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1202.2709
Potential Theory for Directed Networks
physics.data-an cs.IR cs.SI physics.soc-ph
Uncovering factors underlying the network formation is a long-standing challenge for data mining and network analysis. In particular, the microscopic organizing principles of directed networks are less understood than those of undirected networks. This article proposes a hypothesis named potential theory, which assumes that every directed link corresponds to a decrease of a unit potential and subgraphs with definable potential values for all nodes are preferred. Combining the potential theory with the clustering and homophily mechanisms, it is deduced that the Bi-fan structure consisting of 4 nodes and 4 directed links is the most favored local structure in directed networks. Our hypothesis receives strongly positive supports from extensive experiments on 15 directed networks drawn from disparate fields, as indicated by the most accurate and robust performance of Bi-fan predictor within the link prediction framework. In summary, our main contribution is twofold: (i) We propose a new mechanism for the local organization of directed networks; (ii) We design the corresponding link prediction algorithm, which can not only testify our hypothesis, but also find out direct applications in missing link prediction and friendship recommendation.
1202.2745
Multi-column Deep Neural Networks for Image Classification
cs.CV cs.AI
Traditional methods of computer vision and machine learning cannot match human performance on tasks such as the recognition of handwritten digits or traffic signs. Our biologically plausible deep artificial neural network architectures can. Small (often minimal) receptive fields of convolutional winner-take-all neurons yield large network depth, resulting in roughly as many sparsely connected neural layers as found in mammals between retina and visual cortex. Only winner neurons are trained. Several deep neural columns become experts on inputs preprocessed in different ways; their predictions are averaged. Graphics cards allow for fast training. On the very competitive MNIST handwriting benchmark, our method is the first to achieve near-human performance. On a traffic sign recognition benchmark it outperforms humans by a factor of two. We also improve the state-of-the-art on a plethora of common image classification benchmarks.
1202.2759
Iterative Reconstruction of Rank-One Matrices in Noise
cs.IT math.IT
We consider the problem of estimating a rank-one matrix in Gaussian noise under a probabilistic model for the left and right factors of the matrix. The probabilistic model can impose constraints on the factors including sparsity and positivity that arise commonly in learning problems. We propose a family of algorithms that reduce the problem to a sequence of scalar estimation computations. These algorithms are similar to approximate message passing techniques based on Gaussian approximations of loopy belief propagation that have been used recently in compressed sensing. Leveraging analysis methods by Bayati and Montanari, we show that the asymptotic behavior of the algorithm is described by a simple scalar equivalent model, where the distribution of the estimates at each iteration is identical to certain scalar estimates of the variables in Gaussian noise. Moreover, the effective Gaussian noise level is described by a set of state evolution equations. The proposed approach to deriving algorithms thus provides a computationally simple and general method for rank-one estimation problems with a precise analysis in certain high-dimensional settings.
1202.2770
Multi-Level Error-Resilient Neural Networks with Learning
cs.NE cs.AI cs.IT math.IT
The problem of neural network association is to retrieve a previously memorized pattern from its noisy version using a network of neurons. An ideal neural network should include three components simultaneously: a learning algorithm, a large pattern retrieval capacity and resilience against noise. Prior works in this area usually improve one or two aspects at the cost of the third. Our work takes a step forward in closing this gap. More specifically, we show that by forcing natural constraints on the set of learning patterns, we can drastically improve the retrieval capacity of our neural network. Moreover, we devise a learning algorithm whose role is to learn those patterns satisfying the above mentioned constraints. Finally we show that our neural network can cope with a fair amount of noise.
1202.2771
Multi-Scale Matrix Sampling and Sublinear-Time PageRank Computation
cs.DS cs.SI
A fundamental problem arising in many applications in Web science and social network analysis is, given an arbitrary approximation factor $c>1$, to output a set $S$ of nodes that with high probability contains all nodes of PageRank at least $\Delta$, and no node of PageRank smaller than $\Delta/c$. We call this problem {\sc SignificantPageRanks}. We develop a nearly optimal, local algorithm for the problem with runtime complexity $\tilde{O}(n/\Delta)$ on networks with $n$ nodes. We show that any algorithm for solving this problem must have runtime of ${\Omega}(n/\Delta)$, rendering our algorithm optimal up to logarithmic factors. Our algorithm comes with two main technical contributions. The first is a multi-scale sampling scheme for a basic matrix problem that could be of interest on its own. In the abstract matrix problem it is assumed that one can access an unknown {\em right-stochastic matrix} by querying its rows, where the cost of a query and the accuracy of the answers depend on a precision parameter $\epsilon$. At a cost propositional to $1/\epsilon$, the query will return a list of $O(1/\epsilon)$ entries and their indices that provide an $\epsilon$-precision approximation of the row. Our task is to find a set that contains all columns whose sum is at least $\Delta$, and omits any column whose sum is less than $\Delta/c$. Our multi-scale sampling scheme solves this problem with cost $\tilde{O}(n/\Delta)$, while traditional sampling algorithms would take time $\Theta((n/\Delta)^2)$. Our second main technical contribution is a new local algorithm for approximating personalized PageRank, which is more robust than the earlier ones developed in \cite{JehW03,AndersenCL06} and is highly efficient particularly for networks with large in-degrees or out-degrees. Together with our multiscale sampling scheme we are able to optimally solve the {\sc SignificantPageRanks} problem.
1202.2773
Decentralized Multi-agent Plan Repair in Dynamic Environments
cs.AI cs.MA
Achieving joint objectives by teams of cooperative planning agents requires significant coordination and communication efforts. For a single-agent system facing a plan failure in a dynamic environment, arguably, attempts to repair the failed plan in general do not straightforwardly bring any benefit in terms of time complexity. However, in multi-agent settings the communication complexity might be of a much higher importance, possibly a high communication overhead might be even prohibitive in certain domains. We hypothesize that in decentralized systems, where coordination is enforced to achieve joint objectives, attempts to repair failed multi-agent plans should lead to lower communication overhead than replanning from scratch. The contribution of the presented paper is threefold. Firstly, we formally introduce the multi-agent plan repair problem and formally present the core hypothesis underlying our work. Secondly, we propose three algorithms for multi-agent plan repair reducing the problem to specialized instances of the multi-agent planning problem. Finally, we present results of experimental validation confirming the core hypothesis of the paper.
1202.2774
Beyond the Bethe Free Energy of LDPC Codes via Polymer Expansions
cs.IT cond-mat.stat-mech math-ph math.IT math.MP
The loop series provides a formal way to write down corrections to the Bethe entropy (and/or free energy) of graphical models. We provide methods to rigorously control such expansions for low-density parity-check codes used over a highly noisy binary symmetric channel. We prove that in the asymptotic limit of large size, with high probability, the Bethe expression gives an exact formula for the entropy (per bit) of the input word conditioned on the output of the channel. Our methods also apply to more general models.
1202.2778
Polymer Expansions for Cycle LDPC Codes
cs.IT cond-mat.stat-mech math-ph math.IT math.MP
We prove that the Bethe expression for the conditional input-output entropy of cycle LDPC codes on binary symmetric channels above the MAP threshold is exact in the large block length limit. The analysis relies on methods from statistical physics. The finite size corrections to the Bethe expression are expressed through a polymer expansion which is controlled thanks to expander and counting arguments.
1202.2794
Query Matrices for Retrieving Binary Vectors Based on the Hamming Distance Oracle
cs.DM cs.IR cs.IT math.IT
The Hamming oracle returns the Hamming distance between an unknown binary $n$-vector $x$ and a binary query $n$-vector y. The objective is to determine $x$ uniquely using a sequence of $m$ queries. What are the minimum number of queries required in the worst case? We consider the query ratio $m/n$ to be our figure of merit and derive upper bounds on the query ratio by explicitly constructing $(m,n)$ query matrices. We show that our recursive and algebraic construction results in query ratios arbitrarily close to zero. Our construction is based on codes of constant weight. A decoding algorithm for recovering the unknown binary vector is also described.
1202.2803
Efficient Relay Selection Scheme for Delay-Limited Non-Orthogonal Hybrid-ARQ Relay Channels
cs.IT math.IT
We consider a half-duplex wireless relay network with hybrid-automatic retransmission request (HARQ) and Rayleigh fading channels. In this paper, we analyze the outage probability of the multi-relay delay-limited HARQ system with opportunistic relaying scheme in decode-and-forward mode, in which the \emph{best} relay is selected to transmit the source's regenerated signal. A simple and distributed relay selection strategy is proposed for multi-relay HARQ channels. Then, we utilize the non-orthogonal cooperative transmission between the source and selected relay for retransmitting of the source data toward the destination if needed, using space-time codes or beamforming techniques. We analyze the performance of the system. We first derive the cumulative density function (CDF) and probability density function (PDF) of the selected relay HARQ channels. Then, the CDF and PDF are used to determine the outage probability in the $l$-th round of HARQ. The outage probability is required to compute the throughput-delay performance of this half-duplex opportunistic relaying protocol. The packet delay constraint is represented by $L$, the maximum number of HARQ rounds. An outage is declared if the packet is unsuccessful after $L$ HARQ rounds. Furthermore, closed-form upper-bounds on outage probability are derived and subsequently are used to investigate the diversity order of the system. Based on the derived upper-bound expressions, it is shown that the proposed schemes achieve the full spatial diversity order of $N+1$, where $N$ is the number of potential relays. Our analytical results are confirmed by simulation results.
1202.2826
Error Floor Approximation for LDPC Codes in the AWGN Channel
cs.IT math.IT
This paper addresses the prediction of error floors of low-density parity-check (LDPC) codes with variable nodes of constant degree in the additive white Gaussian noise (AWGN) channel. Specifically, we focus on the performance of the sum-product algorithm (SPA) decoder formulated in the log-likelihood ratio (LLR) domain. We hypothesize that several published error floor levels are due to the manner in which decoder implementations handled the LLRs at high SNRs. We employ an LLR-domain SPA decoder that does not saturate near-certain messages and find the error rates of our decoder to be lower by at least several orders of magnitude. We study the behavior of trapping sets (or near-codewords) that are the dominant cause of the reported error floors. We develop a refined linear model, based on the work of Sun and others, that accurately predicts error floors caused by elementary tapping sets for saturating decoders. Performance results of several codes at several levels of decoder saturation are presented.
1202.2875
Uplink Performance Analysis of Multicell MU-MIMO Systems with ZF Receivers
cs.IT math.IT
We consider the uplink of a multicell multiuser multiple-input multiple-output system where the channel experiences both small and large-scale fading. The data detection is done by using the linear zero-forcing technique, assuming the base station (BS) has perfect channel state information. We derive new, exact closed-form expressions for the uplink rate, symbol error rate, and outage probability per user, as well as a lower bound on the achievable rate. This bound is very tight and becomes exact in the large-number-of-antennas limit. We further study the asymptotic system performance in the regimes of high signal-to-noise ratio (SNR), large number of antennas, and large number of users per cell. We show that at high SNRs, the system is interference-limited and hence, we cannot improve the system performance by increasing the transmit power of each user. Instead, by increasing the number of BS antennas, the effects of interference and noise can be reduced, thereby improving the system performance. We demonstrate that, with very large antenna arrays at the BS, the transmit power of each user can be made inversely proportional to the number of BS antennas while maintaining a desired quality-of-service. Numerical results are presented to verify our analysis.
1202.2880
Approximate Recall Confidence Intervals
cs.IR
Recall, the proportion of relevant documents retrieved, is an important measure of effectiveness in information retrieval, particularly in the legal, patent, and medical domains. Where document sets are too large for exhaustive relevance assessment, recall can be estimated by assessing a random sample of documents; but an indication of the reliability of this estimate is also required. In this article, we examine several methods for estimating two-tailed recall confidence intervals. We find that the normal approximation in current use provides poor coverage in many circumstances, even when adjusted to correct its inappropriate symmetry. Analytic and Bayesian methods based on the ratio of binomials are generally more accurate, but are inaccurate on small populations. The method we recommend derives beta-binomial posteriors on retrieved and unretrieved yield, with fixed hyperparameters, and a Monte Carlo estimate of the posterior distribution of recall. We demonstrate that this method gives mean coverage at or near the nominal level, across several scenarios, while being balanced and stable. We offer advice on sampling design, including the allocation of assessments to the retrieved and unretrieved segments, and compare the proposed beta-binomial with the officially reported normal intervals for recent TREC Legal Track iterations.
1202.2887
Semi-Quantitative Group Testing
cs.IT math.IT
We consider a novel group testing procedure, termed semi-quantitative group testing, motivated by a class of problems arising in genome sequence processing. Semi-quantitative group testing (SQGT) is a non-binary pooling scheme that may be viewed as a combination of an adder model followed by a quantizer. For the new testing scheme we define the capacity and evaluate the capacity for some special choices of parameters using information theoretic methods. We also define a new class of disjunct codes suitable for SQGT, termed SQ-disjunct codes. We also provide both explicit and probabilistic code construction methods for SQGT with simple decoding algorithms.
1202.2888
Exploiting the `Web of Trust' to improve efficiency in collaborative networks
cs.SI
Maintaining high quality content is one of the foremost objectives of any web-based collaborative service that depends on a large number of users. In such systems, it is nearly impossible for automated scripts to judge semantics as it is to expect all editors to review the content. This catalyzes the need for trust-based mechanisms to ensure quality of an article immediately after an edit. In this paper, we build on previous work and develop a framework based on the `web of trust' concept to calculate satisfaction scores for all users without the need for perusing the article. We derive some bounds for systems based on our mechanism and show that the optimization problem of selecting the best users to review an article is NP-Hard. Extensive simulations validate our model and results, and show that trust-based mechanisms are essential to improve efficiency in any online collaborative editing platform.
1202.2892
Recommender System Based on Algorithm of Bicluster Analysis RecBi
cs.AI cs.IR stat.ML
In this paper we propose two new algorithms based on biclustering analysis, which can be used at the basis of a recommender system for educational orientation of Russian School graduates. The first algorithm was designed to help students make a choice between different university faculties when some of their preferences are known. The second algorithm was developed for the special situation when nothing is known about their preferences. The final version of this recommender system will be used by Higher School of Economics.
1202.2895
Concept Relation Discovery and Innovation Enabling Technology (CORDIET)
cs.AI cs.IR stat.ML
Concept Relation Discovery and Innovation Enabling Technology (CORDIET), is a toolbox for gaining new knowledge from unstructured text data. At the core of CORDIET is the C-K theory which captures the essential elements of innovation. The tool uses Formal Concept Analysis (FCA), Emergent Self Organizing Maps (ESOM) and Hidden Markov Models (HMM) as main artifacts in the analysis process. The user can define temporal, text mining and compound attributes. The text mining attributes are used to analyze the unstructured text in documents, the temporal attributes use these document's timestamps for analysis. The compound attributes are XML rules based on text mining and temporal attributes. The user can cluster objects with object-cluster rules and can chop the data in pieces with segmentation rules. The artifacts are optimized for efficient data analysis; object labels in the FCA lattice and ESOM map contain an URL on which the user can click to open the selected document.
1202.2903
Scaling Laws in Human Language
physics.data-an cs.IR physics.soc-ph
Zipf's law on word frequency is observed in English, French, Spanish, Italian, and so on, yet it does not hold for Chinese, Japanese or Korean characters. A model for writing process is proposed to explain the above difference, which takes into account the effects of finite vocabulary size. Experiments, simulations and analytical solution agree well with each other. The results show that the frequency distribution follows a power law with exponent being equal to 1, at which the corresponding Zipf's exponent diverges. Actually, the distribution obeys exponential form in the Zipf's plot. Deviating from the Heaps' law, the number of distinct words grows with the text length in three stages: It grows linearly in the beginning, then turns to a logarithmical form, and eventually saturates. This work refines previous understanding about Zipf's law and Heaps' law in language systems.
1202.2907
The weight Enumerator of some irreducible cyclic codes
cs.CR cs.IT math.IT
Irreducible cyclic codes are one of the largest known classes of block codes which have been investigated for a long time. However, their weight distributions are known only for a few cases. In this paper, a class of irreducible cyclic codes are studied and their weight distributions are determined. Moreover, all codewords of some irreducible cyclic codes are obtained through programming in order to explain their distributions. The number of distinct nonzero weights in these codes dealt with in this paper varies among 1,2,3,6,8.
1202.2926
Detection of Calendar-Based Periodicities of Interval-Based Temporal Patterns
cs.DB
We present a novel technique to identify calendar-based (annual, monthly and daily) periodicities of an interval-based temporal pattern. An interval-based temporal pattern is a pattern that occurs across a time-interval, then disappears for some time, again recurs across another time-interval and so on and so forth. Given the sequence of time-intervals in which an interval-based temporal pattern has occurred, we propose a method for identifying the extent to which the pattern is periodic with respect to a calendar cycle. In comparison to previous work, our method is asymptotically faster. We also show an interesting relationship between periodicities across different levels of any hierarchical timestamp (year/month/day, hour/minute/second etc.).
1202.2928
The Diffusion of Networking Technologies
cs.SI cs.DS cs.NI physics.soc-ph
There has been significant interest in the networking community on the impact of cascade effects on the diffusion of networking technology upgrades in the Internet. Thinking of the global Internet as a graph, where each node represents an economically-motivated Internet Service Provider (ISP), a key problem is to determine the smallest set of nodes that can trigger a cascade that causes every other node in the graph to adopt the protocol. We design the first approximation algorithm with a provable performance guarantee for this problem, in a model that captures the following key issue: a node's decision to upgrade should be influenced by the decisions of the remote nodes it wishes to communicate with. Given an internetwork G(V,E) and threshold function \theta, we assume that node $u$ activates (upgrades to the new technology) when it is adjacent to a connected component of active nodes in G of size exceeding node $u$'s threshold \theta(u). Our objective is to choose the smallest set of nodes that can cause the rest of the graph to activate. Our main contribution is an approximation algorithm based on linear programming, which we complement with computational hardness results and a near-optimum integrality gap. Our algorithm, which does not rely on submodular optimization techniques, also highlights the substantial algorithmic difference between our problem and similar questions studied in the context of social networks.
1202.2944
Diversity Analysis, Code Design and Tight Error Rate Lower Bound for Binary Joint Network-Channel Coding
cs.IT math.IT
Joint network-channel codes (JNCC) can improve the performance of communication in wireless networks, by combining, at the physical layer, the channel codes and the network code as an overall error-correcting code. JNCC is increasingly proposed as an alternative to a standard layered construction, such as the OSI-model. The main performance metrics for JNCCs are scalability to larger networks and error rate. The diversity order is one of the most important parameters determining the error rate. The literature on JNCC is growing, but a rigorous diversity analysis is lacking, mainly because of the many degrees of freedom in wireless networks, which makes it very hard to prove general statements on the diversity order. In this paper, we consider a network with slowly varying fading point-to-point links, where all sources also act as relay and additional non-source relays may be present. We propose a general structure for JNCCs to be applied in such network. In the relay phase, each relay transmits a linear transform of a set of source codewords. Our main contributions are the proposition of an upper and lower bound on the diversity order, a scalable code design and a new lower bound on the word error rate to asses the performance of the network code. The lower bound on the diversity order is only valid for JNCCs where the relays transform only two source codewords. We then validate this analysis with an example which compares the JNCC performance to that of a standard layered construction. Our numerical results suggest that as networks grow, it is difficult to perform significantly better than a standard layered construction, both on a fundamental level, expressed by the outage probability, as on a practical level, expressed by the word error rate.
1202.2963
Maximum Multiflow in Wireless Network Coding
cs.IT math.IT
In a multihop wireless network, wireless interference is crucial to the maximum multiflow (MMF) problem, which studies the maximum throughput between multiple pairs of sources and sinks. In this paper, we observe that network coding could help to decrease the impacts of wireless interference, and propose a framework to study the MMF problem for multihop wireless networks with network coding. Firstly, a network model is set up to describe the new conflict relations modified by network coding. Then, we formulate a linear programming problem to compute the maximum throughput and show its superiority over one in networks without coding. Finally, the MMF problem in wireless network coding is shown to be NP-hard and a polynomial approximation algorithm is proposed.
1202.2998
Fast Adaptive S-ALOHA Scheme for Event-driven Machine-to-Machine Communications
cs.IT math.IT
Machine-to-Machine (M2M) communication is now playing a market-changing role in a wide range of business world. However, in event-driven M2M communications, a large number of devices activate within a short period of time, which in turn causes high radio congestions and severe access delay. To address this issue, we propose a Fast Adaptive S-ALOHA (FASA) scheme for M2M communication systems with bursty traffic. The statistics of consecutive idle and collision slots, rather than the observation in a single slot, are used in FASA to accelerate the tracking process of network status. Furthermore, the fast convergence property of FASA is guaranteed by using drift analysis. Simulation results demonstrate that the proposed FASA scheme achieves near-optimal performance in reducing access delay, which outperforms that of traditional additive schemes such as PB-ALOHA. Moreover, compared to multiplicative schemes, FASA shows its robustness even under heavy traffic load in addition to better delay performance.
1202.3021
No-reference image quality assessment through the von Mises distribution
cs.CV
An innovative way of calculating the von Mises distribution (VMD) of image entropy is introduced in this paper. The VMD's concentration parameter and some fitness parameter that will be later defined, have been analyzed in the experimental part for determining their suitability as a image quality assessment measure in some particular distortions such as Gaussian blur or additive Gaussian noise. To achieve such measure, the local R\'{e}nyi entropy is calculated in four equally spaced orientations and used to determine the parameters of the von Mises distribution of the image entropy. Considering contextual images, experimental results after applying this model show that the best-in-focus noise-free images are associated with the highest values for the von Mises distribution concentration parameter and the highest approximation of image data to the von Mises distribution model. Our defined von Misses fitness parameter experimentally appears also as a suitable no-reference image quality assessment indicator for no-contextual images.
1202.3046
Segmentation of Offline Handwritten Bengali Script
cs.CV cs.AI
Character segmentation has long been one of the most critical areas of optical character recognition process. Through this operation, an image of a sequence of characters, which may be connected in some cases, is decomposed into sub-images of individual alphabetic symbols. In this paper, segmentation of cursive handwritten script of world's fourth popular language, Bengali, is considered. Unlike English script, Bengali handwritten characters and its components often encircle the main character, making the conventional segmentation methodologies inapplicable. Experimental results, using the proposed segmentation technique, on sample cursive handwritten data containing 218 ideal segmentation points show a success rate of 97.7%. Further feature-analysis on these segments may lead to actual recognition of handwritten cursive Bengali script.
1202.3059
Synchronization in Scale Free networks with degree correlation
physics.soc-ph cond-mat.stat-mech cs.SI
In this paper we study a model of synchronization process on scale free networks with degree-degree correlations. This model was already studied on this kind of networks without correlations by Pastore y Piontti {\it et al.}, Phys. Rev. E {\bf 76}, 046117 (2007). Here, we study the effects of the degree-degree correlation on the behavior of the load fluctuations $W_s$ in the steady state. We found that for assortative networks there exist a specific correlation where the system is optimal synchronized. In addition, we found that close to this optimally value the fluctuations does not depend on the system size and therefore the system becomes fully scalable. This result could be very important for some technological applications. On the other hand, far from the optimal correlation, $W_s$ scales logarithmically with the system size.
1202.3062
Correlated dynamics in egocentric communication networks
physics.soc-ph cs.SI
We investigate the communication sequences of millions of people through two different channels and analyze the fine grained temporal structure of correlated event trains induced by single individuals. By focusing on correlations between the heterogeneous dynamics and the topology of egocentric networks we find that the bursty trains usually evolve for pairs of individuals rather than for the ego and his/her several neighbors thus burstiness is a property of the links rather than of the nodes. We compare the directional balance of calls and short messages within bursty trains to the average on the actual link and show that for the trains of voice calls the imbalance is significantly enhanced, while for short messages the balance within the trains increases. These effects can be partly traced back to the technological constrains (for short messages) and partly to the human behavioral features (voice calls). We define a model that is able to reproduce the empirical results and may help us to understand better the mechanisms driving technology mediated human communication dynamics.
1202.3074
Conedy: a scientific tool to investigate Complex Network Dynamics
physics.comp-ph cs.SI physics.soc-ph
We present Conedy, a performant scientific tool to numerically investigate dynamics on complex networks. Conedy allows to create networks and provides automatic code generation and compilation to ensure performant treatment of arbitrary node dynamics. Conedy can be interfaced via an internal script interpreter or via a Python module.
1202.3079
Towards minimax policies for online linear optimization with bandit feedback
cs.LG stat.ML
We address the online linear optimization problem with bandit feedback. Our contribution is twofold. First, we provide an algorithm (based on exponential weights) with a regret of order $\sqrt{d n \log N}$ for any finite action set with $N$ actions, under the assumption that the instantaneous loss is bounded by 1. This shaves off an extraneous $\sqrt{d}$ factor compared to previous works, and gives a regret bound of order $d \sqrt{n \log n}$ for any compact set of actions. Without further assumptions on the action set, this last bound is minimax optimal up to a logarithmic factor. Interestingly, our result also shows that the minimax regret for bandit linear optimization with expert advice in $d$ dimension is the same as for the basic $d$-armed bandit with expert advice. Our second contribution is to show how to use the Mirror Descent algorithm to obtain computationally efficient strategies with minimax optimal regret bounds in specific examples. More precisely we study two canonical action sets: the hypercube and the Euclidean ball. In the former case, we obtain the first computationally efficient algorithm with a $d \sqrt{n}$ regret, thus improving by a factor $\sqrt{d \log n}$ over the best known result for a computationally efficient algorithm. In the latter case, our approach gives the first algorithm with a $\sqrt{d n \log n}$ regret, again shaving off an extraneous $\sqrt{d}$ compared to previous works.
1202.3102
Evolution of Zipf's Law for Indian Urban Agglomerations vis-\`{a}-vis Chinese Urban Agglomerations
physics.soc-ph cs.SI
We investigate into the rank-size distributions of urban agglomerations for India between 1981 to 2011. The incidence of a power law tail is prominent. A relevant question persists regarding the evolution of the power tail coefficient. We have developed a methodology to meaningfully track the power law coefficient over time, when a country experience population growth. A relevant dynamic law, Gibrat's law, is empirically tested in this connection. We argue that these empirical findings for India goes in contrast with the findings in case of China, another country with population growth but monolithic political system.
1202.3162
Social Contagion: An Empirical Study of Information Spread on Digg and Twitter Follower Graphs
cs.SI cs.CY physics.data-an physics.soc-ph
Social networks have emerged as a critical factor in information dissemination, search, marketing, expertise and influence discovery, and potentially an important tool for mobilizing people. Social media has made social networks ubiquitous, and also given researchers access to massive quantities of data for empirical analysis. These data sets offer a rich source of evidence for studying dynamics of individual and group behavior, the structure of networks and global patterns of the flow of information on them. However, in most previous studies, the structure of the underlying networks was not directly visible but had to be inferred from the flow of information from one individual to another. As a result, we do not yet understand dynamics of information spread on networks or how the structure of the network affects it. We address this gap by analyzing data from two popular social news sites. Specifically, we extract follower graphs of active Digg and Twitter users and track how interest in news stories cascades through the graph. We compare and contrast properties of information cascades on both sites and elucidate what they tell us about dynamics of information flow on networks.
1202.3179
Randomization Resilient To Sensitive Reconstruction
cs.DB
With the randomization approach, sensitive data items of records are randomized to protect privacy of individuals while allowing the distribution information to be reconstructed for data analysis. In this paper, we distinguish between reconstruction that has potential privacy risk, called micro reconstruction, and reconstruction that does not, called aggregate reconstruction. We show that the former could disclose sensitive information about a target individual, whereas the latter is more useful for data analysis than for privacy breaches. To limit the privacy risk of micro reconstruction, we propose a privacy definition, called (epsilon,delta)-reconstruction-privacy. Intuitively, this privacy notion requires that micro reconstruction has a large error with a large probability. The promise of this approach is that micro reconstruction is more sensitive to the number of independent trials in the randomization process than aggregate reconstruction is; therefore, reducing the number of independent trials helps achieve (epsilon,delta)-reconstruction-privacy while preserving the accuracy of aggregate reconstruction. We present an algorithm based on this idea and evaluate the effectiveness of this approach using real life data sets.
1202.3184
Asymptotic Behavior of the Maximum and Minimum Singular Value of Random Vandermonde Matrices
math.PR cs.IT math.IT
This work examines various statistical distributions in connection with random Vandermonde matrices and their extension to $d$--dimensional phase distributions. Upper and lower bound asymptotics for the maximum singular value are found to be $O(\log^{1/2}{N^{d}})$ and $\Omega((\log N^{d} /(\log \log N^d))^{1/2})$ respectively where $N$ is the dimension of the matrix, generalizing the results in \cite{TW}. We further study the behavior of the minimum singular value of these random matrices. In particular, we prove that the minimum singular value is at most $N\exp(-C\sqrt{N}))$ with high probability where $C$ is a constant independent on $N$. Furthermore, the value of the constant $C$ is determined explicitly. The main result is obtained in two different ways. One approach uses techniques from stochastic processes and in particular, a construction related to the Brownian bridge. The other one is a more direct analytical approach involving combinatorics and complex analysis. As a consequence, we obtain a lower bound for the maximum absolute value of a random complex polynomial on the unit circle, which may be of independent mathematical interest. Lastly, for each sequence of positive integers ${k_p}_{p=1}^{\infty}$ we present a generalized version of the previously discussed matrices. The classical random Vandermonde matrix corresponds to the sequence $k_{p}=p-1$. We find a combinatorial formula for their moments and we show that the limit eigenvalue distribution converges to a probability measure supported on $[0,\infty)$. Finally, we show that for the sequence $k_p=2^{p}$ the limit eigenvalue distribution is the famous Marchenko--Pastur distribution.
1202.3185
Improving News Ranking by Community Tweets
cs.IR cs.SI
Users frequently express their information needs by means of short and general queries that are difficult for ranking algorithms to interpret correctly. However, users' social contexts can offer important additional information about their information needs which can be leveraged by ranking algorithms to provide augmented, personalized results. Existing methods mostly rely on users' individual behavioral data such as clickstream and log data, but as a result suffer from data sparsity and privacy issues. Here, we propose a Community Tweets Voting Model (CTVM) to re-rank Google and Yahoo news search results on the basis of open, large-scale Twitter community data. Experimental results show that CTVM outperforms baseline rankings from Google and Yahoo for certain online communities. We propose an application scenario of CTVM and provide an agenda for further research.
1202.3188
Clustering assortativity, communities and functional modules in real-world networks
physics.soc-ph cs.SI physics.data-an
Complex networks of real-world systems are believed to be controlled by common phenomena, producing structures far from regular or random. Clustering, community structure and assortative mixing by degree are perhaps among most prominent examples of the latter. Although generally accepted for social networks, these properties only partially explain the structure of other networks. We first show that degree-corrected clustering is in contrast to standard definition highly assortative. Yet interesting on its own, we further note that non-social networks contain connected regions with very low clustering. Hence, the structure of real-world networks is beyond communities. We here investigate the concept of functional modules---groups of regularly equivalent nodes---and show that such structures could explain for the properties observed in non-social networks. Real-world networks might be composed of functional modules that are overlaid by communities. We support the latter by proposing a simple network model that generates scale-free small-world networks with tunable clustering and degree mixing. Model has a natural interpretation in many real-world networks, while it also gives insights into an adequate community extraction framework. We also present an algorithm for detection of arbitrary structural modules without any prior knowledge. Algorithm is shown to be superior to state-of-the-art, while application to real-world networks reveals well supported composites of different structural modules that are consistent with the underlying systems. Clear functional modules are identified in all types of networks including social. Our findings thus expose functional modules as another key ingredient of complex real-world networks.
1202.3215
Data quality measurement on categorical data using genetic algorithm
cs.DB
Data quality on categorical attribute is a difficult problem that has not received as much attention as numerical counterpart. Our basic idea is to employ association rule for the purpose of data quality measurement. Strong rule generation is an important area of data mining. Association rule mining problems can be considered as a multi objective problem rather than as a single objective one. The main area of concentration was the rules generated by association rule mining using genetic algorithm. The advantage of using genetic algorithm is to discover high level prediction rules is that they perform a global search and cope better with attribute interaction than the greedy rule induction algorithm often used in data mining. Genetic algorithm based approach utilizes the linkage between association rule and feature selection. In this paper, we put forward a Multi objective genetic algorithm approach for data quality on categorical attributes. The result shows that our approach is outperformed by the objectives like accuracy, completeness, comprehensibility and interestingness.
1202.3253
Small Count Privacy and Large Count Utility in Data Publishing
cs.DB
While the introduction of differential privacy has been a major breakthrough in the study of privacy preserving data publication, some recent work has pointed out a number of cases where it is not possible to limit inference about individuals. The dilemma that is intrinsic in the problem is the simultaneous requirement of data utility in the published data. Differential privacy does not aim to protect information about an individual that can be uncovered even without the participation of the individual. However, this lack of coverage may violate the principle of individual privacy. Here we propose a solution by providing protection to sensitive information, by which we refer to the answers for aggregate queries with small counts. Previous works based on $\ell$-diversity can be seen as providing a special form of this kind of protection. Our method is developed with another goal which is to provide differential privacy guarantee, and for that we introduce a more refined form of differential privacy to deal with certain practical issues. Our empirical studies show that our method can preserve better utilities than a number of state-of-the-art methods although these methods do not provide the protections that we provide.
1202.3255
Scalability of Data Binding in ASP.NET Web Applications
cs.DB cs.SE
ASP.NET web applications typically employ server controls to provide dynamic web pages, and data-bound server controls to display and maintain database data. Most developers use default properties of ASP.NET server controls when developing web applications, which allows for rapid development of workable applications. However, creating a high-performance, multi-user, and scalable web application requires enhancement of server controls using custom-made code. In this empirical study we evaluate the impact of various technical approaches for paging and sorting functionality in data-driven ASP.NET web applications: automatic data paging and sorting in web server controls on web server; paging and sorting on database server; indexed and non-indexed database columns; clustered vs. non-clustered indices. We observed significant performance improvements when custom paging based on SQL stored procedure and clustered index is used.
1202.3258
Stiffness matrix of manipulators with passive joints: computational aspects
cs.RO
The paper focuses on stiffness matrix computation for manipulators with passive joints, compliant actuators and flexible links. It proposes both explicit analytical expressions and an efficient recursive procedure that are applicable in the general case and allow obtaining the desired matrix either in analytical or numerical form. Advantages of the developed technique and its ability to produce both singular and non-singular stiffness matrices are illustrated by application examples that deal with stiffness modeling of two Stewart-Gough platforms.
1202.3261
Quick Detection of Nodes with Large Degrees
cs.DS cs.SI physics.soc-ph
Our goal is to quickly find top $k$ lists of nodes with the largest degrees in large complex networks. If the adjacency list of the network is known (not often the case in complex networks), a deterministic algorithm to find a node with the largest degree requires an average complexity of O(n), where $n$ is the number of nodes in the network. Even this modest complexity can be very high for large complex networks. We propose to use the random walk based method. We show theoretically and by numerical experiments that for large networks the random walk method finds good quality top lists of nodes with high probability and with computational savings of orders of magnitude. We also propose stopping criteria for the random walk method which requires very little knowledge about the structure of the network.
1202.3323
Mirror Descent Meets Fixed Share (and feels no regret)
cs.LG stat.ML
Mirror descent with an entropic regularizer is known to achieve shifting regret bounds that are logarithmic in the dimension. This is done using either a carefully designed projection or by a weight sharing technique. Via a novel unified analysis, we show that these two approaches deliver essentially equivalent bounds on a notion of regret generalizing shifting, adaptive, discounted, and other related regrets. Our analysis also captures and extends the generalized weight sharing technique of Bousquet and Warmuth, and can be refined in several ways, including improvements for small losses and adaptive tuning of parameters.
1202.3335
An efficient high-quality hierarchical clustering algorithm for automatic inference of software architecture from the source code of a software system
cs.AI cs.LG cs.SE
It is a high-quality algorithm for hierarchical clustering of large software source code. This effectively allows to break the complexity of tens of millions lines of source code, so that a human software engineer can comprehend a software system at high level by means of looking at its architectural diagram that is reconstructed automatically from the source code of the software system. The architectural diagram shows a tree of subsystems having OOP classes in its leaves (in the other words, a nested software decomposition). The tool reconstructs the missing (inconsistent/incomplete/inexistent) architectural documentation for a software system from its source code. This facilitates software maintenance: change requests can be performed substantially faster. Simply speaking, this unique tool allows to lift the comprehensible grain of object-oriented software systems from OOP class-level to subsystem-level. It is estimated that a commercial tool, developed on the basis of this work, will reduce software maintenance expenses 10 times on the current needs, and will allow to implement next-generation software systems which are currently too complex to be within the range of human comprehension, therefore can't yet be designed or implemented. Implemented prototype in Open Source: http://sourceforge.net/p/insoar/code-0/1/tree/
1202.3338
New constructions of CSS codes obtained by moving to higher alphabets
quant-ph cs.IT math.IT
We generalize a construction of non-binary quantum LDPC codes over $\F_{2^m}$ due to \cite{KHIS11a} and apply it in particular to toric codes. We obtain in this way not only codes with better rates than toric codes but also improve dramatically the performance of standard iterative decoding. Moreover, the new codes obtained in this fashion inherit the distance properties of the underlying toric codes and have therefore a minimum distance which grows as the square root of the length of the code for fixed $m$.
1202.3399
Optimal error of query sets under the differentially-private matrix mechanism
cs.DB cs.CR
A common goal of privacy research is to release synthetic data that satisfies a formal privacy guarantee and can be used by an analyst in place of the original data. To achieve reasonable accuracy, a synthetic data set must be tuned to support a specified set of queries accurately, sacrificing fidelity for other queries. This work considers methods for producing synthetic data under differential privacy and investigates what makes a set of queries "easy" or "hard" to answer. We consider answering sets of linear counting queries using the matrix mechanism, a recent differentially-private mechanism that can reduce error by adding complex correlated noise adapted to a specified workload. Our main result is a novel lower bound on the minimum total error required to simultaneously release answers to a set of workload queries. The bound reveals that the hardness of a query workload is related to the spectral properties of the workload when it is represented in matrix form. The bound is most informative for $(\epsilon,\delta)$-differential privacy but also applies to $\epsilon$-differential privacy.
1202.3405
On the Feasibility of Precoding-Based Network Alignment for Three Unicast Sessions
cs.IT math.IT
We consider the problem of network coding across three unicast sessions over a directed acyclic graph, when each session has min-cut one. Previous work by Das et al. adapted a precoding-based interference alignment technique, originally developed for the wireless interference channel, specifically to this problem. We refer to this approach as precoding-based network alignment (PBNA). Similar to the wireless setting, PBNA asymptotically achieves half the minimum cut; different from the wireless setting, its feasibility depends on the graph structure. Das et al. provided a set of feasibility conditions for PBNA with respect to a particular precoding matrix. However, the set consisted of an infinite number of conditions, which is impossible to check in practice. Furthermore, the conditions were purely algebraic, without interpretation with regards to the graph structure. In this paper, we first prove that the set of conditions provided by Das. et al are also necessary for the feasibility of PBNA with respect to any precoding matrix. Then, using two graph-related properties and a degree-counting technique, we reduce the set to just four conditions. This reduction enables an efficient algorithm for checking the feasibility of PBNA on a given graph.
1202.3451
The Future of Search and Discovery in Big Data Analytics: Ultrametric Information Spaces
cs.IR stat.ML
Consider observation data, comprised of n observation vectors with values on a set of attributes. This gives us n points in attribute space. Having data structured as a tree, implied by having our observations embedded in an ultrametric topology, offers great advantage for proximity searching. If we have preprocessed data through such an embedding, then an observation's nearest neighbor is found in constant computational time, i.e. O(1) time. A further powerful approach is discussed in this work: the inducing of a hierarchy, and hence a tree, in linear computational time, i.e. O(n) time for n observations. It is with such a basis for proximity search and best match that we can address the burgeoning problems of processing very large, and possibly also very high dimensional, data sets.
1202.3461
Adaptively Sharing Time-Series with Differential Privacy
cs.DB
Sharing real-time aggregate statistics of private data is of great value to the public to perform data mining for understanding important phenomena, such as Influenza outbreaks and traffic congestion. However, releasing time-series data with standard differential privacy mechanism has limited utility due to high correlation between data values. We propose FAST, a novel framework to release real-time aggregate statistics under differential privacy based on filtering and adaptive sampling. To minimize the overall privacy cost, FAST adaptively samples long time-series according to the detected data dynamics. To improve the accuracy of data release per time stamp, FAST predicts data values at non-sampling points and corrects noisy observations at sampling points. Our experiments with real-world as well as synthetic data sets confirm that FAST improves the accuracy of released aggregates even under small privacy cost and can be used to enable a wide range of monitoring applications.
1202.3467
Joint source-channel coding for a quantum multiple access channel
quant-ph cs.IT math.IT
Suppose that two senders each obtain one share of the output of a classical, bivariate, correlated information source. They would like to transmit the correlated source to a receiver using a quantum multiple access channel. In prior work, Cover, El Gamal, and Salehi provided a combined source-channel coding strategy for a classical multiple access channel which outperforms the simpler "separation" strategy where separate codebooks are used for the source coding and the channel coding tasks. In the present paper, we prove that a coding strategy similar to the Cover-El Gamal-Salehi strategy and a corresponding quantum simultaneous decoder allow for the reliable transmission of a source over a quantum multiple access channel, as long as a set of information inequalities involving the Holevo quantity hold.
1202.3468
Partially-blind Estimation of Reciprocal Channels for AF Two-Way Relay Networks Employing M-PSK Modulation
cs.IT math.IT stat.OT
We consider the problem of channel estimation for amplify-and-forward two-way relays assuming channel reciprocity and M-PSK modulation. In an earlier work, a partially-blind maximum-likelihood estimator was derived by treating the data as deterministic unknowns. We prove that this estimator approaches the true channel with high probability at high signal-to-noise ratio (SNR) but is not consistent. We then propose an alternative estimator which is consistent and has similarly favorable high SNR performance. We also derive the Cramer-Rao bound on the variance of unbiased estimators.
1202.3471
Quantum Navigation and Ranking in Complex Networks
quant-ph cond-mat.stat-mech cs.SI physics.soc-ph
Complex networks are formal frameworks capturing the interdependencies between the elements of large systems and databases. This formalism allows to use network navigation methods to rank the importance that each constituent has on the global organization of the system. A key example is Pagerank navigation which is at the core of the most used search engine of the World Wide Web. Inspired in this classical algorithm, we define a quantum navigation method providing a unique ranking of the elements of a network. We analyze the convergence of quantum navigation to the stationary rank of networks and show that quantumness decreases the number of navigation steps before convergence. In addition, we show that quantum navigation allows to solve degeneracies found in classical ranks. By implementing the quantum algorithm in real networks, we confirm these improvements and show that quantum coherence unveils new hierarchical features about the global organization of complex systems.
1202.3473
Are we there yet? When to stop a Markov chain while generating random graphs
cs.SI physics.data-an physics.soc-ph
Markov chains are a convenient means of generating realizations of networks, since they require little more than a procedure for rewiring edges. If a rewiring procedure exists for generating new graphs with specified statistical properties, then a Markov chain sampler can generate an ensemble of graphs with prescribed characteristics. However, successive graphs in a Markov chain cannot be used when one desires independent draws from the distribution of graphs; the realizations are correlated. Consequently, one runs a Markov chain for N iterations before accepting the realization as an independent sample. In this work, we devise two methods for calculating N. They are both based on the binary "time-series" denoting the occurrence/non-occurrence of edge (u, v) between vertices u and v in the Markov chain of graphs generated by the sampler. They differ in their underlying assumptions. We test them on the generation of graphs with a prescribed joint degree distribution. We find the N proportional |E|, where |E| is the number of edges in the graph. The two methods are compared by sampling on real, sparse graphs with 10^3 - 10^4 vertices.
1202.3492
Why does attention to web articles fall with time?
cs.IR physics.soc-ph
We analyze access statistics of a hundred and fifty blog entries and news articles, for periods of up to three years. Access rate falls as an inverse power of time passed since publication. The power law holds for periods of up to thousand days. The exponents are different for different blogs and are distributed between 0.6 and 3.2. We argue that the decay of attention to a web article is caused by the link to it first dropping down the list of links on the website's front page, and then disappearing from the front page and its subsequent movement further into background. The other proposed explanations that use a decaying with time novelty factor, or some intricate theory of human dynamics cannot explain all of the experimental observations.
1202.3504
They Know Where You Live!
cs.SI
In this paper, we demonstrate the possibility of predicting people's hometowns by using their geotagged photos posted on Flickr website. We employ Kruskal's algorithm to cluster photos taken by a user and predict the user's hometown. Our results prove that using social profiles of photographers allows researchers to predict the locations of their taken photos with higher accuracies. This in return can improve the previous methods which were purely based on visual features of photos \cite{Hays:im2gps}.
1202.3505
Near-optimal Coresets For Least-Squares Regression
cs.DS cs.LG
We study (constrained) least-squares regression as well as multiple response least-squares regression and ask the question of whether a subset of the data, a coreset, suffices to compute a good approximate solution to the regression. We give deterministic, low order polynomial-time algorithms to construct such coresets with approximation guarantees, together with lower bounds indicating that there is not much room for improvement upon our results.
1202.3510
Energy Efficiency Optimization for MIMO Broadcast Channels
cs.IT math.IT
Characterizing the fundamental energy efficiency (EE) limits of MIMO broadcast channels (BC) is significant for the development of green wireless communications. We address the EE optimization problem for MIMO-BC in this paper and consider a practical power model, i.e., taking into account a transmit independent power which is related to the number of active transmit antennas. Under this setup, we propose a new optimization approach, in which the transmit covariance is optimized under fixed active transmit antenna sets, and then active transmit antenna selection (ATAS) is utilized. During the transmit covariance optimization, we propose a globally optimal energy efficient iterative water-filling scheme through solving a series of concave fractional programs based on the block-coordinate ascent algorithm. After that, ATAS is employed to determine the active transmit antenna set. Since activating more transmit antennas can achieve higher sum-rate but at the cost of larger transmit independent power consumption, there exists a tradeoff between the sum-rate gain and the power consumption. Here ATAS can exploit the best tradeoff and thus further improve the EE. Optimal exhaustive search and low-complexity norm based ATAS schemes are developed. Through simulations, we discuss the effect of different parameters on the EE of the MIMO-BC.
1202.3514
A Note on Weight Distributions of Irreducible Cyclic Codes
cs.IT math.IT
Usually, it is difficult to determine the weight distribution of an irreducible cyclic code. In this paper, we discuss the case when an irreducible cyclic code has the maximal number of distinct nonzero weights and give a necessary and sufficient condition. In this case, we also obtain a divisible property for the weight of a codeword. Further, we present a necessary and sufficient condition for an irreducible cyclic code with only one nonzero weight. Finally, we determine the weight distribution of an irreducible cyclic code for some cases.
1202.3531
Recovering Jointly Sparse Signals via Joint Basis Pursuit
cs.IT math.IT math.OC
This work considers recovery of signals that are sparse over two bases. For instance, a signal might be sparse in both time and frequency, or a matrix can be low rank and sparse simultaneously. To facilitate recovery, we consider minimizing the sum of the $\ell_1$-norms that correspond to each basis, which is a tractable convex approach. We find novel optimality conditions which indicates a gain over traditional approaches where $\ell_1$ minimization is done over only one basis. Next, we analyze these optimality conditions for the particular case of time-frequency bases. Denoting sparsity in the first and second bases by $k_1,k_2$ respectively, we show that, for a general class of signals, using this approach, one requires as small as $O(\max\{k_1,k_2\}\log\log n)$ measurements for successful recovery hence overcoming the classical requirement of $\Theta(\min\{k_1,k_2\}\log(\frac{n}{\min\{k_1,k_2\}}))$ for $\ell_1$ minimization when $k_1\approx k_2$. Extensive simulations show that, our analysis is approximately tight.
1202.3538
Refinement Modal Logic
cs.LO cs.AI
In this paper we present {\em refinement modal logic}. A refinement is like a bisimulation, except that from the three relational requirements only `atoms' and `back' need to be satisfied. Our logic contains a new operator 'all' in addition to the standard modalities 'box' for each agent. The operator 'all' acts as a quantifier over the set of all refinements of a given model. As a variation on a bisimulation quantifier, this refinement operator or refinement quantifier 'all' can be seen as quantifying over a variable not occurring in the formula bound by it. The logic combines the simplicity of multi-agent modal logic with some powers of monadic second-order quantification. We present a sound and complete axiomatization of multi-agent refinement modal logic. We also present an extension of the logic to the modal mu-calculus, and an axiomatization for the single-agent version of this logic. Examples and applications are also discussed: to software verification and design (the set of agents can also be seen as a set of actions), and to dynamic epistemic logic. We further give detailed results on the complexity of satisfiability, and on succinctness.
1202.3572
Calculation of statistical entropic measures in a model of solids
nlin.AO cond-mat.other cs.IT math.IT
In this work, a one-dimensional model of crystalline solids based on the Dirac comb limit of the Kronig-Penney model is considered. From the wave functions of the valence electrons, we calculate a statistical measure of complexity and the Fisher-Shannon information for the lower energy electronic bands appearing in the system. All these magnitudes present an extremal value for the case of solids having half-filled bands, a configuration where in general a high conductivity is attained in real solids, such as it happens with the monovalent metals.
1202.3602
Towards quantitative measures in applied ontology
cs.AI q-bio.QM
Applied ontology is a relatively new field which aims to apply theories and methods from diverse disciplines such as philosophy, cognitive science, linguistics and formal logics to perform or improve domain-specific tasks. To support the development of effective research methodologies for applied ontology, we critically discuss the question how its research results should be evaluated. We propose that results in applied ontology must be evaluated within their domain of application, based on some ontology-based task within the domain, and discuss quantitative measures which would facilitate the objective evaluation and comparison of research results in applied ontology.
1202.3625
From Linear Codes to Hyperplane Arrangements via Thomas Decomposition
cs.IT math.IT
We establish a connection between linear codes and hyperplane arrangements using the Thomas decomposition of polynomial systems and the resulting counting polynomial. This yields both a generalization and a refinement of the weight enumerator of a linear code. In particular, one can deal with infinitely many finite fields simultaneously by defining a weight enumerator for codes over infinite fields.
1202.3639
Finding a most biased coin with fewest flips
cs.DS cs.LG
We study the problem of learning a most biased coin among a set of coins by tossing the coins adaptively. The goal is to minimize the number of tosses until we identify a coin i* whose posterior probability of being most biased is at least 1-delta for a given delta. Under a particular probabilistic model, we give an optimal algorithm, i.e., an algorithm that minimizes the expected number of future tosses. The problem is closely related to finding the best arm in the multi-armed bandit problem using adaptive strategies. Our algorithm employs an optimal adaptive strategy -- a strategy that performs the best possible action at each step after observing the outcomes of all previous coin tosses. Consequently, our algorithm is also optimal for any starting history of outcomes. To our knowledge, this is the first algorithm that employs an optimal adaptive strategy under a Bayesian setting for this problem. Our proof of optimality employs tools from the field of Markov games.
1202.3641
Control of Towing Kites for Seagoing Vessels
cs.SY
In this paper we present the basic features of the flight control of the SkySails towing kite system. After introduction of coordinate definitions and basic system dynamics we introduce a novel model used for controller design and justify its main dynamics with results from system identification based on numerous sea trials. We then present the controller design which we successfully use for operational flights for several years. Finally we explain the generation of dynamical flight patterns.
1202.3643
Dynamics of conflicts in Wikipedia
physics.soc-ph cs.SI physics.data-an
In this work we study the dynamical features of editorial wars in Wikipedia (WP). Based on our previously established algorithm, we build up samples of controversial and peaceful articles and analyze the temporal characteristics of the activity in these samples. On short time scales, we show that there is a clear correspondence between conflict and burstiness of activity patterns, and that memory effects play an important role in controversies. On long time scales, we identify three distinct developmental patterns for the overall behavior of the articles. We are able to distinguish cases eventually leading to consensus from those cases where a compromise is far from achievable. Finally, we analyze discussion networks and conclude that edit wars are mainly fought by few editors only.
1202.3653
Information Transmission using the Nonlinear Fourier Transform, Part I: Mathematical Tools
cs.IT math.IT
The nonlinear Fourier transform (NFT), a powerful tool in soliton theory and exactly solvable models, is a method for solving integrable partial differential equations governing wave propagation in certain nonlinear media. The NFT decorrelates signal degrees-of-freedom in such models, in much the same way that the Fourier transform does for linear systems. In this three-part series of papers, this observation is exploited for data transmission over integrable channels such as optical fibers, where pulse propagation is governed by the nonlinear Schr\"odinger equation. In this transmission scheme, which can be viewed as a nonlinear analogue of orthogonal frequency-division multiplexing commonly used in linear channels, information is encoded in the nonlinear frequencies and their spectral amplitudes. Unlike most other fiber-optic transmission schemes, this technique deals with both dispersion and nonlinearity directly and unconditionally without the need for dispersion or nonlinearity compensation methods. This first paper explains the mathematical tools that underlie the method.
1202.3663
Guaranteed clustering and biclustering via semidefinite programming
math.OC cs.LG
Identifying clusters of similar objects in data plays a significant role in a wide range of applications. As a model problem for clustering, we consider the densest k-disjoint-clique problem, whose goal is to identify the collection of k disjoint cliques of a given weighted complete graph maximizing the sum of the densities of the complete subgraphs induced by these cliques. In this paper, we establish conditions ensuring exact recovery of the densest k cliques of a given graph from the optimal solution of a particular semidefinite program. In particular, the semidefinite relaxation is exact for input graphs corresponding to data consisting of k large, distinct clusters and a smaller number of outliers. This approach also yields a semidefinite relaxation for the biclustering problem with similar recovery guarantees. Given a set of objects and a set of features exhibited by these objects, biclustering seeks to simultaneously group the objects and features according to their expression levels. This problem may be posed as partitioning the nodes of a weighted bipartite complete graph such that the sum of the densities of the resulting bipartite complete subgraphs is maximized. As in our analysis of the densest k-disjoint-clique problem, we show that the correct partition of the objects and features can be recovered from the optimal solution of a semidefinite program in the case that the given data consists of several disjoint sets of objects exhibiting similar features. Empirical evidence from numerical experiments supporting these theoretical guarantees is also provided.
1202.3667
On Directly Mapping Relational Databases to RDF and OWL (Extended Version)
cs.DB
Mapping relational databases to RDF is a fundamental problem for the development of the Semantic Web. We present a solution, inspired by draft methods defined by the W3C where relational databases are directly mapped to RDF and OWL. Given a relational database schema and its integrity constraints, this direct mapping produces an OWL ontology, which, provides the basis for generating RDF instances. The semantics of this mapping is defined using Datalog. Two fundamental properties are information preservation and query preservation. We prove that our mapping satisfies both conditions, even for relational databases that contain null values. We also consider two desirable properties: monotonicity and semantics preservation. We prove that our mapping is monotone and also prove that no monotone mapping, including ours, is semantic preserving. We realize that monotonicity is an obstacle for semantic preservation and thus present a non-monotone direct mapping that is semantics preserving.
1202.3684
Generalized Boundaries from Multiple Image Interpretations
cs.CV
Boundary detection is essential for a variety of computer vision tasks such as segmentation and recognition. In this paper we propose a unified formulation and a novel algorithm that are applicable to the detection of different types of boundaries, such as intensity edges, occlusion boundaries or object category specific boundaries. Our formulation leads to a simple method with state-of-the-art performance and significantly lower computational cost than existing methods. We evaluate our algorithm on different types of boundaries, from low-level boundaries extracted in natural images, to occlusion boundaries obtained using motion cues and RGB-D cameras, to boundaries from soft-segmentation. We also propose a novel method for figure/ground soft-segmentation that can be used in conjunction with our boundary detection method and improve its accuracy at almost no extra computational cost.
1202.3686
Inferential or Differential: Privacy Laws Dictate
cs.DB
So far, privacy models follow two paradigms. The first paradigm, termed inferential privacy in this paper, focuses on the risk due to statistical inference of sensitive information about a target record from other records in the database. The second paradigm, known as differential privacy, focuses on the risk to an individual when included in, versus when not included in, the database. The contribution of this paper consists of two parts. The first part presents a critical analysis on differential privacy with two results: (i) the differential privacy mechanism does not provide inferential privacy, (ii) the impossibility result about achieving Dalenius's privacy goal [5] is based on an adversary simulated by a Turing machine, but a human adversary may behave differently; consequently, the practical implication of the impossibility result remains unclear. The second part of this work is devoted to a solution addressing three major drawbacks in previous approaches to inferential privacy: lack of flexibility for handling variable sensitivity, poor utility, and vulnerability to auxiliary information.
1202.3698
Extended Lifted Inference with Joint Formulas
cs.AI
The First-Order Variable Elimination (FOVE) algorithm allows exact inference to be applied directly to probabilistic relational models, and has proven to be vastly superior to the application of standard inference methods on a grounded propositional model. Still, FOVE operators can be applied under restricted conditions, often forcing one to resort to propositional inference. This paper aims to extend the applicability of FOVE by providing two new model conversion operators: the first and the primary is joint formula conversion and the second is just-different counting conversion. These new operations allow efficient inference methods to be applied directly on relational models, where no existing efficient method could be applied hitherto. In addition, aided by these capabilities, we show how to adapt FOVE to provide exact solutions to Maximum Expected Utility (MEU) queries over relational models for decision under uncertainty. Experimental evaluations show our algorithms to provide significant speedup over the alternatives.
1202.3699
Learning is planning: near Bayes-optimal reinforcement learning via Monte-Carlo tree search
cs.AI
Bayes-optimal behavior, while well-defined, is often difficult to achieve. Recent advances in the use of Monte-Carlo tree search (MCTS) have shown that it is possible to act near-optimally in Markov Decision Processes (MDPs) with very large or infinite state spaces. Bayes-optimal behavior in an unknown MDP is equivalent to optimal behavior in the known belief-space MDP, although the size of this belief-space MDP grows exponentially with the amount of history retained, and is potentially infinite. We show how an agent can use one particular MCTS algorithm, Forward Search Sparse Sampling (FSSS), in an efficient way to act nearly Bayes-optimally for all but a polynomial number of steps, assuming that FSSS can be used to act efficiently in any possible underlying MDP.
1202.3700
Solving Cooperative Reliability Games
cs.GT cs.AI
Cooperative games model the allocation of profit from joint actions, following considerations such as stability and fairness. We propose the reliability extension of such games, where agents may fail to participate in the game. In the reliability extension, each agent only "survives" with a certain probability, and a coalition's value is the probability that its surviving members would be a winning coalition in the base game. We study prominent solution concepts in such games, showing how to approximate the Shapley value and how to compute the core in games with few agent types. We also show that applying the reliability extension may stabilize the game, making the core non-empty even when the base game has an empty core.
1202.3701
Active Diagnosis via AUC Maximization: An Efficient Approach for Multiple Fault Identification in Large Scale, Noisy Networks
cs.LG cs.AI stat.ML
The problem of active diagnosis arises in several applications such as disease diagnosis, and fault diagnosis in computer networks, where the goal is to rapidly identify the binary states of a set of objects (e.g., faulty or working) by sequentially selecting, and observing, (noisy) responses to binary valued queries. Current algorithms in this area rely on loopy belief propagation for active query selection. These algorithms have an exponential time complexity, making them slow and even intractable in large networks. We propose a rank-based greedy algorithm that sequentially chooses queries such that the area under the ROC curve of the rank-based output is maximized. The AUC criterion allows us to make a simplifying assumption that significantly reduces the complexity of active query selection (from exponential to near quadratic), with little or no compromise on the performance quality.
1202.3702
Semi-supervised Learning with Density Based Distances
cs.LG stat.ML
We present a simple, yet effective, approach to Semi-Supervised Learning. Our approach is based on estimating density-based distances (DBD) using a shortest path calculation on a graph. These Graph-DBD estimates can then be used in any distance-based supervised learning method, such as Nearest Neighbor methods and SVMs with RBF kernels. In order to apply the method to very large data sets, we also present a novel algorithm which integrates nearest neighbor computations into the shortest path search and can find exact shortest paths even in extremely large dense graphs. Significant runtime improvement over the commonly used Laplacian regularization method is then shown on a large scale dataset.
1202.3703
Factored Filtering of Continuous-Time Systems
cs.SY cs.AI
We consider filtering for a continuous-time, or asynchronous, stochastic system where the full distribution over states is too large to be stored or calculated. We assume that the rate matrix of the system can be compactly represented and that the belief distribution is to be approximated as a product of marginals. The essential computation is the matrix exponential. We look at two different methods for its computation: ODE integration and uniformization of the Taylor expansion. For both we consider approximations in which only a factored belief state is maintained. For factored uniformization we demonstrate that the KL-divergence of the filtering is bounded. Our experimental results confirm our factored uniformization performs better than previously suggested uniformization methods and the mean field algorithm.
1202.3704
Near-Optimal Target Learning With Stochastic Binary Signals
cs.LG stat.ML
We study learning in a noisy bisection model: specifically, Bayesian algorithms to learn a target value V given access only to noisy realizations of whether V is less than or greater than a threshold theta. At step t = 0, 1, 2, ..., the learner sets threshold theta t and observes a noisy realization of sign(V - theta t). After T steps, the goal is to output an estimate V^ which is within an eta-tolerance of V . This problem has been studied, predominantly in environments with a fixed error probability q < 1/2 for the noisy realization of sign(V - theta t). In practice, it is often the case that q can approach 1/2, especially as theta -> V, and there is little known when this happens. We give a pseudo-Bayesian algorithm which provably converges to V. When the true prior matches our algorithm's Gaussian prior, we show near-optimal expected performance. Our methods extend to the general multiple-threshold setting where the observation noisily indicates which of k >= 2 regions V belongs to.
1202.3705
Filtered Fictitious Play for Perturbed Observation Potential Games and Decentralised POMDPs
cs.GT cs.AI
Potential games and decentralised partially observable MDPs (Dec-POMDPs) are two commonly used models of multi-agent interaction, for static optimisation and sequential decisionmaking settings, respectively. In this paper we introduce filtered fictitious play for solving repeated potential games in which each player's observations of others' actions are perturbed by random noise, and use this algorithm to construct an online learning method for solving Dec-POMDPs. Specifically, we prove that noise in observations prevents standard fictitious play from converging to Nash equilibrium in potential games, which also makes fictitious play impractical for solving Dec-POMDPs. To combat this, we derive filtered fictitious play, and provide conditions under which it converges to a Nash equilibrium in potential games with noisy observations. We then use filtered fictitious play to construct a solver for Dec-POMDPs, and demonstrate our new algorithm's performance in a box pushing problem. Our results show that we consistently outperform the state-of-the-art Dec-POMDP solver by an average of 100% across the range of noise in the observation function.
1202.3706
A Framework for Optimizing Paper Matching
cs.IR cs.AI
At the heart of many scientific conferences is the problem of matching submitted papers to suitable reviewers. Arriving at a good assignment is a major and important challenge for any conference organizer. In this paper we propose a framework to optimize paper-to-reviewer assignments. Our framework uses suitability scores to measure pairwise affinity between papers and reviewers. We show how learning can be used to infer suitability scores from a small set of provided scores, thereby reducing the burden on reviewers and organizers. We frame the assignment problem as an integer program and propose several variations for the paper-to-reviewer matching domain. We also explore how learning and matching interact. Experiments on two conference data sets examine the performance of several learning methods as well as the effectiveness of the matching formulations.
1202.3707
A temporally abstracted Viterbi algorithm
cs.AI
Hierarchical problem abstraction, when applicable, may offer exponential reductions in computational complexity. Previous work on coarse-to-fine dynamic programming (CFDP) has demonstrated this possibility using state abstraction to speed up the Viterbi algorithm. In this paper, we show how to apply temporal abstraction to the Viterbi problem. Our algorithm uses bounds derived from analysis of coarse timescales to prune large parts of the state trellis at finer timescales. We demonstrate improvements of several orders of magnitude over the standard Viterbi algorithm, as well as significant speedups over CFDP, for problems whose state variables evolve at widely differing rates.
1202.3708
Smoothing Proximal Gradient Method for General Structured Sparse Learning
cs.LG stat.ML
We study the problem of learning high dimensional regression models regularized by a structured-sparsity-inducing penalty that encodes prior structural information on either input or output sides. We consider two widely adopted types of such penalties as our motivating examples: 1) overlapping group lasso penalty, based on the l1/l2 mixed-norm penalty, and 2) graph-guided fusion penalty. For both types of penalties, due to their non-separability, developing an efficient optimization method has remained a challenging problem. In this paper, we propose a general optimization approach, called smoothing proximal gradient method, which can solve the structured sparse regression problems with a smooth convex loss and a wide spectrum of structured-sparsity-inducing penalties. Our approach is based on a general smoothing technique of Nesterov. It achieves a convergence rate faster than the standard first-order method, subgradient method, and is much more scalable than the most widely used interior-point method. Numerical results are reported to demonstrate the efficiency and scalability of the proposed method.
1202.3709
EDML: A Method for Learning Parameters in Bayesian Networks
cs.AI
We propose a method called EDML for learning MAP parameters in binary Bayesian networks under incomplete data. The method assumes Beta priors and can be used to learn maximum likelihood parameters when the priors are uninformative. EDML exhibits interesting behaviors, especially when compared to EM. We introduce EDML, explain its origin, and study some of its properties both analytically and empirically.
1202.3710
Strictly Proper Mechanisms with Cooperating Players
cs.GT cs.AI
Prediction markets provide an efficient means to assess uncertain quantities from forecasters. Traditional and competitive strictly proper scoring rules have been shown to incentivize players to provide truthful probabilistic forecasts. However, we show that when those players can cooperate, these mechanisms can instead discourage them from reporting what they really believe. When players with different beliefs are able to cooperate and form a coalition, these mechanisms admit arbitrage and there is a report that will always pay coalition members more than their truthful forecasts. If the coalition were created by an intermediary, such as a web portal, the intermediary would be guaranteed a profit.
1202.3711
A Logical Characterization of Constraint-Based Causal Discovery
cs.AI
We present a novel approach to constraint-based causal discovery, that takes the form of straightforward logical inference, applied to a list of simple, logical statements about causal relations that are derived directly from observed (in)dependencies. It is both sound and complete, in the sense that all invariant features of the corresponding partial ancestral graph (PAG) are identified, even in the presence of latent variables and selection bias. The approach shows that every identifiable causal relation corresponds to one of just two fundamental forms. More importantly, as the basic building blocks of the method do not rely on the detailed (graphical) structure of the corresponding PAG, it opens up a range of new opportunities, including more robust inference, detailed accountability, and application to large models.
1202.3712
Ensembles of Kernel Predictors
cs.LG stat.ML
This paper examines the problem of learning with a finite and possibly large set of p base kernels. It presents a theoretical and empirical analysis of an approach addressing this problem based on ensembles of kernel predictors. This includes novel theoretical guarantees based on the Rademacher complexity of the corresponding hypothesis sets, the introduction and analysis of a learning algorithm based on these hypothesis sets, and a series of experiments using ensembles of kernel predictors with several data sets. Both convex combinations of kernel-based hypotheses and more general Lq-regularized nonnegative combinations are analyzed. These theoretical, algorithmic, and empirical results are compared with those achieved by using learning kernel techniques, which can be viewed as another approach for solving the same problem.
1202.3713
Bayesian network learning with cutting planes
cs.AI
The problem of learning the structure of Bayesian networks from complete discrete data with a limit on parent set size is considered. Learning is cast explicitly as an optimisation problem where the goal is to find a BN structure which maximises log marginal likelihood (BDe score). Integer programming, specifically the SCIP framework, is used to solve this optimisation problem. Acyclicity constraints are added to the integer program (IP) during solving in the form of cutting planes. Finding good cutting planes is the key to the success of the approach -the search for such cutting planes is effected using a sub-IP. Results show that this is a particularly fast method for exact BN learning.
1202.3714
Active Learning for Developing Personalized Treatment
cs.LG stat.ML
The personalization of treatment via bio-markers and other risk categories has drawn increasing interest among clinical scientists. Personalized treatment strategies can be learned using data from clinical trials, but such trials are very costly to run. This paper explores the use of active learning techniques to design more efficient trials, addressing issues such as whom to recruit, at what point in the trial, and which treatment to assign, throughout the duration of the trial. We propose a minimax bandit model with two different optimization criteria, and discuss the computational challenges and issues pertaining to this approach. We evaluate our active learning policies using both simulated data, and data modeled after a clinical trial for treating depressed individuals, and contrast our methods with other plausible active learning policies.
1202.3715
A Unifying Framework for Linearly Solvable Control
cs.SY math.OC
Recent work has led to the development of an elegant theory of Linearly Solvable Markov Decision Processes (LMDPs) and related Path-Integral Control Problems. Traditionally, MDPs have been formulated using stochastic policies and a control cost based on the KL divergence. In this paper, we extend this framework to a more general class of divergences: the Renyi divergences. These are a more general class of divergences parameterized by a continuous parameter that include the KL divergence as a special case. The resulting control problems can be interpreted as solving a risk-sensitive version of the LMDP problem. For a > 0, we get risk-averse behavior (the degree of risk-aversion increases with a) and for a < 0, we get risk-seeking behavior. We recover LMDPs in the limit as a -> 0. This work generalizes the recently developed risk-sensitive path-integral control formalism which can be seen as the continuous-time limit of results obtained in this paper. To the best of our knowledge, this is a general theory of linearly solvable control and includes all previous work as a special case. We also present an alternative interpretation of these results as solving a 2-player (cooperative or competitive) Markov Game. From the linearity follow a number of nice properties including compositionality of control laws and a path-integral representation of the value function. We demonstrate the usefulness of the framework on control problems with noise where different values of lead to qualitatively different control behaviors.
1202.3716
Boosting as a Product of Experts
cs.LG stat.ML
In this paper, we derive a novel probabilistic model of boosting as a Product of Experts. We re-derive the boosting algorithm as a greedy incremental model selection procedure which ensures that addition of new experts to the ensemble does not decrease the likelihood of the data. These learning rules lead to a generic boosting algorithm - POE- Boost which turns out to be similar to the AdaBoost algorithm under certain assumptions on the expert probabilities. The paper then extends the POEBoost algorithm to POEBoost.CS which handles hypothesis that produce probabilistic predictions. This new algorithm is shown to have better generalization performance compared to other state of the art algorithms.
1202.3717
PAC-Bayesian Policy Evaluation for Reinforcement Learning
cs.LG stat.ML
Bayesian priors offer a compact yet general means of incorporating domain knowledge into many learning tasks. The correctness of the Bayesian analysis and inference, however, largely depends on accuracy and correctness of these priors. PAC-Bayesian methods overcome this problem by providing bounds that hold regardless of the correctness of the prior distribution. This paper introduces the first PAC-Bayesian bound for the batch reinforcement learning problem with function approximation. We show how this bound can be used to perform model-selection in a transfer learning scenario. Our empirical results confirm that PAC-Bayesian policy evaluation is able to leverage prior distributions when they are informative and, unlike standard Bayesian RL approaches, ignore them when they are misleading.
1202.3718
On the Complexity of Decision Making in Possibilistic Decision Trees
cs.AI
When the information about uncertainty cannot be quantified in a simple, probabilistic way, the topic of possibilistic decision theory is often a natural one to consider. The development of possibilistic decision theory has lead to a series of possibilistic criteria, e.g pessimistic possibilistic qualitative utility, possibilistic likely dominance, binary possibilistic utility and possibilistic Choquet integrals. This paper focuses on sequential decision making in possibilistic decision trees. It proposes a complexity study of the problem of finding an optimal strategy depending on the monotonicity property of the optimization criteria which allows the application of dynamic programming that offers a polytime reduction of the decision problem. It also shows that possibilistic Choquet integrals do not satisfy this property, and that in this case the optimization problem is NP - hard.
1202.3719
Inference in Probabilistic Logic Programs using Weighted CNF's
cs.AI
Probabilistic logic programs are logic programs in which some of the facts are annotated with probabilities. Several classical probabilistic inference tasks (such as MAP and computing marginals) have not yet received a lot of attention for this formalism. The contribution of this paper is that we develop efficient inference algorithms for these tasks. This is based on a conversion of the probabilistic logic program and the query and evidence to a weighted CNF formula. This allows us to reduce the inference tasks to well-studied tasks such as weighted model counting. To solve such tasks, we employ state-of-the-art methods. We consider multiple methods for the conversion of the programs as well as for inference on the weighted CNF. The resulting approach is evaluated experimentally and shown to improve upon the state-of-the-art in probabilistic logic programming.
1202.3720
Efficient Inference in Markov Control Problems
cs.SY cs.AI
Markov control algorithms that perform smooth, non-greedy updates of the policy have been shown to be very general and versatile, with policy gradient and Expectation Maximisation algorithms being particularly popular. For these algorithms, marginal inference of the reward weighted trajectory distribution is required to perform policy updates. We discuss a new exact inference algorithm for these marginals in the finite horizon case that is more efficient than the standard approach based on classical forward-backward recursions. We also provide a principled extension to infinite horizon Markov Decision Problems that explicitly accounts for an infinite horizon. This extension provides a novel algorithm for both policy gradients and Expectation Maximisation in infinite horizon problems.
1202.3721
Dynamic consistency and decision making under vacuous belief
cs.AI
The ideas about decision making under ignorance in economics are combined with the ideas about uncertainty representation in computer science. The combination sheds new light on the question of how artificial agents can act in a dynamically consistent manner. The notion of sequential consistency is formalized by adapting the law of iterated expectation for plausibility measures. The necessary and sufficient condition for a certainty equivalence operator for Nehring-Puppe's preference to be sequentially consistent is given. This result sheds light on the models of decision making under uncertainty.
1202.3722
Hierarchical Affinity Propagation
cs.LG cs.AI stat.ML
Affinity propagation is an exemplar-based clustering algorithm that finds a set of data-points that best exemplify the data, and associates each datapoint with one exemplar. We extend affinity propagation in a principled way to solve the hierarchical clustering problem, which arises in a variety of domains including biology, sensor networks and decision making in operational research. We derive an inference algorithm that operates by propagating information up and down the hierarchy, and is efficient despite the high-order potentials required for the graphical model formulation. We demonstrate that our method outperforms greedy techniques that cluster one layer at a time. We show that on an artificial dataset designed to mimic the HIV-strain mutation dynamics, our method outperforms related methods. For real HIV sequences, where the ground truth is not available, we show our method achieves better results, in terms of the underlying objective function, and show the results correspond meaningfully to geographical location and strain subtypes. Finally we report results on using the method for the analysis of mass spectra, showing it performs favorably compared to state-of-the-art methods.
1202.3723
Approximation by Quantization
cs.AI
Inference in graphical models consists of repeatedly multiplying and summing out potentials. It is generally intractable because the derived potentials obtained in this way can be exponentially large. Approximate inference techniques such as belief propagation and variational methods combat this by simplifying the derived potentials, typically by dropping variables from them. We propose an alternate method for simplifying potentials: quantizing their values. Quantization causes different states of a potential to have the same value, and therefore introduces context-specific independencies that can be exploited to represent the potential more compactly. We use algebraic decision diagrams (ADDs) to do this efficiently. We apply quantization and ADD reduction to variable elimination and junction tree propagation, yielding a family of bounded approximate inference schemes. Our experimental tests show that our new schemes significantly outperform state-of-the-art approaches on many benchmark instances.
1202.3724
Probabilistic Theorem Proving
cs.AI
Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable elimination and belief propagation, neither of which take logical structure into account. We propose the first method that has the full power of both graphical model inference and first-order theorem proving (in finite domains with Herbrand interpretations). We first define probabilistic theorem proving, their generalization, as the problem of computing the probability of a logical formula given the probabilities or weights of a set of formulas. We then show how this can be reduced to the problem of lifted weighted model counting, and develop an efficient algorithm for the latter. We prove the correctness of this algorithm, investigate its properties, and show how it generalizes previous approaches. Experiments show that it greatly outperforms lifted variable elimination when logical structure is present. Finally, we propose an algorithm for approximate probabilistic theorem proving, and show that it can greatly outperform lifted belief propagation.
1202.3725
Generalized Fisher Score for Feature Selection
cs.LG stat.ML
Fisher score is one of the most widely used supervised feature selection methods. However, it selects each feature independently according to their scores under the Fisher criterion, which leads to a suboptimal subset of features. In this paper, we present a generalized Fisher score to jointly select features. It aims at finding an subset of features, which maximize the lower bound of traditional Fisher score. The resulting feature selection problem is a mixed integer programming, which can be reformulated as a quadratically constrained linear programming (QCLP). It is solved by cutting plane algorithm, in each iteration of which a multiple kernel learning problem is solved alternatively by multivariate ridge regression and projected gradient descent. Experiments on benchmark data sets indicate that the proposed method outperforms Fisher score as well as many other state-of-the-art feature selection methods.
1202.3726
Active Semi-Supervised Learning using Submodular Functions
cs.LG stat.ML
We consider active, semi-supervised learning in an offline transductive setting. We show that a previously proposed error bound for active learning on undirected weighted graphs can be generalized by replacing graph cut with an arbitrary symmetric submodular function. Arbitrary non-symmetric submodular functions can be used via symmetrization. Different choices of submodular functions give different versions of the error bound that are appropriate for different kinds of problems. Moreover, the bound is deterministic and holds for adversarially chosen labels. We show exactly minimizing this error bound is NP-complete. However, we also introduce for any submodular function an associated active semi-supervised learning method that approximately minimizes the corresponding error bound. We show that the error bound is tight in the sense that there is no other bound of the same form which is better. Our theoretical results are supported by experiments on real data.
1202.3727
Bregman divergence as general framework to estimate unnormalized statistical models
cs.LG stat.ML
We show that the Bregman divergence provides a rich framework to estimate unnormalized statistical models for continuous or discrete random variables, that is, models which do not integrate or sum to one, respectively. We prove that recent estimation methods such as noise-contrastive estimation, ratio matching, and score matching belong to the proposed framework, and explain their interconnection based on supervised learning. Further, we discuss the role of boosting in unsupervised learning.