OpenRaiser/Intern-Atlas huggingface dataset:
Ranked bandits in metric spaces: learning optimally diverse rankings over large document collections
Venue: arXiv cs.LG 2012
Year: 2012

Most learning to rank research has assumed that the utility of different documents is independent, which results in learned ranking functions that return redundant results. The few approaches that avoid this have rather unsatisfyingly lacked theoretical foundations, or do not scale. We present a learning-to-rank formulation that optimizes the fraction of satisfied users, with several scalable algorithms that explicitly takes document similarity and ranking context into account. Our formulation is a non-trivial common generalization of two multi-armed bandit models from the literature: "ranked bandits" (Radlinski et al., ICML 2008) and "Lipschitz bandits" (Kleinberg et al., STOC 2008). We present theoretical justifications for this approach, as well as a near-optimal algorithm. Our evaluation adds optimizations that improve empirical performance, and shows that our algorithms learn orders of magnitude more quickly than previous approaches.
Transceiver Design for Dual-Hop Non-regenerative MIMO-OFDM Relay Systems Under Channel Uncertainties
Venue: arXiv cs.IT 2012
Year: 2012

In this paper, linear transceiver design for dual-hop non-regenerative (amplify-and-forward (AF)) MIMO-OFDM systems under channel estimation errors is investigated. Second order moments of channel estimation errors in the two hops are first deduced. Then based on the Bayesian framework, joint design of linear forwarding matrix at the relay and equalizer at the destination under channel estimation errors is proposed to minimize the total mean-square-error (MSE) of the output signal at the destination. The optimal designs for both correlated and uncorrelated channel estimation errors are considered. The relationship with existing algorithms is also disclosed. Moreover, this design is extended to the joint design involving source precoder design. Simulation results show that the proposed design outperforms the design based on estimated channel state information only.
Approximated Structured Prediction for Learning Large Scale Graphical Models
Venue: arXiv cs.LG 2012
Year: 2012

This manuscripts contains the proofs for "A Primal-Dual Message-Passing Algorithm for Approximated Large Scale Structured Prediction".
Competitive Equilibria in Two Sided Matching Markets with Non-transferable Utilities
Venue: arXiv cs.GT 2012
Year: 2012

We consider two sided matching markets consisting of agents with non-transferable utilities; agents from the opposite sides form matching pairs (e.g., buyers-sellers) and negotiate the terms of their math which may include a monetary transfer. Competitive equilibria are the elements of the core of this game. We present the first combinatorial characterization of competitive equilibria that relates the utility of each agent at equilibrium to the equilibrium utilities of other agents in a strictly smaller market excluding that agent; thus automatically providing a constructive proof of existence of competitive equilibria in such markets. Our characterization also yields a group strategyproof mechanism for allocating indivisible goods to unit demand buyers with non-quasilinear utilities that highly resembles the Vickrey Clarke Groves (VCG) mechanism. As a direct application of this, we present a group strategyproof welfare maximizing mechanism for Ad-Auctions without requiring the usual assumption that search engine and advertisers have consistent estimates of the clickthrough rates.
An Optimal Lower Bound for Buffer Management in Multi-Queue Switches
Venue: arXiv cs.DS 2012
Year: 2012

In the online packet buffering problem (also known as the unweighted FIFO variant of buffer management), we focus on a single network packet switching device with several input ports and one output port. This device forwards unit-size, unit-value packets from input ports to the output port. Buffers attached to input ports may accumulate incoming packets for later transmission; if they cannot accommodate all incoming packets, their excess is lost. A packet buffering algorithm has to choose from which buffers to transmit packets in order to minimize the number of lost packets and thus maximize the throughput. We present a tight lower bound of e/(e-1) ~ 1.582 on the competitive ratio of the throughput maximization, which holds even for fractional or randomized algorithms. This improves the previously best known lower bound of 1.4659 and matches the performance of the algorithm Random Schedule. Our result contradicts the claimed performance of the algorithm Random Permutation; we point out a flaw in its original analysis.
Runtime Analysis of Probabilistic Programs with Unbounded Recursion
Venue: arXiv cs.LO 2012
Year: 2012

We study termination time and recurrence time in programs with unbounded recursion, which are either randomized or operate on some statistically quantified inputs. As the underlying formal model for such programs we use probabilistic pushdown automata (pPDA) which are equivalent to probabilistic recursive state machines. We obtain tail bounds for the distribution of termination time for pPDA. We also study the recurrence time for probabilistic recursive programs that are not supposed to terminate (such as system daemons, network servers, etc.). Typically, such programs react to certain requests generated by their environment, and hence operate in finite request-service cycles. We obtain bounds for the frequency of long request-service cycles.
On the Applicability of Post's Lattice
Venue: arXiv cs.CC 2012
Year: 2012

For decision problems P defined over Boolean circuits from a restricted set of gates, we have that P(B) AC0 many-one reduces to P(B') for all finite sets B and B' of gates such that all gates from B can be computed by circuits over gates from B'. In this paper, we show that a weaker version of this statement holds for decision problems defined over Boolean formulae, namely that P(B) NC2 many-one reduces to P(B' union {and,or}) and that P(B) NC2 many-one reduces to P(B' union {false,true}), for all finite sets B and B' of Boolean functions such that all f in B can be defined in B'.
Efficient Submodular Function Maximization under Linear Packing Constraints
Venue: arXiv cs.DS 2012
Year: 2012

We study the problem of maximizing a monotone submodular set function subject to linear packing constraints. An instance of this problem consists of a matrix $A \in [0,1]^{m \times n}$, a vector $b \in [1,\infty)^m$, and a monotone submodular set function $f: 2^{[n]} \rightarrow \bbR_+$. The objective is to find a set $S$ that maximizes $f(S)$ subject to $A x_{S} \leq b$, where $x_S$ stands for the characteristic vector of the set $S$. A well-studied special case of this problem is when $f$ is linear. This special case captures the class of packing integer programs. Our main contribution is an efficient combinatorial algorithm that achieves an approximation ratio of $Ω(1 / m^{1/W})$, where $W = \min\{b_i / A_{ij} : A_{ij} > 0\}$ is the width of the packing constraints. This result matches the best known performance guarantee for the linear case. One immediate corollary of this result is that the algorithm under consideration achieves constant factor approximation when the number of constraints is constant or when the width of the constraints is sufficiently large. This motivates us to study the large width setting, trying to determine its exact approximability. We develop an algorithm that has an approximation ratio of $(1 - ε)(1 - 1/e)$ when $W = Ω(\ln m / ε^2)$. This result essentially matches the theoretical lower bound of $1 - 1/e$. We also study the special setting in which the matrix $A$ is binary and $k$-column sparse. A $k$-column sparse matrix has at most $k$ non-zero entries in each of its column. We design a fast combinatorial algorithm that achieves an approximation ratio of $Ω(1 / (Wk^{1/W}))$, that is, its performance guarantee only depends on the sparsity and width parameters.
LP-rounding algorithms for facility-location problems
Venue: arXiv cs.DS 2012
Year: 2012

We study LP-rounding approximation algorithms for metric uncapacitated facility-location problems. We first give a new analysis for the algorithm of Chudak and Shmoys, which differs from the analysis of Byrka and Aardal in that now we do not need any bound based on the solution to the dual LP program. Besides obtaining the optimal bifactor approximation as do Byrka and Aardal, we can now also show that the algorithm with scaling parameter equaling 1.58 is, in fact, an 1.58-approximation algorithm. More importantly, we suggest an approach based on additional randomization and analyses such as ours, which could achieve or approach the conjectured optimal 1.46...--approximation for this basic problem. Next, using essentially the same techniques, we obtain improved approximation algorithms in the 2-stage stochastic variant of the problem, where we must open a subset of facilities having only stochastic information about the future demand from the clients. For this problem we obtain a 2.2975-approximation algorithm in the standard setting, and a 2.4957-approximation in the more restricted, per-scenario setting. We then study robust fault-tolerant facility location, introduced by Chechik and Peleg: solutions here are designed to provide low connection cost in case of failure of up to $k$ facilities. Chechik and Peleg gave a 6.5-approximation algorithm for $k=1$ and a ($7.5k + 1.5$)-approximation algorithm for general $k$. We improve this to an LP-rounding $(k+5+4/k)$-approximation algorithm. We also observe that in case of oblivious failures the expected approximation ratio can be reduced to $k + 1.5$, and that the integrality gap of the natural LP-relaxation of the problem is at least $k + 1$.
Introduction to clarithmetic III
Venue: arXiv cs.LO 2012
Year: 2012

The present paper constructs three new systems of clarithmetic (arithmetic based on computability logic --- see http://www.cis.upenn.edu/~giorgi/cl.html): CLA8, CLA9 and CLA10. System CLA8 is shown to be sound and extensionally complete with respect to PA-provably recursive time computability. This is in the sense that an arithmetical problem A has a t-time solution for some PA-provably recursive function t iff A is represented by some theorem of CLA8. System CLA9 is shown to be sound and intensionally complete with respect to constructively PA-provable computability. This is in the sense that a sentence X is a theorem of CLA9 iff, for some particular machine M, PA proves that M computes (the problem represented by) X. And system CLA10 is shown to be sound and intensionally complete with respect to not-necessarily-constructively PA-provable computability. This means that a sentence X is a theorem of CLA10 iff PA proves that X is computable, even if PA does not "know" of any particular machine M that computes X.
Good Random Matrices over Finite Fields
Venue: arXiv cs.IT 2012
Year: 2012

The random matrix uniformly distributed over the set of all m-by-n matrices over a finite field plays an important role in many branches of information theory. In this paper a generalization of this random matrix, called k-good random matrices, is studied. It is shown that a k-good random m-by-n matrix with a distribution of minimum support size is uniformly distributed over a maximum-rank-distance (MRD) code of minimum rank distance min{m,n}-k+1, and vice versa. Further examples of k-good random matrices are derived from homogeneous weights on matrix modules. Several applications of k-good random matrices are given, establishing links with some well-known combinatorial problems. Finally, the related combinatorial concept of a k-dense set of m-by-n matrices is studied, identifying such sets as blocking sets with respect to (m-k)-dimensional flats in a certain m-by-n matrix geometry and determining their minimum size in special cases.
Modeling Dynamical Influence in Human Interaction Patterns
Venue: arXiv cs.SI 2012
Year: 2012

How can we model influence between individuals in a social system, even when the network of interactions is unknown? In this article, we review the literature on the "influence model," which utilizes independent time series to estimate how much the state of one actor affects the state of another actor in the system. We extend this model to incorporate dynamical parameters that allow us to infer how influence changes over time, and we provide three examples of how this model can be applied to simulated and real data. The results show that the model can recover known estimates of influence, it generates results that are consistent with other measures of social networks, and it allows us to uncover important shifts in the way states may be transmitted between actors at different points in time.
Online Advertisement, Optimization and Stochastic Networks
Venue: arXiv cs.DS 2012
Year: 2012

In this paper, we propose a stochastic model to describe how search service providers charge client companies based on users' queries for the keywords related to these companies' ads by using certain advertisement assignment strategies. We formulate an optimization problem to maximize the long-term average revenue for the service provider under each client's long-term average budget constraint, and design an online algorithm which captures the stochastic properties of users' queries and click-through behaviors. We solve the optimization problem by making connections to scheduling problems in wireless networks, queueing theory and stochastic networks. Unlike prior models, we do not assume that the number of query arrivals is known. Due to the stochastic nature of the arrival process considered here, either temporary "free" service, i.e., service above the specified budget or under-utilization of the budget is unavoidable. We prove that our online algorithm can achieve a revenue that is within $O(ε)$ of the optimal revenue while ensuring that the overdraft or underdraft is $O(1/ε)$, where $ε$ can be arbitrarily small. With a view towards practice, we can show that one can always operate strictly under the budget. In addition, we extend our results to a click-through rate maximization model, and also show how our algorithm can be modified to handle non-stationary query arrival processes and clients with short-term contracts. Our algorithm allows us to quantify the effect of errors in click-through rate estimation on the achieved revenue. We also show that in the long run, an expected overdraft level of $Ω(\log(1/ε))$ is unavoidable (a universal lower bound) under any stationary ad assignment algorithm which achieves a long-term average revenue within $O(ε)$ of the offline optimum.
Optimized IR-HARQ Schemes Based on Punctured LDPC Codes over the BEC
Venue: arXiv cs.IT 2012
Year: 2012

We study incremental redundancy hybrid ARQ (IR-HARQ) schemes based on punctured, finite-length, LDPC codes. The transmission is assumed to take place over time varying binary erasure channels, such as mobile wireless channels at the applications layer. We analyze and optimize the throughput and delay performance of these IR-HARQ protocols under iterative, message-passing decoding. We derive bounds on the performance that are achievable by such schemes, and show that, with a simple extension, the iteratively decoded, punctured LDPC code based IR-HARQ protocol can be made rateless, and operating close to the general theoretical optimum for a wide range of channel erasure rates.
Numerical values of the growth rates of power-free languages
Venue: arXiv cs.FL 2012
Year: 2012

We present upper and two-sided bounds of the exponential growth rate for a wide range of power-free languages. All bounds are obtained with the use of algorithms previously developed by the author.
Canonizable Partial Order Generators and Regular Slice Languages
Venue: arXiv cs.FL 2012
Year: 2012

In a previous work we introduced slice graphs as a way to specify both infinite languages of directed acyclic graphs (DAGs) and infinite languages of partial orders. Therein we focused on the study of Hasse diagram generators, i.e., slice graphs that generate only transitive reduced DAGs, and showed that they could be used to solve several problems related to the partial order behavior of p/t-nets. In the present work we show that both slice graphs and Hasse diagram generators are worth studying on their own. First, we prove that any slice graph SG can be effectively transformed into a Hasse diagram generator HG representing the same set of partial orders. Thus from an algorithmic standpoint we introduce a method of transitive reducing infinite families of DAGs specified by slice graphs. Second, we identify the class of saturated slice graphs. By using our transitive reduction algorithm, we prove that the class of partial order languages representable by saturated slice graphs is closed under union, intersection and even under a suitable notion of complementation (cut-width complementation). Furthermore partial order languages belonging to this class can be tested for inclusion and admit canonical representatives in terms of Hasse diagram generators. As an application of our results, we give stronger forms of some results in our previous work, and establish some unknown connections between the partial order behavior of $p/t$-nets and other well known formalisms for the specification of infinite families of partial orders, such as Mazurkiewicz trace languages and message sequence chart (MSC) languages.
Robust Recovery of Subspace Structures by Low-Rank Representation
Venue: arXiv cs.IT 2012
Year: 2012

In this work we address the subspace recovery problem. Given a set of data samples (vectors) approximately drawn from a union of multiple subspaces, our goal is to segment the samples into their respective subspaces and correct the possible errors as well. To this end, we propose a novel method termed Low-Rank Representation (LRR), which seeks the lowest-rank representation among all the candidates that can represent the data samples as linear combinations of the bases in a given dictionary. It is shown that LRR well solves the subspace recovery problem: when the data is clean, we prove that LRR exactly captures the true subspace structures; for the data contaminated by outliers, we prove that under certain conditions LRR can exactly recover the row space of the original data and detect the outlier as well; for the data corrupted by arbitrary errors, LRR can also approximately recover the row space with theoretical guarantees. Since the subspace membership is provably determined by the row space, these further imply that LRR can perform robust subspace segmentation and error correction, in an efficient way.
Generalized Approximate Message Passing for Estimation with Random Linear Mixing
Venue: arXiv cs.IT 2012
Year: 2012

We consider the estimation of an i.i.d.\ random vector observed through a linear transform followed by a componentwise, probabilistic (possibly nonlinear) measurement channel. A novel algorithm, called generalized approximate message passing (GAMP), is presented that provides computationally efficient approximate implementations of max-sum and sum-problem loopy belief propagation for such problems. The algorithm extends earlier approximate message passing methods to incorporate arbitrary distributions on both the input and output of the transform and can be applied to a wide range of problems in nonlinear compressed sensing and learning. Extending an analysis by Bayati and Montanari, we argue that the asymptotic componentwise behavior of the GAMP method under large, i.i.d. Gaussian transforms is described by a simple set of state evolution (SE) equations. From the SE equations, one can \emph{exactly} predict the asymptotic value of virtually any componentwise performance metric including mean-squared error or detection accuracy. Moreover, the analysis is valid for arbitrary input and output distributions, even when the corresponding optimization problems are non-convex. The results match predictions by Guo and Wang for relaxed belief propagation on large sparse matrices and, in certain instances, also agree with the optimal performance predicted by the replica method. The GAMP methodology thus provides a computationally efficient methodology, applicable to a large class of non-Gaussian estimation problems with precise asymptotic performance guarantees.
Enumerating Finitary Processes
Venue: arXiv cs.FL 2012
Year: 2012

We show how to efficiently enumerate a class of finite-memory stochastic processes using the causal representation of epsilon-machines. We characterize epsilon-machines in the language of automata theory and adapt a recent algorithm for generating accessible deterministic finite automata, pruning this over-large class down to that of epsilon-machines. As an application, we exactly enumerate topological epsilon-machines up to eight states and six-letter alphabets.
Complexity Adjusted Soft-Output Sphere Decoding by Adaptive LLR Clipping
Venue: arXiv cs.IT 2012
Year: 2012

A-posteriori probability (APP) receivers operating over multiple-input, multiple-output channels provide enhanced bit error rate (BER) performance at the cost of increased complexity. However, employing full APP processing over favorable transmission environments, where less efficient approaches may already provide the required performance at a reduced complexity, results in unnecessary processing. For slowly varying channel statistics substantial complexity savings can be achieved by simple adaptive schemes. Such schemes track the BER performance and adjust the complexity of the soft output sphere decoder by adaptively setting the related log-likelihood ratio (LLR) clipping value.
Secure Communication over Parallel Relay Channel
Venue: arXiv cs.IT 2012
Year: 2012

We investigate the problem of secure communication over parallel relay channel in the presence of a passive eavesdropper. We consider a four terminal relay-eavesdropper channel which consists of multiple relay-eavesdropper channels as subchannels. For the discrete memoryless model, we establish outer and inner bounds on the rate-equivocation region. The inner bound allows mode selection at the relay. For each subchannel, secure transmission is obtained through one of two coding schemes at the relay: decoding-and-forwarding the source message or confusing the eavesdropper through noise injection. For the Gaussian memoryless channel, we establish lower and upper bounds on the perfect secrecy rate. Furthermore, we study a special case in which the relay does not hear the source and show that under certain conditions the lower and upper bounds coincide. The results established for the parallel Gaussian relay-eavesdropper channel are then applied to study the fading relay-eavesdropper channel. Analytical results are illustrated through some numerical examples.
Technology Choices and Pricing Policies in Public and Private Wireless Networks
Venue: arXiv cs.GT 2012
Year: 2012

This paper studies the provision of a wireless network by a monopolistic provider who may be either benevolent (seeking to maximize social welfare) or selfish (seeking to maximize provider profit). The paper addresses questions that do not seem to have been studied before in the engineering literature on wireless networks: Under what circumstances is it feasible for a provider, either benevolent or selfish, to operate a network in such a way as to cover costs? How is the optimal behavior of a benevolent provider different from the optimal behavior of a selfish provider, and how does this difference affect social welfare? And, most importantly, how does the medium access control (MAC) technology influence the answers to these questions? To address these questions, we build a general model, and provide analysis and simulations for simplified but typical scenarios; the focus in these scenarios is on the contrast between the outcomes obtained under carrier-sensing multiple access (CSMA) and outcomes obtained under time-division multiple access (TDMA). Simulation results demonstrate that differences in MAC technology can have a significant effect on social welfare, on provider profit, and even on the (financial) feasibility of a wireless network.