OpenRaiser/Intern-Atlas huggingface dataset:
Learning Poisson Binomial Distributions
Venue: arXiv cs.DS 2015
Year: 2015

We consider a basic problem in unsupervised learning: learning an unknown \emph{Poisson Binomial Distribution}. A Poisson Binomial Distribution (PBD) over $\{0,1,\dots,n\}$ is the distribution of a sum of $n$ independent Bernoulli random variables which may have arbitrary, potentially non-equal, expectations. These distributions were first studied by S. Poisson in 1837 \cite{Poisson:37} and are a natural $n$-parameter generalization of the familiar Binomial Distribution. Surprisingly, prior to our work this basic learning problem was poorly understood, and known results for it were far from optimal. We essentially settle the complexity of the learning problem for this basic class of distributions. As our first main result we give a highly efficient algorithm which learns to $\eps$-accuracy (with respect to the total variation distance) using $\tilde{O}(1/\eps^3)$ samples \emph{independent of $n$}. The running time of the algorithm is \emph{quasilinear} in the size of its input data, i.e., $\tilde{O}(\log(n)/\eps^3)$ bit-operations. (Observe that each draw from the distribution is a $\log(n)$-bit string.) Our second main result is a {\em proper} learning algorithm that learns to $\eps$-accuracy using $\tilde{O}(1/\eps^2)$ samples, and runs in time $(1/\eps)^{\poly (\log (1/\eps))} \cdot \log n$. This is nearly optimal, since any algorithm {for this problem} must use $Ω(1/\eps^2)$ samples. We also give positive and negative results for some extensions of this learning problem to weighted sums of independent Bernoulli random variables.
Diversity Analysis of Bit-Interleaved Coded Multiple Beamforming with Orthogonal Frequency Division Multiplexing
Venue: arXiv cs.IT 2015
Year: 2015

For broadband wireless communication systems, Orthogonal Frequency Division Multiplexing (OFDM) has been combined with Multi-Input Multi-Output (MIMO) techniques. Bit-Interleaved Coded Multiple Beamforming (BICMB) can achieve both spatial diversity and spatial multiplexing for flat fading MIMO channels. For frequency selective fading MIMO channels, BICMB with OFDM (BICMB-OFDM) can be applied to achieve both spatial diversity and multipath diversity, making it an important technique. However, analyzing the diversity of BICMB-OFDM is a challenging problem. In this paper, the diversity analysis of BICMB-OFDM is carried out. First, the maximum achievable diversity is derived and a full diversity condition RcSL <= 1 is proved, where Rc, S, and L are the code rate, the number of parallel steams transmitted at each subcarrier, and the number of channel taps, respectively. Then, the performance degradation due to the correlation among subcarriers is investigated. Finally, the subcarrier grouping technique is employed to combat the performance degradation and provide multi-user compatibility.
On Bidding with Securities: Risk Aversion and Positive Dependence
Venue: arXiv cs.GT 2015
Year: 2015

DeMarzo et al. (2005) consider auctions in which bids are selected from a completely ordered family of securities whose values are tied to the resource being auctioned. The paper defines a notion of relative steepness of families of securities and shows that a steeper family provides greater expected revenue to the seller. Two assumptions are: the buyers are risk-neutral; the random variables through which values and signals of the buyers are realized are affiliated. We show that this revenue ranking holds for the second price auction in the case of risk-aversion. However, it does not hold if affiliation is relaxed to a less restrictive form of positive dependence, namely first order stochastic dominance (FOSD). We define the relative strong steepness of families of securities and show that it provides a necessary and sufficient condition for comparing two families in the FOSD case. All results extend to the English auction.
State Amplification Subject To Masking Constraints
Venue: arXiv cs.IT 2015
Year: 2015

This paper considers a state dependent broadcast channel with one transmitter, Alice, and two receivers, Bob and Eve. The problem is to effectively convey ("amplify") the channel state sequence to Bob while "masking" it from Eve. The extent to which the state sequence cannot be masked from Eve is referred to as leakage. This can be viewed as a secrecy problem, where we desire that the channel state itself be minimally leaked to Eve while being communicated to Bob. The paper is aimed at characterizing the trade-off region between amplification and leakage rates for such a system. An achievable coding scheme is presented, wherein the transmitter transmits a partial state information over the channel to facilitate the amplification process. For the case when Bob observes a stronger signal than Eve, the achievable coding scheme is enhanced with secure refinement. Outer bounds on the trade-off region are also derived, and used in characterizing some special case results. In particular, the optimal amplification-leakage rate difference, called as differential amplification capacity, is characterized for the reversely degraded discrete memoryless channel, the degraded binary, and the degraded Gaussian channels. In addition, for the degraded Gaussian model, the extremal corner points of the trade-off region are characterized, and the gap between the outer bound and achievable rate-regions is shown to be less than half a bit for a wide set of channel parameters.
Multispectral Palmprint Recognition Using a Hybrid Feature
Venue: arXiv cs.CV 2015
Year: 2015

Personal identification problem has been a major field of research in recent years. Biometrics-based technologies that exploit fingerprints, iris, face, voice and palmprints, have been in the center of attention to solve this problem. Palmprints can be used instead of fingerprints that have been of the earliest of these biometrics technologies. A palm is covered with the same skin as the fingertips but has a larger surface, giving us more information than the fingertips. The major features of the palm are palm-lines, including principal lines, wrinkles and ridges. Using these lines is one of the most popular approaches towards solving the palmprint recognition problem. Another robust feature is the wavelet energy of palms. In this paper we used a hybrid feature which combines both of these features. %Moreover, multispectral analysis is applied to improve the performance of the system. At the end, minimum distance classifier is used to match test images with one of the training samples. The proposed algorithm has been tested on a well-known multispectral palmprint dataset and achieved an average accuracy of 98.8\%.
Space-Constrained Interval Selection
Venue: arXiv cs.DS 2015
Year: 2015

We study streaming algorithms for the interval selection problem: finding a maximum cardinality subset of disjoint intervals on the line. A deterministic 2-approximation streaming algorithm for this problem is developed, together with an algorithm for the special case of proper intervals, achieving improved approximation ratio of 3/2. We complement these upper bounds by proving that they are essentially best possible in the streaming setting: it is shown that an approximation ratio of $2 - ε$ (or $3 / 2 - ε$ for proper intervals) cannot be achieved unless the space is linear in the input size. In passing, we also answer an open question of Adler and Azar \cite{AdlerAzar03} regarding the space complexity of constant-competitive randomized preemptive online algorithms for the same problem.
A polynomial time approximation scheme for computing the supremum of Gaussian processes
Venue: arXiv cs.DS 2015
Year: 2015

We give a polynomial time approximation scheme (PTAS) for computing the supremum of a Gaussian process. That is, given a finite set of vectors $V\subseteq\mathbb{R}^d$, we compute a $(1+\varepsilon)$-factor approximation to $\mathop {\mathbb{E}}_{X\leftarrow\mathcal{N}^d}[\sup_{v\in V}|\langle v,X\rangle|]$ deterministically in time $\operatorname {poly}(d)\cdot|V|^{O_{\varepsilon}(1)}$. Previously, only a constant factor deterministic polynomial time approximation algorithm was known due to the work of Ding, Lee and Peres [Ann. of Math. (2) 175 (2012) 1409-1471]. This answers an open question of Lee (2010) and Ding [Ann. Probab. 42 (2014) 464-496]. The study of supremum of Gaussian processes is of considerable importance in probability with applications in functional analysis, convex geometry, and in light of the recent breakthrough work of Ding, Lee and Peres [Ann. of Math. (2) 175 (2012) 1409-1471], to random walks on finite graphs. As such our result could be of use elsewhere. In particular, combining with the work of Ding [Ann. Probab. 42 (2014) 464-496], our result yields a PTAS for computing the cover time of bounded-degree graphs. Previously, such algorithms were known only for trees. Along the way, we also give an explicit oblivious estimator for semi-norms in Gaussian space with optimal query complexity. Our algorithm and its analysis are elementary in nature, using two classical comparison inequalities, Slepian's lemma and Kanter's lemma.
Pebble Games and Linear Equations
Venue: arXiv cs.LO 2015
Year: 2015

We give a new, simplified and detailed account of the correspondence between levels of the Sherali-Adams relaxation of graph isomorphism and levels of pebble-game equivalence with counting (higher-dimensional Weisfeiler-Lehman colour refinement). The correspondence between basic colour refinement and fractional isomorphism, due to Tinhofer (1986, 1991) and Ramana, Scheinerman and Ullman (1994), is re-interpreted as the base level of Sherali-Adams and generalised to higher levels in this sense by Atserias and Maneva (2012) and Malkin (2014), who prove that the two resulting hierarchies interleave. In carrying this analysis further, we here give (a) a precise characterisation of the level-k Sherali-Adams relaxation in terms of a modified counting pebble game; (b) a variant of the Sherali-Adams levels that precisely match the k-pebble counting game; (c) a proof that the interleaving between these two hierarchies is strict. We also investigate the variation based on boolean arithmetic instead of real/rational arithmetic and obtain analogous correspondences and separations for plain k-pebble equivalence (without counting). Our results are driven by considerably simplified accounts of the underlying combinatorics and linear algebra.
Directed Information Graphs
Venue: arXiv cs.IT 2015
Year: 2015

We propose a graphical model for representing networks of stochastic processes, the minimal generative model graph. It is based on reduced factorizations of the joint distribution over time. We show that under appropriate conditions, it is unique and consistent with another type of graphical model, the directed information graph, which is based on a generalization of Granger causality. We demonstrate how directed information quantifies Granger causality in a particular sequential prediction setting. We also develop efficient methods to estimate the topological structure from data that obviate estimating the joint statistics. One algorithm assumes upper-bounds on the degrees and uses the minimal dimension statistics necessary. In the event that the upper-bounds are not valid, the resulting graph is nonetheless an optimal approximation. Another algorithm uses near-minimal dimension statistics when no bounds are known but the distribution satisfies a certain criterion. Analogous to how structure learning algorithms for undirected graphical models use mutual information estimates, these algorithms use directed information estimates. We characterize the sample-complexity of two plug-in directed information estimators and obtain confidence intervals. For the setting when point estimates are unreliable, we propose an algorithm that uses confidence intervals to identify the best approximation that is robust to estimation error. Lastly, we demonstrate the effectiveness of the proposed algorithms through analysis of both synthetic data and real data from the Twitter network. In the latter case, we identify which news sources influence users in the network by merely analyzing tweet times.
Disconnectivity and Relative Positions in Simultaneous Embeddings
Venue: arXiv cs.DS 2015
Year: 2015

The problem Simultaneous Embedding with Fixed Edges (SEFE) asks for two planar graph $G^1 = (V^1, E^1)$ and $G^2 = (V^2, E^2)$ sharing a common subgraph $G = G^1 \cap G^2$ whether they admit planar drawings such that the common graph is drawn the same in both. Previous results on this problem require $G$, $G^1$ and $G^2$ to be connected. This paper is a first step towards solving instances where these graphs are disconnected. First, we show that an instance of the general SEFE-problem can be reduced in linear time to an equivalent instance where $V^1 = V^2$ and $G^1$ and $G^2$ are connected. This shows that it can be assumed without loss of generality that both input graphs are connected. Second, we consider instances where $G$ is disconnected. We show that SEFE can be solved in linear time if $G$ is a family of disjoint cycles by introducing the CC-tree, which represents all simultaneous embeddings. We extend these results (including the CC-tree) to the case where $G$ consists of arbitrary connected components, each with a fixed embedding. Note that previous results require $G$ to be connected and thus do not need to care about relative positions of connected components. By contrast, we assume the embedding of each connected component to be fixed and thus focus on these relative positions. As SEFE requires to deal with both, embeddings of connected components and their relative positions, this complements previous work.
Improved Quantum LDPC Decoding Strategies For The Misidentified Quantum Depolarizing Channel
Venue: arXiv cs.IT 2015
Year: 2015

Quantum cryptography via key distribution mechanisms that utilize quantum entanglement between sender-receiver pairs will form the basis of future large-scale quantum networks. A key engineering challenge in such networks will be the ability to correct for decoherence effects in the distributed entanglement resources. It is widely believed that sophisticated quantum error correction codes, such as quantum low-density parity-check (LDPC) codes, will be pivotal in such a role. However, recently the importance of the channel mismatch effect in degrading the performance of deployed quantum LDPC codes has been pointed out. In this work we help remedy this situation by proposing new quantum LDPC decoding strategies that can significantly reduce performance degradation by as much as $50\%$. Our new strategies for the quantum LDPC decoder are based on previous insights from classical LDPC decoders in mismatched channels, where an asymmetry in performance is known as a function of the estimated channel noise. We show how similar asymmetries carry over to the quantum depolarizing channel, and how an estimate of the depolarization flip parameter weighted to larger values leads to significant performance improvement.
Low-complexity Optimal Scheduling over Correlated Fading Channels with ARQ Feedback
Venue: arXiv cs.NI 2015
Year: 2015

We investigate the downlink scheduling problem under Markovian ON/OFF fading channels, where the instantaneous channel state information is not directly accessible, but is revealed via ARQ-type feedback. The scheduler can exploit the temporal correlation/channel memory inherent in the Markovian channels to improve network performance. However, designing low-complexity and throughput-optimal algorithms under temporal correlation is a challenging problem. In this paper, we find that under an average number of transmissions constraint, a low-complexity index policy is throughput-optimal. The policy uses Whittle's index value, which was previously used to capture opportunistic scheduling under temporally correlated channels. Our results build on the interesting finding that, under the intricate queue length and channel memory evolutions, the importance of scheduling a user is captured by a simple multiplication of its queue length and Whittle's index value. The proposed queue-based index policy has provably low complexity. Numerical results show that significant throughput gains can be realized by exploiting the channel memory using the proposed low-complexity policy.
Parametrized Complexity of Weak Odd Domination Problems
Venue: arXiv cs.CC 2015
Year: 2015

Given a graph $G=(V,E)$, a subset $B\subseteq V$ of vertices is a weak odd dominated (WOD) set if there exists $D \subseteq V {\setminus} B$ such that every vertex in $B$ has an odd number of neighbours in $D$. $κ(G)$ denotes the size of the largest WOD set, and $κ'(G)$ the size of the smallest non-WOD set. The maximum of $κ(G)$ and $|V|-κ'(G)$, denoted $κ_Q(G)$, plays a crucial role in quantum cryptography. In particular deciding, given a graph $G$ and $k>0$, whether $κ_Q(G)\le k$ is of practical interest in the design of graph-based quantum secret sharing schemes. The decision problems associated with the quantities $κ$, $κ'$ and $κ_Q$ are known to be NP-Complete. In this paper, we consider the approximation of these quantities and the parameterized complexity of the corresponding problems. We mainly prove the fixed-parameter intractability (W$[1]$-hardness) of these problems. Regarding the approximation, we show that $κ_Q$, $κ$ and $κ'$ admit a constant factor approximation algorithm, and that $κ$ and $κ'$ have no polynomial approximation scheme unless P=NP.
Algorithms on Minimizing the Maximum Sensor Movement for Barrier Coverage of a Linear Domain
Venue: arXiv cs.CG 2015
Year: 2015

In this paper, we study the problem of moving $n$ sensors on a line to form a barrier coverage of a specified segment of the line such that the maximum moving distance of the sensors is minimized. Previously, it was an open question whether this problem on sensors with arbitrary sensing ranges is solvable in polynomial time. We settle this open question positively by giving an $O(n^2 \log n)$ time algorithm. For the special case when all sensors have the same-size sensing range, the previously best solution takes $O(n^2)$ time. We present an $O(n \log n)$ time algorithm for this case; further, if all sensors are initially located on the coverage segment, our algorithm takes $O(n)$ time. Also, we extend our techniques to the cycle version of the problem where the barrier coverage is for a simple cycle and the sensors are allowed to move only along the cycle. For sensors with the same-size sensing range, we solve the cycle version in $O(n)$ time, improving the previously best $O(n^2)$ time solution.
Interference Alignment with Quantized Grassmannian Feedback in the K-user Constant MIMO Interference Channel
Venue: arXiv cs.IT 2015
Year: 2015

A simple channel state information (CSI) feedback scheme is proposed for interference alignment (IA) over the K-user constant Multiple-Input-Multiple-Output Interference Channel (MIMO IC). The proposed technique relies on the identification of invariants in the IA equations, which enables the reformulation of the CSI quantization problem as a single quantization on the Grassmann manifold at each receiver. The scaling of the number of feedback bits with the transmit power sufficient to preserve the multiplexing gain that can be achieved under perfect CSI is established. We show that the CSI feedback requirements of the proposed technique are better (lower) than what is required when using previously published methods, for system dimensions (number of users and antennas) of practical interest. Furthermore, we show through simulations that this advantage persists at low SNR, in the sense that the proposed technique yields a higher sum-rate performance for a given number of feedback bits. Finally, to complement our analysis, we introduce a statistical model that faithfully captures the properties of the quantization error obtained for random vector quantization (RVQ) on the Grassmann manifold for large codebooks; this enables the numerical (Monte-Carlo) analysis of general Grassmannian RVQ schemes for codebook sizes that would be impractically large to simulate.
Fast Distributed PageRank Computation
Venue: arXiv cs.DC 2015
Year: 2015

Over the last decade, PageRank has gained importance in a wide range of applications and domains, ever since it first proved to be effective in determining node importance in large graphs (and was a pioneering idea behind Google's search engine). In distributed computing alone, PageRank vector, or more generally random walk based quantities have been used for several different applications ranging from determining important nodes, load balancing, search, and identifying connectivity structures. Surprisingly, however, there has been little work towards designing provably efficient fully-distributed algorithms for computing PageRank. The difficulty is that traditional matrix-vector multiplication style iterative methods may not always adapt well to the distributed setting owing to communication bandwidth restrictions and convergence rates. In this paper, we present fast random walk-based distributed algorithms for computing PageRanks in general graphs and prove strong bounds on the round complexity. We first present a distributed algorithm that takes $O\big(\log n/\eps \big)$ rounds with high probability on any graph (directed or undirected), where $n$ is the network size and $\eps$ is the reset probability used in the PageRank computation (typically $\eps$ is a fixed constant). We then present a faster algorithm that takes $O\big(\sqrt{\log n}/\eps \big)$ rounds in undirected graphs. Both of the above algorithms are scalable, as each node sends only small ($\polylog n$) number of bits over each edge per round. To the best of our knowledge, these are the first fully distributed algorithms for computing PageRank vector with provably efficient running time.
Compression of dynamic fuzzy relation information systems
Venue: arXiv cs.IT 2015
Year: 2015

This paper further investigates the data compression of fuzzy relation information systems. First, we introduce an algorithm for constructing the homomorphism between fuzzy relation information systems. Then, we discuss that how to compress the dynamic fuzzy relation information systems by utilizing the compression of the original systems. Afterwards, several illustrative examples are employed to show that the data compression of fuzzy relation information systems and dynamic fuzzy relation information systems can be simplified significantly by our proposed
Transient Reward Approximation for Continuous-Time Markov Chains
Venue: arXiv cs.LO 2015
Year: 2015

We are interested in the analysis of very large continuous-time Markov chains (CTMCs) with many distinct rates. Such models arise naturally in the context of reliability analysis, e.g., of computer network performability analysis, of power grids, of computer virus vulnerability, and in the study of crowd dynamics. We use abstraction techniques together with novel algorithms for the computation of bounds on the expected final and accumulated rewards in continuous-time Markov decision processes (CTMDPs). These ingredients are combined in a partly symbolic and partly explicit (symblicit) analysis approach. In particular, we circumvent the use of multi-terminal decision diagrams, because the latter do not work well if facing a large number of different rates. We demonstrate the practical applicability and efficiency of the approach on two case studies.