OpenRaiser/Intern-Atlas huggingface dataset:
On the Noise Robustness of Simultaneous Orthogonal Matching Pursuit
Venue: arXiv cs.IT 2017
Year: 2017

In this paper, the joint support recovery of several sparse signals whose supports present similarities is examined. Each sparse signal is acquired using the same noisy linear measurement process, which returns fewer observations than the dimension of the sparse signals. The measurement noise is assumed additive, Gaussian, and admits different variances for each sparse signal that is measured. Using the theory of compressed sensing, the performance of simultaneous orthogonal matching pursuit (SOMP) is analysed for the envisioned signal model. The cornerstone of this paper is a novel analysis method upper bounding the probability that SOMP recovers at least one incorrect entry of the joint support during a prescribed number of iterations. Furthermore, the probability of SOMP failing is investigated whenever the number of sparse signals being recovered simultaneously increases and tends to infinity. In particular, convincing observations and theoretical results suggest that SOMP committing no mistake in the noiseless case does not guarantee the absence of error in the noisy case whenever the number of acquired sparse signals scales to infinity. Finally, simulation results confirm the validity of the theoretical results.
Achieving Budget-optimality with Adaptive Schemes in Crowdsourcing
Venue: arXiv cs.LG 2017
Year: 2017

Crowdsourcing platforms provide marketplaces where task requesters can pay to get labels on their data. Such markets have emerged recently as popular venues for collecting annotations that are crucial in training machine learning models in various applications. However, as jobs are tedious and payments are low, errors are common in such crowdsourced labels. A common strategy to overcome such noise in the answers is to add redundancy by getting multiple answers for each task and aggregating them using some methods such as majority voting. For such a system, there is a fundamental question of interest: how can we maximize the accuracy given a fixed budget on how many responses we can collect on the crowdsourcing system. We characterize this fundamental trade-off between the budget (how many answers the requester can collect in total) and the accuracy in the estimated labels. In particular, we ask whether adaptive task assignment schemes lead to a more efficient trade-off between the accuracy and the budget. Adaptive schemes, where tasks are assigned adaptively based on the data collected thus far, are widely used in practical crowdsourcing systems to efficiently use a given fixed budget. However, existing theoretical analyses of crowdsourcing systems suggest that the gain of adaptive task assignments is minimal. To bridge this gap, we investigate this question under a strictly more general probabilistic model, which has been recently introduced to model practical crowdsourced annotations. Under this generalized Dawid-Skene model, we characterize the fundamental trade-off between budget and accuracy. We introduce a novel adaptive scheme that matches this fundamental limit. We further quantify the fundamental gap between adaptive and non-adaptive schemes, by comparing the trade-off with the one for non-adaptive schemes. Our analyses confirm that the gap is significant.
Optimization of Caching Devices with Geometric Constraints
Venue: arXiv cs.NI 2017
Year: 2017

It has been recently advocated that in large communication systems it is beneficial both for the users and for the network as a whole to store content closer to users. One particular implementation of such an approach is to co-locate caches with wireless base stations. In this paper we study geographically distributed caching of a fixed collection of files. We model cache placement with the help of stochastic geometry and optimize the allocation of storage capacity among files in order to minimize the cache miss probability. We consider both per cache capacity constraints as well as an average capacity constraint over all caches. The case of per cache capacity constraints can be efficiently solved using dynamic programming, whereas the case of the average constraint leads to a convex optimization problem. We demonstrate that the average constraint leads to significantly smaller cache miss probability. Finally, we suggest a simple LRU-based policy for geographically distributed caching and show that its performance is close to the optimal.
Interplay between Social Influence and Network Centrality: A Comparative Study on Shapley Centrality and Single-Node-Influence Centrality
Venue: arXiv cs.SI 2017
Year: 2017

We study network centrality based on dynamic influence propagation models in social networks. To illustrate our integrated mathematical-algorithmic approach for understanding the fundamental interplay between dynamic influence processes and static network structures, we focus on two basic centrality measures: (a) Single Node Influence (SNI) centrality, which measures each node's significance by its influence spread; and (b) Shapley Centrality, which uses the Shapley value of the influence spread function --- formulated based on a fundamental cooperative-game-theoretical concept --- to measure the significance of nodes. We present a comprehensive comparative study of these two centrality measures. Mathematically, we present axiomatic characterizations, which precisely capture the essence of these two centrality measures and their fundamental differences. Algorithmically, we provide scalable algorithms for approximating them for a large family of social-influence instances. Empirically, we demonstrate their similarity and differences in a number of real-world social networks, as well as the efficiency of our scalable algorithms. Our results shed light on their applicability: SNI centrality is suitable for assessing individual influence in isolation while Shapley centrality assesses individuals' performance in group influence settings.
Deterministic graph connectivity in the broadcast congested clique
Venue: arXiv cs.DC 2017
Year: 2017

We present deterministic constant-round protocols for the graph connectivity problem in the model where each of the $n$ nodes of a graph receives a row of the adjacency matrix, and broadcasts a single sublinear size message to all other nodes. Communication rounds are synchronous. This model is sometimes called the broadcast congested clique. Specifically, we exhibit a deterministic protocol that computes the connected components of the input graph in $\lceil 1/ε\rceil$ rounds, each player communicating $\mathcal{O}(n^ε \cdot \log n)$ bits per round, with $0 < ε\leq 1$. We also provide a deterministic one-round protocol for connectivity, in the model when each node receives as input the graph induced by the nodes at distance at most $r>0$, and communicates $\mathcal{O}(n^{1/r} \cdot \log n)$ bits. This result is based on a $d$-pruning protocol, which consists in successively removing nodes of degree at most $d$ until obtaining a graph with minimum degree larger than $d$. Our technical novelty is the introduction of deterministic sparse linear sketches: a linear compression function that permits to recover sparse Boolean vectors deterministically.
On Gröbner Bases and Krull Dimension of Residue Class Rings of Polynomial Rings over Integral Domains
Venue: arXiv cs.SC 2017
Year: 2017

Given an ideal $\mathfrak{a}$ in $A[x_1, \ldots, x_n]$, where $A$ is a Noetherian integral domain, we propose an approach to compute the Krull dimension of $A[x_1,\ldots,x_n]/\mathfrak{a}$, when the residue class polynomial ring is a free $A$-module. When $A$ is a field, the Krull dimension of $A[x_1,\ldots,x_n]/\mathfrak{a}$ has several equivalent algorithmic definitions by which it can be computed. But this is not true in the case of arbitrary Noetherian rings. For a Noetherian integral domain, $A$ we introduce the notion of combinatorial dimension of $A[x_1, \ldots,x_n]/\mathfrak{a}$ and give a Gröbner basis method to compute it for residue class polynomial rings that have a free $A$-module representation w.r.t. a lexicographic ordering. For such $A$-algebras, we derive a relation between Krull dimension and combinatorial dimension of $A[x_1, \ldots, x_n]/\mathfrak{a}$. An immediate application of this relation is that it gives a uniform method, the first of its kind, to compute the dimension of $A[x_1, \ldots, x_n]/\mathfrak{a}$ without having to consider individual properties of the ideal. For $A$-algebras that have a free $A$-module representation w.r.t. degree compatible monomial orderings, we introduce the concepts of Hilbert function, Hilbert series and Hilbert polynomials and show that Gröbner basis methods can be used to compute these quantities. We then proceed to show that the combinatorial dimension of such $A$-algebras is equal to the degree of the Hilbert polynomial. This enables us to extend the relation between Krull dimension and combinatorial dimension to $A$-algebras with a free $A$-module representation w.r.t. a degree compatible ordering as well.
Measuring multivariate redundant information with pointwise common change in surprisal
Venue: arXiv cs.IT 2017
Year: 2017

The problem of how to properly quantify redundant information is an open question that has been the subject of much recent research. Redundant information refers to information about a target variable S that is common to two or more predictor variables Xi. It can be thought of as quantifying overlapping information content or similarities in the representation of S between the Xi. We present a new measure of redundancy which measures the common change in surprisal shared between variables at the local or pointwise level. We provide a game-theoretic operational definition of unique information, and use this to derive constraints which are used to obtain a maximum entropy distribution. Redundancy is then calculated from this maximum entropy distribution by counting only those local co-information terms which admit an unambiguous interpretation as redundant information. We show how this redundancy measure can be used within the framework of the Partial Information Decomposition (PID) to give an intuitive decomposition of the multivariate mutual information into redundant, unique and synergistic contributions. We compare our new measure to existing approaches over a range of example systems, including continuous Gaussian variables. Matlab code for the measure is provided, including all considered examples.
Online Bounded Analysis
Venue: arXiv cs.DS 2017
Year: 2017

Though competitive analysis is often a very good tool for the analysis of online algorithms, sometimes it does not give any insight and sometimes it gives counter-intuitive results. Much work has gone into exploring other performance measures, in particular targeted at what seems to be the core problem with competitive analysis: the comparison of the performance of an online algorithm is made to a too powerful adversary. We consider a new approach to restricting the power of the adversary, by requiring that when judging a given online algorithm, the optimal offline algorithm must perform as well as the online algorithm, not just on the entire final request sequence, but also on any prefix of that sequence. This is limiting the adversary's usual advantage of being able to exploit that it knows the sequence is continuing beyond the current request. Through a collection of online problems, including machine scheduling, bin packing, dual bin packing, and seat reservation, we investigate the significance of this particular offline advantage.
Shortest path embeddings of graphs on surfaces
Venue: arXiv cs.CG 2017
Year: 2017

The classical theorem of Fáry states that every planar graph can be represented by an embedding in which every edge is represented by a straight line segment. We consider generalizations of Fáry's theorem to surfaces equipped with Riemannian metrics. In this setting, we require that every edge is drawn as a shortest path between its two endpoints and we call an embedding with this property a shortest path embedding. The main question addressed in this paper is whether given a closed surface S, there exists a Riemannian metric for which every topologically embeddable graph admits a shortest path embedding. This question is also motivated by various problems regarding crossing numbers on surfaces. We observe that the round metrics on the sphere and the projective plane have this property. We provide flat metrics on the torus and the Klein bottle which also have this property. Then we show that for the unit square flat metric on the Klein bottle there exists a graph without shortest path embeddings. We show, moreover, that for large g, there exist graphs G embeddable into the orientable surface of genus g, such that with large probability a random hyperbolic metric does not admit a shortest path embedding of G, where the probability measure is proportional to the Weil-Petersson volume on moduli space. Finally, we construct a hyperbolic metric on every orientable surface S of genus g, such that every graph embeddable into S can be embedded so that every edge is a concatenation of at most O(g) shortest paths.
Lower bounds on the redundancy in computations from random oracles via betting strategies with restricted wagers
Venue: arXiv cs.CC 2017
Year: 2017

The Kučera-Gács theorem is a landmark result in algorithmic randomness asserting that every real is computable from a Martin-Löf random real. If the computation of the first $n$ bits of a sequence requires $n+h(n)$ bits of the random oracle, then $h$ is the redundancy of the computation. Kučera implicitly achieved redundancy $n\log n$ while Gács used a more elaborate coding procedure which achieves redundancy $\sqrt{n}\log n$. A similar upper bound is implicit in the later proof by Merkle and Mihailović. In this paper we obtain strict optimal lower bounds on the redundancy in computations from Martin-Löf random oracles. We show that any nondecreasing computable function $g$ such that $\sum_n 2^{-g(n)}=\infty$ is not a general upper bound on the redundancy in computations from Martin-Löf random oracles. In fact, there exists a real $X$ such that the redundancy $g$ of any computation of $X$ from a Martin-Löf random oracle satisfies $\sum_n 2^{-g(n)}<\infty$. Moreover, the class of such reals is comeager and includes a $Δ^0_2$ real as well as all weakly 2-generic reals. This excludes many slow growing functions such as $\log n$ from bounding the redundancy in computations from random oracles for a large class of reals. On the other hand it was recently shown that if $\sum_n 2^{-g(n)}<\infty$ then $g$ is a general upper bound for the redundancy in computations of any real from some Martin-Löf random oracle. Our results are obtained as an application of a theory of effective betting strategies with restricted wagers which we develop.
A Complete Logic for Database Abstract State Machines
Venue: arXiv cs.LO 2017
Year: 2017

In database theory, the term $\textit{database transformation}$ was used to refer to a unifying treatment for computable queries and updates. Recently, it was shown that non-deterministic database transformations can be captured exactly by a variant of ASMs, the so-called Database Abstract State Machines (DB-ASMs). In this article we present a logic for DB-ASMs, extending the logic of Nanchen and Stärk for ASMs. In particular, we develop a rigorous proof system for the logic for DB-ASMs, which is proven to be sound and complete. The most difficult challenge to be handled by the extension is a proper formalisation capturing non-determinism of database transformations and all its related features such as consistency, update sets or multisets associated with DB-ASM rules. As the database part of a state of database transformations is a finite structure and DB-ASMs are restricted by allowing quantifiers only over the database part of a state, we resolve this problem by taking update sets explicitly into the logic, i.e. by using an additional modal operator $[X]$, where $X$ is interpreted as an update set $Δ$ generated by a DB-ASM rule. The DB-ASM logic provides a powerful verification tool to study properties of database transformations.
Enhancing Contention Resolution ALOHA using Combining Techniques
Venue: arXiv cs.IT 2017
Year: 2017

Recently, random access protocols have acquired a new wave of interest, not only from the satellite communication community, but also from researchers active in fields like Internet of Things and machine-to-machine. Asynchronous (slot- and frame-wise) ALOHA-like random access protocols, are very attractive for such applications, enabling low complexity transmitters and avoiding time synchronization requirements. Evolutions of ALOHA employ time diversity through proactive replication of packets, but the time diversity is not fully exploited at the receiver. Combining techniques, as selection combining and maximal-ratio combining, are beneficial and are adopted in the enhanced contention resolution ALOHA (ECRA) scheme, presented here. A tight approximation of the packet loss rate for asynchronous random access, including ECRA, well suited for the low channel load region is derived. Finally, ECRA is evaluated in terms of spectral efficiency, throughput and packet loss rate in comparison with recent protocols, showing that it is able to largely outperform both slotted synchronous and asynchronous schemes.
Expectation Consistent Approximate Inference: Generalizations and Convergence
Venue: arXiv cs.IT 2017
Year: 2017

Approximations of loopy belief propagation, including expectation propagation and approximate message passing, have attracted considerable attention for probabilistic inference problems. This paper proposes and analyzes a generalization of Opper and Winther's expectation consistent (EC) approximate inference method. The proposed method, called Generalized Expectation Consistency (GEC), can be applied to both maximum a posteriori (MAP) and minimum mean squared error (MMSE) estimation. Here we characterize its fixed points, convergence, and performance relative to the replica prediction of optimality.
Time-Space Trade-offs in Population Protocols
Venue: arXiv cs.DC 2017
Year: 2017

Population protocols are a popular model of distributed computing, in which randomly-interacting agents with little computational power cooperate to jointly perform computational tasks. Inspired by developments in molecular computation, and in particular DNA computing, recent algorithmic work has focused on the complexity of solving simple yet fundamental tasks in the population model, such as leader election (which requires stabilization to a single agent in a special "leader" state), and majority (in which agents must stabilize to a decision as to which of two possible initial states had higher initial count). Known results point towards an inherent trade-off between the time complexity of such algorithms, and the space complexity, i.e. size of the memory available to each agent. In this paper, we explore this trade-off and provide new upper and lower bounds for majority and leader election. First, we prove a unified lower bound, which relates the space available per node with the time complexity achievable by a protocol: for instance, our result implies that any protocol solving either of these tasks for $n$ agents using $O( \log \log n )$ states must take $Ω( n / \rm{polylog} n )$ expected time. This is the first result to characterize time complexity for protocols which employ super-constant number of states per node, and proves that fast, poly-logarithmic running times require protocols to have relatively large space costs. On the positive side, we give algorithms showing that fast, poly-logarithmic stabilization time can be achieved using $O( \log^2 n )$ space per node, in the case of both tasks. Overall, our results highlight a time complexity separation between $O(\log \log n)$ and $Θ( \log^2 n )$ state space size for both majority and leader election in population protocols, and introduce new techniques, which should be applicable more broadly.
We don't need no bounding-boxes: Training object class detectors using only human verification
Venue: arXiv cs.CV 2017
Year: 2017

Training object class detectors typically requires a large set of images in which objects are annotated by bounding-boxes. However, manually drawing bounding-boxes is very time consuming. We propose a new scheme for training object detectors which only requires annotators to verify bounding-boxes produced automatically by the learning algorithm. Our scheme iterates between re-training the detector, re-localizing objects in the training images, and human verification. We use the verification signal both to improve re-training and to reduce the search space for re-localisation, which makes these steps different to what is normally done in a weakly supervised setting. Extensive experiments on PASCAL VOC 2007 show that (1) using human verification to update detectors and reduce the search space leads to the rapid production of high-quality bounding-box annotations; (2) our scheme delivers detectors performing almost as good as those trained in a fully supervised setting, without ever drawing any bounding-box; (3) as the verification task is very quick, our scheme substantially reduces total annotation time by a factor 6x-9x.
Heterogeneous Multi-Tier Networks: Improper Signaling For Joint Rate-Energy Optimization
Venue: arXiv cs.IT 2017
Year: 2017

Wireless nodes in future communication systems need to overcome three barriers when compared to their transitional counterparts, namely to support significantly higher data rates, have long-lasting energy supplies and remain fully operational in interference-limited heterogeneous networks. This could be partially achieved by providing three promising features, which are radio frequency (RF) energy harvesting, improper Gaussian signaling and operating in full-duplex communication mode, i.e., transmit and receive at the same time within the same frequency band. In this paper, we consider these aspects jointly in a multi-antenna heterogeneous two-tier network. In this network, the users in the femto- cell are sharing the scarce resources with the cellular users in the macro-cell and have to cope with the interference from the macro-cell base station as well as the transmitter noise and residual self- interference (RSI) due to imperfect full-duplex operation. Interestingly enough, while these impairments are detrimental from the achievable rate perspective, they are beneficial from the energy harvesting aspect as they carry RF energy. In this paper, we consider this natural trade-off jointly and propose appropriate optimization problems for beamforming and optimal resource allocation. Moreover, various receiver structures are employed for both information detection (ID) and energy harvesting (EH) capabilities. The paper aims at characterizing the trade-off between the achievable rates and harvested energies. Rate and energy maximization problems are thoroughly investigated. Finally, the numerical illustrations demonstrate the impact of energy harvesting on the achievable rate performance.