OpenRaiser/Intern-Atlas huggingface dataset:
Zero-Error Capacity of a Class of Timing Channels
Venue: arXiv cs.IT 2014
Year: 2014

We analyze the problem of zero-error communication through timing channels that can be interpreted as discrete-time queues with bounded waiting times. The channel model includes the following assumptions: 1) Time is slotted, 2) at most $ N $ "particles" are sent in each time slot, 3) every particle is delayed in the channel for a number of slots chosen randomly from the set $ \{0, 1, \ldots, K\} $, and 4) the particles are identical. It is shown that the zero-error capacity of this channel is $ \log r $, where $ r $ is the unique positive real root of the polynomial $ x^{K+1} - x^{K} - N $. Capacity-achieving codes are explicitly constructed, and a linear-time decoding algorithm for these codes devised. In the particular case $ N = 1 $, $ K = 1 $, the capacity is equal to $ \log ϕ$, where $ ϕ= (1 + \sqrt{5}) / 2 $ is the golden ratio, and the constructed codes give another interpretation of the Fibonacci sequence.
Relating and contrasting plain and prefix Kolmogorov complexity
Venue: arXiv cs.CC 2014
Year: 2014

In [3] a short proof is given that some strings have maximal plain Kolmogorov complexity but not maximal prefix-free complexity. The proof uses Levin's symmetry of information, Levin's formula relating plain and prefix complexity and Gacs' theorem that complexity of complexity given the string can be high. We argue that the proof technique and results mentioned above are useful to simplify existing proofs and to solve open questions. We present a short proof of Solovay's result [21] relating plain and prefix complexity: $K (x) = C (x) + CC (x) + O(CCC (x))$ and $C (x) = K (x) - KK (x) + O(KKK (x))$, (here $CC(x)$ denotes $C(C(x))$, etc.). We show that there exist $ω$ such that $\liminf C(ω_1\dots ω_n) - C(n)$ is infinite and $\liminf K(ω_1\dots ω_n) - K(n)$ is finite, i.e. the infinitely often C-trivial reals are not the same as the infinitely often K-trivial reals (i.e. [1,Question 1]). Solovay showed that for infinitely many $x$ we have $|x| - C (x) \le O(1)$ and $|x| + K (|x|) - K (x) \ge \log^{(2)} |x| - O(\log^{(3)} |x|)$, (here $|x|$ denotes the length of $x$ and $\log^{(2)} = \log\log$, etc.). We show that this result holds for prefixes of some 2-random sequences. Finally, we generalize our proof technique and show that no monotone relation exists between expectation and probability bounded randomness deficiency (i.e. [6, Question 1]).
Risk-sensitive Reinforcement Learning
Venue: arXiv cs.LG 2014
Year: 2014

We derive a family of risk-sensitive reinforcement learning methods for agents, who face sequential decision-making tasks in uncertain environments. By applying a utility function to the temporal difference (TD) error, nonlinear transformations are effectively applied not only to the received rewards but also to the true transition probabilities of the underlying Markov decision process. When appropriate utility functions are chosen, the agents' behaviors express key features of human behavior as predicted by prospect theory (Kahneman and Tversky, 1979), for example different risk-preferences for gains and losses as well as the shape of subjective probability curves. We derive a risk-sensitive Q-learning algorithm, which is necessary for modeling human behavior when transition probabilities are unknown, and prove its convergence. As a proof of principle for the applicability of the new framework we apply it to quantify human behavior in a sequential investment task. We find, that the risk-sensitive variant provides a significantly better fit to the behavioral data and that it leads to an interpretation of the subject's responses which is indeed consistent with prospect theory. The analysis of simultaneously measured fMRI signals show a significant correlation of the risk-sensitive TD error with BOLD signal change in the ventral striatum. In addition we find a significant correlation of the risk-sensitive Q-values with neural activity in the striatum, cingulate cortex and insula, which is not present if standard Q-values are used.
Neighborhood filters and the decreasing rearrangement
Venue: arXiv cs.CV 2014
Year: 2014

Nonlocal filters are simple and powerful techniques for image denoising. In this paper, we give new insights into the analysis of one kind of them, the Neighborhood filter, by using a classical although not very common transformation: the decreasing rearrangement of a function (the image). Independently of the dimension of the image, we reformulate the Neighborhood filter and its iterative variants as an integral operator defined in a one-dimensional space. The simplicity of this formulation allows to perform a detailed analysis of its properties. Among others, we prove that the filter behaves asymptotically as a shock filter combined with a border diffusive term, responsible for the staircaising effect and the loss of contrast.
From average case complexity to improper learning complexity
Venue: arXiv cs.LG 2014
Year: 2014

The basic problem in the PAC model of computational learning theory is to determine which hypothesis classes are efficiently learnable. There is presently a dearth of results showing hardness of learning problems. Moreover, the existing lower bounds fall short of the best known algorithms. The biggest challenge in proving complexity results is to establish hardness of {\em improper learning} (a.k.a. representation independent learning).The difficulty in proving lower bounds for improper learning is that the standard reductions from $\mathbf{NP}$-hard problems do not seem to apply in this context. There is essentially only one known approach to proving lower bounds on improper learning. It was initiated in (Kearns and Valiant 89) and relies on cryptographic assumptions. We introduce a new technique for proving hardness of improper learning, based on reductions from problems that are hard on average. We put forward a (fairly strong) generalization of Feige's assumption (Feige 02) about the complexity of refuting random constraint satisfaction problems. Combining this assumption with our new technique yields far reaching implications. In particular, 1. Learning $\mathrm{DNF}$'s is hard. 2. Agnostically learning halfspaces with a constant approximation ratio is hard. 3. Learning an intersection of $ω(1)$ halfspaces is hard.
Families with infants: a general approach to solve hard partition problems
Venue: arXiv cs.DS 2014
Year: 2014

We introduce a general approach for solving partition problems where the goal is to represent a given set as a union (either disjoint or not) of subsets satisfying certain properties. Many NP-hard problems can be naturally stated as such partition problems. We show that if one can find a large enough system of so-called families with infants for a given problem, then this problem can be solved faster than by a straightforward algorithm. We use this approach to improve known bounds for several NP-hard problems as well as to simplify the proofs of several known results. For the chromatic number problem we present an algorithm with $O^*((2-\varepsilon(d))^n)$ time and exponential space for graphs of average degree $d$. This improves the algorithm by Björklund et al. [Theory Comput. Syst. 2010] that works for graphs of bounded maximum (as opposed to average) degree and closes an open problem stated by Cygan and Pilipczuk [ICALP 2013]. For the traveling salesman problem we give an algorithm working in $O^*((2-\varepsilon(d))^n)$ time and polynomial space for graphs of average degree $d$. The previously known results of this kind is a polyspace algorithm by Björklund et al. [ICALP 2008] for graphs of bounded maximum degree and an exponential space algorithm for bounded average degree by Cygan and Pilipczuk [ICALP 2013]. For counting perfect matching in graphs of average degree~$d$ we present an algorithm with running time $O^*((2-\varepsilon(d))^{n/2})$ and polynomial space. Recent algorithms of this kind due to Cygan, Pilipczuk [ICALP 2013] and Izumi, Wadayama [FOCS 2012] (for bipartite graphs only) use exponential space.
Robust Beamforming for Secure Communication in Systems with Wireless Information and Power Transfer
Venue: arXiv cs.IT 2014
Year: 2014

This paper considers a multiuser multiple-input single-output (MISO) downlink system with simultaneous wireless information and power transfer. In particular, we focus on secure communication in the presence of passive eavesdroppers and potential eavesdroppers (idle legitimate receivers). We study the design of a resource allocation algorithm minimizing the total transmit power for the case when the legitimate receivers are able to harvest energy from radio frequency signals. Our design advocates the dual use of both artificial noise and energy signals in providing secure communication and facilitating efficient wireless energy transfer. The algorithm design is formulated as a non-convex optimization problem. The problem formulation takes into account artificial noise and energy signal generation for protecting the transmitted information against both considered types of eavesdroppers when imperfect channel state information (CSI) of the potential eavesdroppers and no CSI of the passive eavesdroppers are available at the transmitter. In light of the intractability of the problem, we reformulate the considered problem by replacing a non-convex probabilistic constraint with a convex deterministic constraint. Then, a semi-definite programming (SDP) relaxation approach is adopted to obtain the optimal solution for the reformulated problem. Furthermore, we propose a suboptimal resource allocation scheme with low computational complexity for providing communication secrecy and facilitating efficient energy transfer. Simulation results demonstrate a close-to-optimal performance achieved by the proposed schemes and significant transmit power savings by optimization of the artificial noise and energy signal generation.
On the Existence of Low-Rank Explanations for Mixed Strategy Behavior
Venue: arXiv cs.GT 2014
Year: 2014

Nash equilibrium is used as a model to explain the observed behavior of players in strategic settings. For example, in many empirical applications we observe player behavior, and the problem is to determine if there exist payoffs for the players for which the equilibrium corresponds to observed player behavior. Computational complexity of Nash equilibria is an important consideration in this framework. If the instance of the model that explains observed player behavior requires players to have solved a computationally hard problem, then the explanation provided is questionable. In this paper we provide conditions under which Nash equilibrium is a reasonable explanation for strategic behavior, i.e., conditions under which observed behavior of players can be explained by games in which Nash equilibria are easy to compute. We identify three structural conditions and show that if the data set of observed behavior satisfies any of these conditions, then it is consistent with payoff matrices for which the observed Nash equilibria could have been computed efficiently. Our conditions admit large and structurally complex data sets of observed behavior, showing that even with complexity considerations, Nash equilibrium is often a reasonable model.
DinTucker: Scaling up Gaussian process models on multidimensional arrays with billions of elements
Venue: arXiv cs.LG 2014
Year: 2014

Infinite Tucker Decomposition (InfTucker) and random function prior models, as nonparametric Bayesian models on infinite exchangeable arrays, are more powerful models than widely-used multilinear factorization methods including Tucker and PARAFAC decomposition, (partly) due to their capability of modeling nonlinear relationships between array elements. Despite their great predictive performance and sound theoretical foundations, they cannot handle massive data due to a prohibitively high training time. To overcome this limitation, we present Distributed Infinite Tucker (DINTUCKER), a large-scale nonlinear tensor decomposition algorithm on MAPREDUCE. While maintaining the predictive accuracy of InfTucker, it is scalable on massive data. DINTUCKER is based on a new hierarchical Bayesian model that enables local training of InfTucker on subarrays and information integration from all local training results. We use distributed stochastic gradient descent, coupled with variational inference, to train this model. We apply DINTUCKER to multidimensional arrays with billions of elements from applications in the "Read the Web" project (Carlson et al., 2010) and in information security and compare it with the state-of-the-art large-scale tensor decomposition method, GigaTensor. On both datasets, DINTUCKER achieves significantly higher prediction accuracy with less computational time.
Exploring universal patterns in human home-work commuting from mobile phone data
Venue: arXiv cs.SI 2014
Year: 2014

Home-work commuting has always attracted significant research attention because of its impact on human mobility. One of the key assumptions in this domain of study is the universal uniformity of commute times. However, a true comparison of commute patterns has often been hindered by the intrinsic differences in data collection methods, which make observation from different countries potentially biased and unreliable. In the present work, we approach this problem through the use of mobile phone call detail records (CDRs), which offers a consistent method for investigating mobility patterns in wholly different parts of the world. We apply our analysis to a broad range of datasets, at both the country and city scale. Additionally, we compare these results with those obtained from vehicle GPS traces in Milan. While different regions have some unique commute time characteristics, we show that the home-work time distributions and average values within a single region are indeed largely independent of commute distance or country (Portugal, Ivory Coast, and Boston)--despite substantial spatial and infrastructural differences. Furthermore, a comparative analysis demonstrates that such distance-independence holds true only if we consider multimodal commute behaviors--as consistent with previous studies. In car-only (Milan GPS traces) and car-heavy (Saudi Arabia) commute datasets, we see that commute time is indeed influenced by commute distance.
A family of optimal locally recoverable codes
Venue: arXiv cs.IT 2014
Year: 2014

A code over a finite alphabet is called locally recoverable (LRC) if every symbol in the encoding is a function of a small number (at most $r$) other symbols. We present a family of LRC codes that attain the maximum possible value of the distance for a given locality parameter and code cardinality. The codewords are obtained as evaluations of specially constructed polynomials over a finite field, and reduce to a Reed-Solomon code if the locality parameter $r$ is set to be equal to the code dimension. The size of the code alphabet for most parameters is only slightly greater than the code length. The recovery procedure is performed by polynomial interpolation over $r$ points. We also construct codes with several disjoint recovering sets for every symbol. This construction enables the system to conduct several independent and simultaneous recovery processes of a specific symbol by accessing different parts of the codeword. This property enables high availability of frequently accessed data ("hot data").
Sparse Matrix Factorization
Venue: arXiv cs.LG 2014
Year: 2014

We investigate the problem of factorizing a matrix into several sparse matrices and propose an algorithm for this under randomness and sparsity assumptions. This problem can be viewed as a simplification of the deep learning problem where finding a factorization corresponds to finding edges in different layers and values of hidden units. We prove that under certain assumptions for a sparse linear deep network with $n$ nodes in each layer, our algorithm is able to recover the structure of the network and values of top layer hidden units for depths up to $\tilde O(n^{1/6})$. We further discuss the relation among sparse matrix factorization, deep learning, sparse recovery and dictionary learning.
Advancements on SEFE and Partitioned Book Embedding Problems
Venue: arXiv cs.CC 2014
Year: 2014

In this work we investigate the complexity of some problems related to the {\em Simultaneous Embedding with Fixed Edges} (SEFE) of $k$ planar graphs and the PARTITIONED $k$-PAGE BOOK EMBEDDING (PBE-$k$) problems, which are known to be equivalent under certain conditions. While the computational complexity of SEFE for $k=2$ is still a central open question in Graph Drawing, the problem is NP-complete for $k \geq 3$ [Gassner {\em et al.}, WG '06], even if the intersection graph is the same for each pair of graphs ({\em sunflower intersection}) [Schaefer, JGAA (2013)]. We improve on these results by proving that SEFE with $k \geq 3$ and sunflower intersection is NP-complete even when the intersection graph is a tree and all the input graphs are biconnected. Also, we prove NP-completeness for $k \geq 3$ of problem PBE-$k$ and of problem PARTITIONED T-COHERENT $k$-PAGE BOOK EMBEDDING (PTBE-$k$) - that is the generalization of PBE-$k$ in which the ordering of the vertices on the spine is constrained by a tree $T$ - even when two input graphs are biconnected. Further, we provide a linear-time algorithm for PTBE-$k$ when $k-1$ pages are assigned a connected graph. Finally, we prove that the problem of maximizing the number of edges that are drawn the same in a SEFE of two graphs is NP-complete in several restricted settings ({\em optimization version of SEFE}, Open Problem $9$, Chapter $11$ of the Handbook of Graph Drawing and Visualization).
Precision improvement of MEMS gyros for indoor mobile robots with horizontal motion inspired by methods of TRIZ
Venue: arXiv cs.RO 2014
Year: 2014

In the paper, the problem of precision improvement for the MEMS gyrosensors on indoor robots with horizontal motion is solved by methods of TRIZ ("the theory of inventive problem solving").
Can a biologically-plausible hierarchy effectively replace face detection, alignment, and recognition pipelines?
Venue: arXiv cs.CV 2014
Year: 2014

The standard approach to unconstrained face recognition in natural photographs is via a detection, alignment, recognition pipeline. While that approach has achieved impressive results, there are several reasons to be dissatisfied with it, among them is its lack of biological plausibility. A recent theory of invariant recognition by feedforward hierarchical networks, like HMAX, other convolutional networks, or possibly the ventral stream, implies an alternative approach to unconstrained face recognition. This approach accomplishes detection and alignment implicitly by storing transformations of training images (called templates) rather than explicitly detecting and aligning faces at test time. Here we propose a particular locality-sensitive hashing based voting scheme which we call "consensus of collisions" and show that it can be used to approximate the full 3-layer hierarchy implied by the theory. The resulting end-to-end system for unconstrained face recognition operates on photographs of faces taken under natural conditions, e.g., Labeled Faces in the Wild (LFW), without aligning or cropping them, as is normally done. It achieves a drastic improvement in the state of the art on this end-to-end task, reaching the same level of performance as the best systems operating on aligned, closely cropped images (no outside training data). It also performs well on two newer datasets, similar to LFW, but more difficult: LFW-jittered (new here) and SUFR-W.
ComReg: A Complex Network Approach to Prioritize Test Cases for Regression Testing
Venue: arXiv cs.SE 2014
Year: 2014

Regression testing is performed to provide confidence that changes in a part of software do not affect other parts of the software. An execution of all existing test cases is the best way to re-establish this confidence. However, regression testing is an expensive process---there might be insufficient resources (e.g., time, workforce) to allow for the re-execution of all test cases. Regression test prioritization techniques attempt to re-order a regression test suite based on some criteria so that highest priority test cases are executed earlier. In this study, we want to prioritize test cases for regression testing based on the dependency network of faults. In software testing, it is common that some faults are consequences of other faults (leading faults). Moreover, dependent faults can be removed if and only if the leading faults have been removed. Our goal is to prioritize test cases so that test cases that exposed leading faults (the most central faults in the fault dependency network) in the system testing phase, are executed first in regression testing. We present ComReg, a test case prioritization technique based on the dependency network of faults. We model a fault dependency network as a directed graph and identify leading faults to prioritize test cases for regression testing. We use a centrality aggregation technique which considers six network representative centrality metrics to identify leading faults in the fault dependency network. We also discuss the use of fault communities to select an arbitrary percentage of the test cases from a prioritized regression test suite. We conduct a case study that evaluates the effectiveness and applicability of the proposed method.
Data Mining of Online Genealogy Datasets for Revealing Lifespan Patterns in Human Population
Venue: arXiv cs.SI 2014
Year: 2014

Online genealogy datasets contain extensive information about millions of people and their past and present family connections. This vast amount of data can assist in identifying various patterns in human population. In this study, we present methods and algorithms which can assist in identifying variations in lifespan distributions of human population in the past centuries, in detecting social and genetic features which correlate with human lifespan, and in constructing predictive models of human lifespan based on various features which can easily be extracted from genealogy datasets. We have evaluated the presented methods and algorithms on a large online genealogy dataset with over a million profiles and over 9 million connections, all of which were collected from the WikiTree website. Our findings indicate that significant but small positive correlations exist between the parents' lifespan and their children's lifespan. Additionally, we found slightly higher and significant correlations between the lifespans of spouses. We also discovered a very small positive and significant correlation between longevity and reproductive success in males, and a small and significant negative correlation between longevity and reproductive success in females. Moreover, our machine learning algorithms presented better than random classification results in predicting which people who outlive the age of 50 will also outlive the age of 80. We believe that this study will be the first of many studies which utilize the wealth of data on human populations, existing in online genealogy datasets, to better understand factors which influence human lifespan. Understanding these factors can assist scientists in providing solutions for successful aging.