Approximate Set Union Via Approximate Randomization

We develop an randomized approximation algorithm for the size of set union problem \arrowvert A_1\cup A_2\cup...\cup A_m\arrowvert, which given a list of sets $A_1,...,A_m$ with approximate set size $m_i$ for $A_i$ with $m_i\in \left((1-\beta_L)|A_i|, (1+\beta_R)|A_i|\right)$, and biased random generators with Prob(x=\randomElm(A_i))\in \left[{1-\alpha_L\over |A_i|},{1+\alpha_R\over |A_i|}\right] for each input set $A_i$ and element $x\in A_i,$ where $i=1, 2, ..., m$. The approximation ratio for \arrowvert A_1\cup A_2\cup...\cup A_m\arrowvert is in the range $[(1-\epsilon)(1-\alpha_L)(1-\beta_L), (1+\epsilon)(1+\alpha_R)(1+\beta_R)]$ for any $\epsilon\in (0,1)$, where $\alpha_L, \alpha_R, \beta_L,\beta_R\in (0,1)$. The complexity of the algorithm is measured by both time complexity, and round complexity. The algorithm is allowed to make multiple membership queries and get random elements from the input sets in one round. Our algorithm makes adaptive accesses to input sets with multiple rounds. Our algorithm gives an approximation scheme with O(\setCount\cdot(\log \setCount)^{O(1)}) running time and $O(\log m)$ rounds, where $m$ is the number of sets. Our algorithm can handle input sets that can generate random elements with bias, and its approximation ratio depends on the bias. Our algorithm gives a flexible tradeoff with time complexity O\left(\setCount^{1+\xi}\right) and round complexity $O\left({1\over \xi}\right)$ for any $\xi\in(0,1)$

TIGS: An Inference Algorithm for Text Infilling with Gradient Search

Text infilling is defined as a task for filling in the missing part of a sentence or paragraph, which is suitable for many real-world natural language generation scenarios. However, given a well-trained sequential generative model, generating missing symbols conditioned on the context is challenging for existing greedy approximate inference algorithms. In this paper, we propose an iterative inference algorithm based on gradient search, which is the first inference algorithm that can be broadly applied to any neural sequence generative models for text infilling tasks. We compare the proposed method with strong baselines on three text infilling tasks with various mask ratios and different mask strategies. The results show that our proposed method is effective and efficient for fill-in-the-blank tasks, consistently outperforming all baselines.Comment: The 57th Annual Meeting of the Association for Computational Linguistics (ACL 2019

DeepICP: An End-to-End Deep Neural Network for 3D Point Cloud Registration

We present DeepICP - a novel end-to-end learning-based 3D point cloud registration framework that achieves comparable registration accuracy to prior state-of-the-art geometric methods. Different from other keypoint based methods where a RANSAC procedure is usually needed, we implement the use of various deep neural network structures to establish an end-to-end trainable network. Our keypoint detector is trained through this end-to-end structure and enables the system to avoid the inference of dynamic objects, leverages the help of sufficiently salient features on stationary objects, and as a result, achieves high robustness. Rather than searching the corresponding points among existing points, the key contribution is that we innovatively generate them based on learned matching probabilities among a group of candidates, which can boost the registration accuracy. Our loss function incorporates both the local similarity and the global geometric constraints to ensure all above network designs can converge towards the right direction. We comprehensively validate the effectiveness of our approach using both the KITTI dataset and the Apollo-SouthBay dataset. Results demonstrate that our method achieves comparable or better performance than the state-of-the-art geometry-based methods. Detailed ablation and visualization analysis are included to further illustrate the behavior and insights of our network. The low registration error and high robustness of our method makes it attractive for substantial applications relying on the point cloud registration task.Comment: 10 pages, 6 figures, 3 tables, typos corrected, experimental results updated, accepted by ICCV 201