We study the underdamped Langevin diffusion when the log of the target distribution is smooth and strongly concave. We present a MCMC algorithm based on its discretization and show that it achieves ε error (in 2-Wasserstein distance) in O( √ d/ε) steps. This is a significant improvement over the best known rate for overdamped Langevin MCMC, which is O(d/ε 2 ) steps under the same smoothness/concavity assumptions.The underdamped Langevin MCMC scheme can be viewed as a version of Hamiltonian Monte Carlo (HMC) which has been observed to outperform overdamped Langevin MCMC methods in a number of application areas. We provide quantitative rates that support this empirical wisdom.

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Background: CRISPR/Cas9 system, as the third-generation genome editing technology, has been widely applied in target gene repair and gene expression regulation. Selection of appropriate sgRNA can improve the on-target knockout efficacy of CRISPR/Cas9 system with high sensitivity and specificity. However, when CRISPR/Cas9 system is operating, unexpected cleavage may occur at some sites, known as off-target. Presently, a number of prediction methods have been developed to predict the off-target propensity of sgRNA at specific DNA fragments. Most of them use artificial feature extraction operations and machine learning techniques to obtain off-target scores. With the rapid expansion of off-target data and the rapid development of deep learning theory, the existing prediction methods can no longer satisfy the prediction accuracy at the clinical level. Results: Here, we propose a prediction method named CnnCrispr to predict the off-target propensity of sgRNA at specific DNA fragments. CnnCrispr automatically trains the sequence features of sgRNA-DNA pairs with GloVe model, and embeds the trained word vector matrix into the deep learning model including biLSTM and CNN with five hidden layers. We conducted performance verification on the data set provided by DeepCrispr, and found that the auROC and auPRC in the "leave-one-sgRNA-out" cross validation could reach 0.957 and 0.429 respectively (the Pearson value and spearman value could reach 0.495 and 0.151 respectively under the same settings). Conclusion: Our results show that CnnCrispr has better classification and regression performance than the existing states-of-art models. The code for CnnCrispr can be freely downloaded from https://github.com/LQYoLH/CnnCrispr.

Modern graph clustering applications require the analysis of large graphs and this can be computationally expensive. In this regard, local spectral graph clustering methods aim to identify well-connected clusters around a given "seed set" of reference nodes without accessing the entire graph. The celebrated Approximate Personalized PageRank (APPR) algorithm in the seminal paper by Andersen et al.[1] is one such method. APPR was introduced and motivated purely from an algorithmic perspective. In other words, there is no a priori notion of objective function/optimality conditions that characterizes the steps taken by APPR. Here, we derive a novel variational formulation which makes explicit the actual optimization problem solved by APPR. In doing so, we draw connections between the local spectral algorithm of [1] and an iterative shrinkage-thresholding algorithm (ISTA). In particular, we show that, appropriately initialized ISTA applied to our variational formulation can recover the sought-after local cluster in a time that only depends on the number of non-zeros of the optimal solution instead of the entire graph. In the process, we show that an optimization algorithm which apparently requires accessing the entire graph, can be made to behave in a completely local manner by accessing only a small number of nodes. This viewpoint builds a bridge across two seemingly disjoint fields of graph processing and numerical optimization, and it allows one to leverage well-studied, numerically robust, and efficient optimization algorithms for processing today's large graphs. * A preliminary version of this work appeared with the title "Exploiting Optimization for Local Graph Clustering" as a technical report [9]. 1 In between global and local algorithms, there is a class of locally-biased algorithms, e.g., [18], whose running time depends on the entire graph, however, the solution is locally-biased toward some input seed set of reference nodes. We don't consider them in this paper.

No abstract