OpenRaiser/Intern-Atlas huggingface dataset:
Adaptive Low-Rank Kernel Subspace Clustering
Venue: arXiv cs.CV 2019
Year: 2019

In this paper, we present a kernel subspace clustering method that can handle non-linear models. In contrast to recent kernel subspace clustering methods which use predefined kernels, we propose to learn a low-rank kernel matrix, with which mapped data in feature space are not only low-rank but also self-expressive. In this manner, the low-dimensional subspace structures of the (implicitly) mapped data are retained and manifested in the high-dimensional feature space. We evaluate the proposed method extensively on both motion segmentation and image clustering benchmarks, and obtain superior results, outperforming the kernel subspace clustering method that uses standard kernels[Patel 2014] and other state-of-the-art linear subspace clustering methods.
Shorter tours and longer detours: Uniform covers and a bit beyond
Venue: arXiv cs.DS 2019
Year: 2019

Motivated by the well known four-thirds conjecture for the traveling salesman problem (TSP), we study the problem of {\em uniform covers}. A graph $G=(V,E)$ has an $α$-uniform cover for TSP (2EC, respectively) if the everywhere $α$ vector (i.e. $\{α\}^{E}$) dominates a convex combination of incidence vectors of tours (2-edge-connected spanning multigraphs, respectively). The polyhedral analysis of Christofides' algorithm directly implies that a 3-edge-connected, cubic graph has a 1-uniform cover for TSP. Sebő asked if such graphs have $(1-ε)$-uniform covers for TSP for some $ε> 0$. Indeed, the four-thirds conjecture implies that such graphs have 8/9-uniform covers. We show that these graphs have 18/19-uniform covers for TSP. We also study uniform covers for 2EC and show that the everywhere 15/17 vector can be efficiently written as a convex combination of 2-edge-connected spanning multigraphs. For a weighted, 3-edge-connected, cubic graph, our results show that if the everywhere 2/3 vector is an optimal solution for the subtour linear programming relaxation, then a tour with weight at most 27/19 times that of an optimal tour can be found efficiently. Node-weighted, 3-edge-connected, cubic graphs fall into this category. In this special case, we can apply our tools to obtain an even better approximation guarantee. To extend our approach to input graphs that are 2-edge-connected, we present a procedure to decompose an optimal solution for the subtour relaxation for TSP into spanning, connected multigraphs that cover each 2-edge cut an even number of times. Using this decomposition, we obtain a 17/12-approximation algorithm for minimum weight 2-edge-connected spanning subgraphs on subcubic, node-weighted graphs.
The Devil is in the Decoder: Classification, Regression and GANs
Venue: arXiv cs.CV 2019
Year: 2019

Many machine vision applications, such as semantic segmentation and depth prediction, require predictions for every pixel of the input image. Models for such problems usually consist of encoders which decrease spatial resolution while learning a high-dimensional representation, followed by decoders who recover the original input resolution and result in low-dimensional predictions. While encoders have been studied rigorously, relatively few studies address the decoder side. This paper presents an extensive comparison of a variety of decoders for a variety of pixel-wise tasks ranging from classification, regression to synthesis. Our contributions are: (1) Decoders matter: we observe significant variance in results between different types of decoders on various problems. (2) We introduce new residual-like connections for decoders. (3) We introduce a novel decoder: bilinear additive upsampling. (4) We explore prediction artifacts.
Load Thresholds for Cuckoo Hashing with Overlapping Blocks
Venue: arXiv cs.DS 2019
Year: 2019

Dietzfelbinger and Weidling [DW07] proposed a natural variation of cuckoo hashing where each of $cn$ objects is assigned $k = 2$ intervals of size $\ell$ in a linear (or cyclic) hash table of size $n$ and both start points are chosen independently and uniformly at random. Each object must be placed into a table cell within its intervals, but each cell can only hold one object. Experiments suggested that this scheme outperforms the variant with blocks in which intervals are aligned at multiples of $\ell$. In particular, the load threshold is higher, i.e. the load $c$ that can be achieved with high probability. For instance, Lehman and Panigrahy [LP09] empirically observed the threshold for $\ell = 2$ to be around $96.5\%$ as compared to roughly $89.7\%$ using blocks. They managed to pin down the asymptotics of the thresholds for large $\ell$, but the precise values resisted rigorous analysis. We establish a method to determine these load thresholds for all $\ell \geq 2$, and, in fact, for general $k \geq 2$. For instance, for $k = \ell = 2$ we get $\approx 96.4995\%$. The key tool we employ is an insightful and general theorem due to Leconte, Lelarge, and Massoulié [LLM13], which adapts methods from statistical physics to the world of hypergraph orientability. In effect, the orientability thresholds for our graph families are determined by belief propagation equations for certain graph limits. As a side note we provide experimental evidence suggesting that placements can be constructed in linear time with loads close to the threshold using an adapted version of an algorithm by Khosla [Kho13].
Greedy Shortest Common Superstring Approximation in Compact Space
Venue: arXiv cs.DS 2019
Year: 2019

Given a set of strings, the shortest common superstring problem is to find the shortest possible string that contains all the input strings. The problem is NP-hard, but a lot of work has gone into designing approximation algorithms for solving the problem. We present the first time and space efficient implementation of the classic greedy heuristic which merges strings in decreasing order of overlap length. Our implementation works in $O(n \log σ)$ time and bits of space, where $n$ is the total length of the input strings in characters, and $σ$ is the size of the alphabet. After index construction, a practical implementation of our algorithm uses roughly $5 n \log σ$ bits of space and reasonable time for a real dataset that consists of DNA fragments.
Monocular Visual Teach and Repeat Aided by Local Ground Planarity
Venue: arXiv cs.RO 2019
Year: 2019

Visual Teach and Repeat (VT\&R) allows an autonomous vehicle to repeat a previously traversed route without a global positioning system. Existing implementations of VT\&R typically rely on 3D sensors such as stereo cameras for mapping and localization, but many mobile robots are equipped with only 2D monocular vision for tasks such as teleoperated bomb disposal. While simultaneous localization and mapping (SLAM) algorithms exist that can recover 3D structure and motion from monocular images, the scale ambiguity inherent in these methods complicates the estimation and control of lateral path-tracking error, which is essential for achieving high-accuracy path following. In this paper, we propose a monocular vision pipeline that enables kilometre-scale route repetition with centimetre-level accuracy by approximating the ground surface near the vehicle as planar (with some uncertainty) and recovering absolute scale from the known position and orientation of the camera relative to the vehicle. This system provides added value to many existing robots by allowing for high-accuracy autonomous route repetition with a simple software upgrade and no additional sensors. We validate our system over 4.3 km of autonomous navigation and demonstrate accuracy on par with the conventional stereo pipeline, even in highly non-planar terrain.
Almost everywhere injectivity conditions for the matrix recovery problem
Venue: arXiv cs.IT 2019
Year: 2019

Matrix recovery is raised in many areas. In this paper, we build up a framework for almost everywhere matrix recovery which means to recover almost all the $P\in {\mathcal M}\subset {\mathbb H}^{p\times q}$ from $Tr(A_jP), j=1,\ldots,N$ where $A_j\in V_j\subset {\mathbb H}^{p\times q}$. We mainly focus on the following question: how many measurements are needed to recover almost all the matrices in ${\mathcal M}$? For the case where both ${\mathcal M}$ and $V_j$ are algebraic varieties, we use the tools from algebraic geometry to study the question and present some results to address it under many different settings.
Approximate Random Matrix Models for Generalized Fading MIMO Channels
Venue: arXiv cs.IT 2019
Year: 2019

Approximate random matrix models for $κ-μ$ and $η-μ$ faded multiple input multiple output (MIMO) communication channels are derived in terms of a complex Wishart matrix. The proposed approximation has the least Kullback-Leibler (KL) divergence from the original matrix distribution. The utility of the results are demonstrated in a) computing the average capacity/rate expressions of $κ-μ$/$η-μ$ MIMO systems b) computing outage probability (OP) expressions for maximum ratio combining (MRC) for $κ-μ$/$η-μ$ faded MIMO channels c) ergodic rate expressions for zero-forcing (ZF) receiver in an uplink single cell massive MIMO scenario with low resolution analog-to-digital converters (ADCs) in the antennas. These approximate expressions are compared with Monte-Carlo simulations and a close match is observed.
Targeting and Signaling in Ad Auctions
Venue: arXiv cs.GT 2019
Year: 2019

Modern ad auctions allow advertisers to target more specific segments of the user population. Unfortunately, this is not always in the best interest of the ad platform. In this paper, we examine the following basic question in the context of second-price ad auctions: how should an ad platform optimally reveal information about the ad opportunity to the advertisers in order to maximize revenue? We consider a model in which bidders' valuations depend on a random state of the ad opportunity. Different from previous work, we focus on a more practical, and challenging, situation where the space of possible realizations of ad opportunities is extremely large. We thus focus on developing algorithms whose running time is independent of the number of ad opportunity realizations. We examine the auctioneer's algorithmic question of designing the optimal signaling scheme. When the auctioneer is restricted to send a public signal to all bidders, we focus on a well-motivated Bayesian valuation setting in which the auctioneer and bidders both have private information, and present two main results: 1. we exhibit a characterization result regarding approximately optimal schemes and prove that any constant-approximate public signaling scheme must use exponentially many signals; 2. we present a "simple" public signaling scheme that serves as a constant approximation under mild assumptions. We then initiate an exploration on the power of being able to send different signals privately to different bidders. Here we examine a basic setting where the auctioneer knows bidders' valuations, and exhibit a polynomial-time private scheme that extracts almost full surplus even in the worst Bayes Nash equilibrium. This illustrates the surprising power of private signaling schemes in extracting revenue.
Combining guaranteed and spot markets in display advertising: Selling guaranteed page views with stochastic demand
Venue: arXiv cs.GT 2019
Year: 2019

While page views are often sold instantly through real-time auctions when users visit websites, they can also be sold in advance via guaranteed contracts. In this paper, we present a dynamic programming model to study how an online publisher should optimally allocate and price page views between guaranteed and spot markets. The problem is challenging because the allocation and pricing of guaranteed contracts affect how advertisers split their purchases between the two markets, and the terminal value of the model is endogenously determined by the updated dual force of supply and demand in auctions. We take the advertisers' purchasing behaviour into consideration, i.e., risk aversion and stochastic demand arrivals, and present a scalable and efficient algorithm for the optimal solution. The model is also empirically validated with a commercial dataset. The experimental results show that selling page views via both channels can increase the publisher's expected total revenue, and the optimal pricing and allocation strategies are robust to different market and advertiser types.
Random Binary Trees for Approximate Nearest Neighbour Search in Binary Space
Venue: arXiv cs.CV 2019
Year: 2019

Approximate nearest neighbour (ANN) search is one of the most important problems in computer science fields such as data mining or computer vision. In this paper, we focus on ANN for high-dimensional binary vectors and we propose a simple yet powerful search method that uses Random Binary Search Trees (RBST). We apply our method to a dataset of 1.25M binary local feature descriptors obtained from a real-life image-based localisation system provided by Google as a part of Project Tango. An extensive evaluation of our method against the state-of-the-art variations of Locality Sensitive Hashing (LSH), namely Uniform LSH and Multi-probe LSH, shows the superiority of our method in terms of retrieval precision with performance boost of over 20%
Extractive Summarization using Deep Learning
Venue: arXiv cs.CL 2019
Year: 2019

This paper proposes a text summarization approach for factual reports using a deep learning model. This approach consists of three phases: feature extraction, feature enhancement, and summary generation, which work together to assimilate core information and generate a coherent, understandable summary. We are exploring various features to improve the set of sentences selected for the summary, and are using a Restricted Boltzmann Machine to enhance and abstract those features to improve resultant accuracy without losing any important information. The sentences are scored based on those enhanced features and an extractive summary is constructed. Experimentation carried out on several articles demonstrates the effectiveness of the proposed approach. Source code available at: https://github.com/vagisha-nidhi/TextSummarizer
Optimally Guarding 2-Reflex Orthogonal Polyhedra by Reflex Edge Guards
Venue: arXiv cs.CG 2019
Year: 2019

Let an orthogonal polyhedron be the union of a finite set of boxes in $\mathbb R^3$ (i.e., cuboids with edges parallel to the coordinate axes), whose surface is a connected 2-manifold. We study the NP-complete problem of guarding a non-convex orthogonal polyhedron having reflex edges in just two directions (as opposed to three, in the general case) by placing the minimum number of edge guards on reflex edges only. We show that $$\left\lfloor \frac{r-g}{2} \right\rfloor +1$$ reflex edge guards are sufficient, where $r$ is the number of reflex edges and $g$ is the polyhedron's genus. This bound is tight for $g=0$. We thereby generalize a classic planar Art Gallery theorem of O'Rourke, which states that the same upper bound holds for vertex guards in an orthogonal polygon with $r$ reflex vertices and $g$ holes. Then we give a similar upper bound in terms of $m$, the total number of edges in the polyhedron. We prove that $$\left\lfloor \frac{m-4}{8} \right\rfloor +g$$ reflex edge guards are sufficient, whereas the previous best known bound was $\lfloor 11m/72+g/6\rfloor-1$ edge guards (not necessarily reflex). We also consider the setting in which guards are open (i.e., they are segments without the endpoints), proving that the same results hold even in this more challenging case. Finally, we show how to compute guard locations matching the above bounds in $O(n \log n)$ time.
Scalable Kernelization for Maximum Independent Sets
Venue: arXiv cs.DS 2019
Year: 2019

The most efficient algorithms for finding maximum independent sets in both theory and practice use reduction rules to obtain a much smaller problem instance called a kernel. The kernel can then be solved quickly using exact or heuristic algorithms---or by repeatedly kernelizing recursively in the branch-and-reduce paradigm. It is of critical importance for these algorithms that kernelization is fast and returns a small kernel. Current algorithms are either slow but produce a small kernel, or fast and give a large kernel. We attempt to accomplish both of these goals simultaneously, by giving an efficient parallel kernelization algorithm based on graph partitioning and parallel bipartite maximum matching. We combine our parallelization techniques with two techniques to accelerate kernelization further: dependency checking that prunes reductions that cannot be applied, and reduction tracking that allows us to stop kernelization when reductions become less fruitful. Our algorithm produces kernels that are orders of magnitude smaller than the fastest kernelization methods, while having a similar execution time. Furthermore, our algorithm is able to compute kernels with size comparable to the smallest known kernels, but up to two orders of magnitude faster than previously possible. Finally, we show that our kernelization algorithm can be used to accelerate existing state-of-the-art heuristic algorithms, allowing us to find larger independent sets faster on large real-world networks and synthetic instances.
An efficient algorithm to decide periodicity of $b$-recognisable sets using LSDF convention
Venue: arXiv cs.FL 2019
Year: 2019

Let $b$ be an integer strictly greater than $1$. Each set of nonnegative integers is represented in base $b$ by a language over $\{0, 1, \dots, b - 1\}$. The set is said to be $b$-recognisable if it is represented by a regular language. It is known that ultimately periodic sets are $b$-recognisable, for every base $b$, and Cobham's theorem implies the converse: no other set is $b$-recognisable in every base $b$. We consider the following decision problem: let $S$ be a set of nonnegative integers that is $b$-recognisable, given as a finite automaton over $\{0,1, \dots, b - 1\}$, is $S$ periodic? Honkala showed in 1986 that this problem is decidable. Later on, Leroux used in 2005 the convention to write number representations with the least significant digit first (LSDF), and designed a quadratic algorithm to solve a more general problem. We use here LSDF convention as well and give a structural description of the minimal automata that accept periodic sets. Then, we show that it can be verified in linear time if a minimal automaton meets this description. In general, this yields a $O(b \log(n))$ procedure to decide whether an automaton with $n$ states accepts an ultimately periodic set of nonnegative integers.
Adaptive Linear Programming Decoding of Nonbinary Linear Codes Over Prime Fields
Venue: arXiv cs.IT 2019
Year: 2019

In this work, we consider adaptive linear programming (ALP) decoding of linear codes over the finite field $\mathbb{F}_p$ of size $p$ where $p$ is a prime. In particular, we provide a general construction of valid inequalities for the codeword polytope of the so-called constant-weight embedding of a single parity-check (SPC) code over any prime field. The construction is based on classes of building blocks that are assembled to form the left-hand side of an inequality according to several rules. In the case of almost doubly-symmetric valid classes we prove that the resulting inequalities are all facet-defining, while we conjecture this to be true if and only if the class is valid and symmetric. For $p=3$, there is only a single valid symmetric class and we prove that the resulting inequalities together with the so-called simplex constraints give a completely and irredundant description of the codeword polytope of the embedded SPC code. For $p>5$, we show that there are additional facets beyond those from the proposed construction. We use these inequalities to develop an efficient (relaxed) ALP decoder for general (non-SPC) linear codes over prime fields. The key ingredient is an efficient separation algorithm based on the principle of dynamic programming. Furthermore, we construct a decoder for linear codes over arbitrary fields $\mathbb{F}_q$ with $q=p^m$ and $m>1$ by a factor graph representation that reduces to several instances of the case $m=1$, which results, in general, in a relaxation of the original decoding polytope. Finally, we present an efficient cut-generating algorithm to search for redundant parity-checks to further improve the performance towards maximum-likelihood decoding for short-to-medium block lengths. Numerical experiments confirm that our new decoder is very efficient compared to a static LP decoder for various field sizes, check-node degrees, and block lengths.
Gap-planar Graphs
Venue: arXiv cs.CG 2019
Year: 2019

We introduce the family of $k$-gap-planar graphs for $k \geq 0$, i.e., graphs that have a drawing in which each crossing is assigned to one of the two involved edges and each edge is assigned at most $k$ of its crossings. This definition is motivated by applications in edge casing, as a $k$-gap-planar graph can be drawn crossing-free after introducing at most $k$ local gaps per edge. We present results on the maximum density of $k$-gap-planar graphs, their relationship to other classes of beyond-planar graphs, characterization of $k$-gap-planar complete graphs, and the computational complexity of recognizing $k$-gap-planar graphs.
Deep Learning for Video Game Playing
Venue: arXiv cs.AI 2019
Year: 2019

In this article, we review recent Deep Learning advances in the context of how they have been applied to play different types of video games such as first-person shooters, arcade games, and real-time strategy games. We analyze the unique requirements that different game genres pose to a deep learning system and highlight important open challenges in the context of applying these machine learning methods to video games, such as general game playing, dealing with extremely large decision spaces and sparse rewards.
Degrees-of-Freedom of the MIMO Three-Way Channel with Node-Intermittency
Venue: arXiv cs.IT 2019
Year: 2019

The characterization of fundamental performance bounds of many-to-many communication systems in which participating nodes are active in an intermittent way is one of the major challenges in communication theory. In order to address this issue, we introduce the multiple-input multiple-output (MIMO) three-way channel (3WC) with an intermittent node and study its degrees-of-freedom (DoF) region and sum-DoF. We devise a non-adaptive encoding scheme based on zero-forcing, interference alignment and erasure coding, and show its DoF region (and thus sum-DoF) optimality for non-intermittent 3WCs and its sum-DoF optimality for (node-)intermittent 3WCs. However, we show by example that in general some DoF tuples in the intermittent 3WC can only be achieved by adaptive schemes, such as decode-forward relaying. This shows that non-adaptive encoding is sufficient for the non-intermittent 3WC and for the sum-DoF of intermittent 3WCs, but adaptive encoding is necessary for the DoF region of intermittent 3WCs. Our work contributes to a better understanding of the fundamental limits of multi-way communication systems with intermittency and the impact of adaptation therein.