for advanced generative modeling. The code is available at https://github.com/checkcrab/SDSB.

Compared to the existing function-based models in deep generative modeling, the recently proposed diffusion models have achieved outstanding performance with a stochastic-process-based approach. But a long sampling time is required for this approach due to many timesteps for discretization. Schr\"odinger bridge (SB)-based models attempt to tackle this problem by training bidirectional stochastic processes between distributions. However, they still have a slow sampling speed compared to generative models such as generative adversarial networks. And due to the training of the bidirectional stochastic processes, they require a relatively long training time. Therefore, this study tried to reduce the number of timesteps and training time required and proposed regularization terms to the existing SB models to make the bidirectional stochastic processes consistent and stable with a reduced number of timesteps. Each regularization term was integrated into a single term to enable more efficient training in computation time and memory usage. Applying this regularized stochastic process to various generation tasks, the desired translations between different distributions were obtained, and accordingly, the possibility of generative modeling based on a stochastic process with faster sampling speed could be confirmed. The code is available at https://github.com/KiUngSong/RSB.

Double-strand DNA breaks (DSBs) are a form of DNA damage that can cause abnormal chromosomal rearrangements. Recent technologies based on high-throughput experiments have obvious high costs and technical challenges.Therefore, we design a graph neural network based method to predict DSBs (GraphDSB), using DNA sequence features and chromosome structure information. In order to improve the expression ability of the model, we introduce Jumping Knowledge architecture and several effective structural encoding methods. The contribution of structural information to the prediction of DSBs is verified by the experiments on datasets from normal human epidermal keratinocytes (NHEK) and chronic myeloid leukemia cell line (K562), and the ablation studies further demonstrate the effectiveness of the designed components in the proposed GraphDSB framework. Finally, we use GNNExplainer to analyze the contribution of node features and topology to DSBs prediction, and proved the high contribution of 5-mer DNA sequence features and two chromatin interaction modes.

Julian and I independently wrote summaries of our solution to the 2017 Data Science Bowl. What is below is my (Daniel's) summary. For the other half of the story, see Julian's post here. Julian is a freelance software/machine learning engineer so check out his site and work if you are looking to apply machine intelligence to your work. He won 3rd in last year's Data Science Bowl too!

Hot on the heels of confirmed reports that China is getting ready to equip cruise missiles with artificial intelligence targeting capability, a "summer study" on autonomy done by the Defense Science Board shows that the U.S. has already been thinking of weaponizing artificial intelligence. The DSB is a federal advisory committee to the U.S. Secretary of Defense, also known as SecDef, a post currently held by Ashton Carter. He is also the CEO of the United States Department of Defense. According to the publicly available DSB study, it "offers important recommendations to identify the science, engineering, and policy problems that must be solved to permit greater operational use of autonomy across all warfighting domains." The report also outlines various projects that the government can undertake that will utilize the power of artificial intelligence, machine learning and data analytics to automate several dangerous processes that are currently carried out manually, such as "offensive maritime mining" and "mine counter measure" missions.