OpenRaiser/Intern-Atlas huggingface dataset:
The Truth Behind the Myth of the Folk Theorem
Venue: arXiv cs.GT 2015
Year: 2015

We study the problem of computing an $ε$-Nash equilibrium in repeated games. Earlier work by Borgs et al. [2010] suggests that this problem is intractable. We show that if we make a slight change to their model---modeling the players as polynomial-time Turing machines that maintain state ---and make some standard cryptographic hardness assumptions (the existence of public-key encryption), the problem can actually be solved in polynomial time. Our algorithm works not only for games with a finite number of players, but also for constant-degree graphical games. As Nash equilibrium is a weak solution concept for extensive form games, we additionally define and study an appropriate notion of a subgame-perfect equilibrium for computationally bounded players, and show how to efficiently find such an equilibrium in repeated games (again, making standard cryptographic hardness assumptions).
High-quality Image Restoration from Partial Mixed Adaptive-Random Measurements
Venue: arXiv cs.IT 2015
Year: 2015

A novel framework to construct an efficient sensing (measurement) matrix, called mixed adaptive-random (MAR) matrix, is introduced for directly acquiring a compressed image representation. The mixed sampling (sensing) procedure hybridizes adaptive edge measurements extracted from a low-resolution image with uniform random measurements predefined for the high-resolution image to be recovered. The mixed sensing matrix seamlessly captures important information of an image, and meanwhile approximately satisfies the restricted isometry property. To recover the high-resolution image from MAR measurements, the total variation algorithm based on the compressive sensing theory is employed for solving the Lagrangian regularization problem. Both peak signal-to-noise ratio and structural similarity results demonstrate the MAR sensing framework shows much better recovery performance than the completely random sensing one. The work is particularly helpful for high-performance and lost-cost data acquisition.
Efficient Multi-Robot Motion Planning for Unlabeled Discs in Simple Polygons
Venue: arXiv cs.CG 2015
Year: 2015

We consider the following motion-planning problem: we are given $m$ unit discs in a simple polygon with $n$ vertices, each at their own start position, and we want to move the discs to a given set of $m$ target positions. Contrary to the standard (labeled) version of the problem, each disc is allowed to be moved to any target position, as long as in the end every target position is occupied. We show that this unlabeled version of the problem can be solved in $O(n\log n+mn+m^2)$ time, assuming that the start and target positions are at least some minimal distance from each other. This is in sharp contrast to the standard (labeled) and more general multi-robot motion-planning problem for discs moving in a simple polygon, which is known to be strongly NP-hard.
The Throughput-Outage Tradeoff of Wireless One-Hop Caching Networks
Venue: arXiv cs.IT 2015
Year: 2015

We consider a wireless device-to-device (D2D) network where the nodes have pre-cached information from a library of available files. Nodes request files at random. If the requested file is not in the on-board cache, then it is downloaded from some neighboring node via one-hop "local" communication. An outage event occurs when a requested file is not found in the neighborhood of the requesting node, or if the network admission control policy decides not to serve the request. We characterize the optimal throughput-outage tradeoff in terms of tight scaling laws for various regimes of the system parameters, when both the number of nodes and the number of files in the library grow to infinity. Our analysis is based on Gupta and Kumar {\em protocol model} for the underlying D2D wireless network, widely used in the literature on capacity scaling laws of wireless networks without caching. Our results show that the combination of D2D spectrum reuse and caching at the user nodes yields a per-user throughput independent of the number of users, for any fixed outage probability in $(0,1)$. This implies that the D2D caching network is "scalable": even though the number of users increases, each user achieves constant throughput. This behavior is very different from the classical Gupta and Kumar result on ad-hoc wireless networks, for which the per-user throughput vanishes as the number of users increases. Furthermore, we show that the user throughput is directly proportional to the fraction of cached information over the whole file library size. Therefore, we can conclude that D2D caching networks can turn "memory" into "bandwidth" (i.e., doubling the on-board cache memory on the user devices yields a 100\% increase of the user throughout).
Stable Camera Motion Estimation Using Convex Programming
Venue: arXiv cs.CV 2015
Year: 2015

We study the inverse problem of estimating n locations $t_1, ..., t_n$ (up to global scale, translation and negation) in $R^d$ from noisy measurements of a subset of the (unsigned) pairwise lines that connect them, that is, from noisy measurements of $\pm (t_i - t_j)/\|t_i - t_j\|$ for some pairs (i,j) (where the signs are unknown). This problem is at the core of the structure from motion (SfM) problem in computer vision, where the $t_i$'s represent camera locations in $R^3$. The noiseless version of the problem, with exact line measurements, has been considered previously under the general title of parallel rigidity theory, mainly in order to characterize the conditions for unique realization of locations. For noisy pairwise line measurements, current methods tend to produce spurious solutions that are clustered around a few locations. This sensitivity of the location estimates is a well-known problem in SfM, especially for large, irregular collections of images. In this paper we introduce a semidefinite programming (SDP) formulation, specially tailored to overcome the clustering phenomenon. We further identify the implications of parallel rigidity theory for the location estimation problem to be well-posed, and prove exact (in the noiseless case) and stable location recovery results. We also formulate an alternating direction method to solve the resulting semidefinite program, and provide a distributed version of our formulation for large numbers of locations. Specifically for the camera location estimation problem, we formulate a pairwise line estimation method based on robust camera orientation and subspace estimation. Lastly, we demonstrate the utility of our algorithm through experiments on real images.
Giving the AI definition a form suitable for the engineer
Venue: arXiv cs.AI 2015
Year: 2015

Artificial Intelligence - what is this? That is the question! In earlier papers we already gave a formal definition for AI, but if one desires to build an actual AI implementation, the following issues require attention and are treated here: the data format to be used, the idea of Undef and Nothing symbols, various ways for defining the "meaning of life", and finally, a new notion of "incorrect move". These questions are of minor importance in the theoretical discussion, but we already know the answer of the question "Does AI exist?" Now we want to make the next step and to create this program.
Local algorithms for interactive clustering
Venue: arXiv cs.DS 2015
Year: 2015

We study the design of interactive clustering algorithms for data sets satisfying natural stability assumptions. Our algorithms start with any initial clustering and only make local changes in each step; both are desirable features in many applications. We show that in this constrained setting one can still design provably efficient algorithms that produce accurate clusterings. We also show that our algorithms perform well on real-world data.
Relay Broadcast Channel with Confidential Messages
Venue: arXiv cs.IT 2015
Year: 2015

We investigate the effects of an additional relay node on the secrecy of broadcast channels by considering the model of relay broadcast channels with confidential messages. We show that this additional relay node can increase the achievable secrecy rate region of the broadcast channels with confidential messages. More specifically, first, we investigate the discrete memoryless relay broadcast channels with two confidential messages and one common message. Three inner bounds (with respect to decode-forward, generalized noise-forward and compress-forward strategies) and an outer bound on the capacity-equivocation region are provided. Second, we investigate the discrete memoryless relay broadcast channels with two confidential messages. Inner and outer bounds on the capacity-equivocation region are provided. Finally, we investigate the discrete memoryless relay broadcast channels with one confidential message and one common message. Inner and outer bounds on the capacity-equivocation region are provided, and the results are further explained via a Gaussian example. Compared with Csiszar-Korner's work on broadcast channels with confidential messages (BCC), we find that with the help of the relay node, the secrecy capacity region of the Gaussian BCC is enhanced.
On the Learning Behavior of Adaptive Networks - Part I: Transient Analysis
Venue: arXiv cs.MA 2015
Year: 2015

This work carries out a detailed transient analysis of the learning behavior of multi-agent networks, and reveals interesting results about the learning abilities of distributed strategies. Among other results, the analysis reveals how combination policies influence the learning process of networked agents, and how these policies can steer the convergence point towards any of many possible Pareto optimal solutions. The results also establish that the learning process of an adaptive network undergoes three (rather than two) well-defined stages of evolution with distinctive convergence rates during the first two stages, while attaining a finite mean-square-error (MSE) level in the last stage. The analysis reveals what aspects of the network topology influence performance directly and suggests design procedures that can optimize performance by adjusting the relevant topology parameters. Interestingly, it is further shown that, in the adaptation regime, each agent in a sparsely connected network is able to achieve the same performance level as that of a centralized stochastic-gradient strategy even for left-stochastic combination strategies. These results lead to a deeper understanding and useful insights on the convergence behavior of coupled distributed learners. The results also lead to effective design mechanisms to help diffuse information more thoroughly over networks.
Semi-constrained Systems
Venue: arXiv cs.IT 2015
Year: 2015

When transmitting information over a noisy channel, two approaches, dating back to Shannon's work, are common: assuming the channel errors are independent of the transmitted content and devising an error-correcting code, or assuming the errors are data dependent and devising a constrained-coding scheme that eliminates all offending data patterns. In this paper we analyze a middle road, which we call a semiconstrained system. In such a system, which is an extension of the channel with cost constraints model, we do not eliminate the error-causing sequences entirely, but rather restrict the frequency in which they appear. We address several key issues in this study. The first is proving closed-form bounds on the capacity which allow us to bound the asymptotics of the capacity. In particular, we bound the rate at which the capacity of the semiconstrained $(0,k)$-RLL tends to $1$ as $k$ grows. The second key issue is devising efficient encoding and decoding procedures that asymptotically achieve capacity with vanishing error. Finally, we consider delicate issues involving the continuity of the capacity and a relaxation of the definition of semiconstrained systems.
Multicast Network Coding and Field Sizes
Venue: arXiv cs.IT 2015
Year: 2015

In an acyclic multicast network, it is well known that a linear network coding solution over GF($q$) exists when $q$ is sufficiently large. In particular, for each prime power $q$ no smaller than the number of receivers, a linear solution over GF($q$) can be efficiently constructed. In this work, we reveal that a linear solution over a given finite field does \emph{not} necessarily imply the existence of a linear solution over all larger finite fields. Specifically, we prove by construction that: (i) For every source dimension no smaller than 3, there is a multicast network linearly solvable over GF(7) but not over GF(8), and another multicast network linearly solvable over GF(16) but not over GF(17); (ii) There is a multicast network linearly solvable over GF(5) but not over such GF($q$) that $q > 5$ is a Mersenne prime plus 1, which can be extremely large; (iii) A multicast network linearly solvable over GF($q^{m_1}$) and over GF($q^{m_2}$) is \emph{not} necessarily linearly solvable over GF($q^{m_1+m_2}$); (iv) There exists a class of multicast networks with a set $T$ of receivers such that the minimum field size $q_{min}$ for a linear solution over GF($q_{min}$) is lower bounded by $Θ(\sqrt{|T|})$, but not every larger field than GF($q_{min}$) suffices to yield a linear solution. The insight brought from this work is that not only the field size, but also the order of subgroups in the multiplicative group of a finite field affects the linear solvability of a multicast network.
Democratic Representations
Venue: arXiv cs.IT 2015
Year: 2015

Minimization of the $\ell_{\infty}$ (or maximum) norm subject to a constraint that imposes consistency to an underdetermined system of linear equations finds use in a large number of practical applications, including vector quantization, approximate nearest neighbor search, peak-to-average power ratio (or "crest factor") reduction in communication systems, and peak force minimization in robotics and control. This paper analyzes the fundamental properties of signal representations obtained by solving such a convex optimization problem. We develop bounds on the maximum magnitude of such representations using the uncertainty principle (UP) introduced by Lyubarskii and Vershynin, and study the efficacy of $\ell_{\infty}$-norm-based dynamic range reduction. Our analysis shows that matrices satisfying the UP, such as randomly subsampled Fourier or i.i.d. Gaussian matrices, enable the computation of what we call democratic representations, whose entries all have small and similar magnitude, as well as low dynamic range. To compute democratic representations at low computational complexity, we present two new, efficient convex optimization algorithms. We finally demonstrate the efficacy of democratic representations for dynamic range reduction in a DVB-T2-based broadcast system.
Capacity Regions of Families of Continuous-Time Multi-User Gaussian Channels
Venue: arXiv cs.IT 2015
Year: 2015

In this paper, we propose to use Brownian motions to model families of continuous-time multiuser Gaussian channels without bandwidth limit. It turns out that such a formulation allows parallel translation of many fundamental notions and techniques from the discrete-time setting to the continuous-time regime, which enables us to derive the capacity regions of a continuous-time white Gaussian multiple access channel with/without feedback, a continuous-time white Gaussian interference channel without feedback and a continuous-time white Gaussian broadcast channel without feedback. In theory, these capacity results give the fundamental transmission limit modulation/coding schemes can achieve for families of continuous-time Gaussian one-hop channels without bandwidth limit; in practice, the explicit capacity regions derived and capacity achieving modulation/coding scheme proposed may provide engineering insights on designing multi-user communication systems operating on an ultra-wideband regime.
Discrete Convexity and Stochastic Approximation for Cross-layer On-off Transmission Control
Venue: arXiv cs.IT 2015
Year: 2015

This paper considers the discrete convexity of a cross-layer on-off transmission control problem in wireless communications. In this system, a scheduler decides whether or not to transmit in order to optimize the long-term quality of service (QoS) incurred by the queueing effects in the data link layer and the transmission power consumption in the physical (PHY) layer simultaneously. Using a Markov decision process (MDP) formulation, we show that the optimal policy can be determined by solving a minimization problem over a set of queue thresholds if the dynamic programming (DP) is submodular. We prove that this minimization problem is discrete convex. In order to search the minimizer, we consider two discrete stochastic approximation (DSA) algorithms: discrete simultaneous perturbation stochastic approximation (DSPSA) and L-natural-convex stochastic approximation (L-natural-convex SA). Through numerical studies, we show that the two DSA algorithms converge significantly faster than the existing continuous simultaneous perturbation stochastic approximation (CSPSA) algorithm in multi-user systems. Finally, we compare the convergence results and complexity of two DSA and CSPSA algorithms where we show that DSPSA achieves the best trade-off between complexity and accuracy in multi-user systems.
Scalable Capacity Bounding Models for Wireless Networks
Venue: arXiv cs.IT 2015
Year: 2015

The framework of network equivalence theory developed by Koetter et al. introduces a notion of channel emulation to construct noiseless networks as upper (resp. lower) bounding models, which can be used to calculate the outer (resp. inner) bounds for the capacity region of the original noisy network. Based on the network equivalence framework, this paper presents scalable upper and lower bounding models for wireless networks with potentially many nodes. A channel decoupling method is proposed to decompose wireless networks into decoupled multiple-access channels (MACs) and broadcast channels (BCs). The upper bounding model, consisting of only point-to-point bit pipes, is constructed by firstly extending the "one-shot" upper bounding models developed by Calmon et al. and then integrating them with network equivalence tools. The lower bounding model, consisting of both point-to-point and point-to-points bit pipes, is constructed based on a two-step update of the lower bounding models to incorporate the broadcast nature of wireless transmission. The main advantages of the proposed methods are their simplicity and the fact that they can be extended easily to large networks with a complexity that grows linearly with the number of nodes. It is demonstrated that the resulting upper and lower bounds can approach the capacity in some setups.
General factorization framework for context-aware recommendations
Venue: arXiv cs.IR 2015
Year: 2015

Context-aware recommendation algorithms focus on refining recommendations by considering additional information, available to the system. This topic has gained a lot of attention recently. Among others, several factorization methods were proposed to solve the problem, although most of them assume explicit feedback which strongly limits their real-world applicability. While these algorithms apply various loss functions and optimization strategies, the preference modeling under context is less explored due to the lack of tools allowing for easy experimentation with various models. As context dimensions are introduced beyond users and items, the space of possible preference models and the importance of proper modeling largely increases. In this paper we propose a General Factorization Framework (GFF), a single flexible algorithm that takes the preference model as an input and computes latent feature matrices for the input dimensions. GFF allows us to easily experiment with various linear models on any context-aware recommendation task, be it explicit or implicit feedback based. The scaling properties makes it usable under real life circumstances as well. We demonstrate the framework's potential by exploring various preference models on a 4-dimensional context-aware problem with contexts that are available for almost any real life datasets. We show in our experiments -- performed on five real life, implicit feedback datasets -- that proper preference modelling significantly increases recommendation accuracy, and previously unused models outperform the traditional ones. Novel models in GFF also outperform state-of-the-art factorization algorithms. We also extend the method to be fully compliant to the Multidimensional Dataspace Model, one of the most extensive data models of context-enriched data. Extended GFF allows the seamless incorporation of information into the fac[truncated]
Optimal Fractional Repetition Codes based on Graphs and Designs
Venue: arXiv cs.IT 2015
Year: 2015

Fractional repetition (FR) codes is a family of codes for distributed storage systems that allow for uncoded exact repairs having the minimum repair bandwidth. However, in contrast to minimum bandwidth regenerating (MBR) codes, where a random set of a certain size of available nodes is used for a node repair, the repairs with FR codes are table based. This usually allows to store more data compared to MBR codes. In this work, we consider bounds on the fractional repetition capacity, which is the maximum amount of data that can be stored using an FR code. Optimal FR codes which attain these bounds are presented. The constructions of these FR codes are based on combinatorial designs and on families of regular and biregular graphs. These constructions of FR codes for given parameters raise some interesting questions in graph theory. These questions and some of their solutions are discussed in this paper. In addition, based on a connection between FR codes and batch codes, we propose a new family of codes for DSS, namely fractional repetition batch codes, which have the properties of batch codes and FR codes simultaneously. These are the first codes for DSS which allow for uncoded efficient exact repairs and load balancing which can be performed by several users in parallel. Other concepts related to FR codes are also discussed.
Localization and centrality in networks
Venue: arXiv cs.SI 2015
Year: 2015

Eigenvector centrality is a common measure of the importance of nodes in a network. Here we show that under common conditions the eigenvector centrality displays a localization transition that causes most of the weight of the centrality to concentrate on a small number of nodes in the network. In this regime the measure is no longer useful for distinguishing among the remaining nodes and its efficacy as a network metric is impaired. As a remedy, we propose an alternative centrality measure based on the nonbacktracking matrix, which gives results closely similar to the standard eigenvector centrality in dense networks where the latter is well behaved, but avoids localization and gives useful results in regimes where the standard centrality fails.