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1212.1824
Stochastic Gradient Descent for Non-smooth Optimization: Convergence Results and Optimal Averaging Schemes
cs.LG math.OC stat.ML
Stochastic Gradient Descent (SGD) is one of the simplest and most popular stochastic optimization methods. While it has already been theoretically studied for decades, the classical analysis usually required non-trivial smoothness assumptions, which do not apply to many modern applications of SGD with non-smooth objective functions such as support vector machines. In this paper, we investigate the performance of SGD without such smoothness assumptions, as well as a running average scheme to convert the SGD iterates to a solution with optimal optimization accuracy. In this framework, we prove that after T rounds, the suboptimality of the last SGD iterate scales as O(log(T)/\sqrt{T}) for non-smooth convex objective functions, and O(log(T)/T) in the non-smooth strongly convex case. To the best of our knowledge, these are the first bounds of this kind, and almost match the minimax-optimal rates obtainable by appropriate averaging schemes. We also propose a new and simple averaging scheme, which not only attains optimal rates, but can also be easily computed on-the-fly (in contrast, the suffix averaging scheme proposed in Rakhlin et al. (2011) is not as simple to implement). Finally, we provide some experimental illustrations.
1212.1839
On Structured Realizability and Stabilizability of Linear Systems
cs.SY math.OC
We study the notion of structured realizability for linear systems defined over graphs. A stabilizable and detectable realization is structured if the state-space matrices inherit the sparsity pattern of the adjacency matrix of the associated graph. In this paper, we demonstrate that not every structured transfer matrix has a structured realization and we reveal the practical meaning of this fact. We also uncover a close connection between the structured realizability of a plant and whether the plant can be stabilized by a structured controller. In particular, we show that a structured stabilizing controller can only exist when the plant admits a structured realization. Finally, we give a parameterization of all structured stabilizing controllers and show that they always have structured realizations.
1212.1863
Self Authentication of image through Daubechies Transform technique (SADT)
cs.CR cs.CV
In this paper a 4 x 4 Daubechies transform based authentication technique termed as SADT has been proposed to authenticate gray scale images. The cover image is transformed into the frequency domain using 4 x 4 mask in a row major order using Daubechies transform technique, resulting four frequency subbands AF, HF, VF and DF. One byte of every band in a mask is embedding with two or four bits of secret information. Experimental results are computed and compared with the existing authentication techniques like Li s method [5], SCDFT [6], Region-Based method [7] and other similar techniques based on Mean Square Error (MSE), Peak Signal to Noise Ratio (PSNR) and Image Fidelity (IF), which shows better performance in SADT.
1212.1881
Deciding Monotone Duality and Identifying Frequent Itemsets in Quadratic Logspace
cs.DS cs.AI cs.CC cs.DB
The monotone duality problem is defined as follows: Given two monotone formulas f and g in iredundant DNF, decide whether f and g are dual. This problem is the same as duality testing for hypergraphs, that is, checking whether a hypergraph H consists of precisely all minimal transversals of a simple hypergraph G. By exploiting a recent problem-decomposition method by Boros and Makino (ICALP 2009), we show that duality testing for hypergraphs, and thus for monotone DNFs, is feasible in DSPACE[log^2 n], i.e., in quadratic logspace. As the monotone duality problem is equivalent to a number of problems in the areas of databases, data mining, and knowledge discovery, the results presented here yield new complexity results for those problems, too. For example, it follows from our results that whenever for a Boolean-valued relation (whose attributes represent items), a number of maximal frequent itemsets and a number of minimal infrequent itemsets are known, then it can be decided in quadratic logspace whether there exist additional frequent or infrequent itemsets.
1212.1901
Kolmogorov Complexity and the Garden of Eden Theorem
nlin.CG cs.IT math.IT
Suppose $\tau$ is a cellular automaton over an amenable group and a finite alphabet. Celebrated Garden of Eden theorem states, that pre-injectivity of $\tau$ is equivalent to non-existence of Garden of Eden configuration. In this paper we will prove, that imposing some mild restrictions, we could add another equivalent assertion: non-existence of Garden of Eden configuration is equivalent to preservation of asymptotic Kolmogorov complexity under the action of cellular automaton. It yields a characterisation of the cellular automata, which preserve the asymptotic Kolmogorov complexity.
1212.1913
Energy-minimizing error-correcting codes
math.CO cs.IT math.IT
We study a discrete model of repelling particles, and we show using linear programming bounds that many familiar families of error-correcting codes minimize a broad class of potential energies when compared with all other codes of the same size and block length. Examples of these universally optimal codes include Hamming, Golay, and Reed-Solomon codes, among many others, and this helps explain their robustness as the channel model varies. Universal optimality of these codes is equivalent to minimality of their binomial moments, which has been proved in many cases by Ashikhmin and Barg. We highlight connections with mathematical physics and the analogy between these results and previous work by Cohn and Kumar in the continuous setting, and we develop a framework for optimizing the linear programming bounds. Furthermore, we show that if these bounds prove a code is universally optimal, then the code remains universally optimal even if one codeword is removed.
1212.1918
Condens\'es de textes par des m\'ethodes num\'eriques
cs.IR cs.CL
Since information in electronic form is already a standard, and that the variety and the quantity of information become increasingly large, the methods of summarizing or automatic condensation of texts is a critical phase of the analysis of texts. This article describes CORTEX a system based on numerical methods, which allows obtaining a condensation of a text, which is independent of the topic and of the length of the text. The structure of the system enables it to find the abstracts in French or Spanish in very short times.
1212.1927
User Taglines: Alternative Presentations of Expertise and Interest in Social Media
cs.SI
Web applications are increasingly showing recommended users from social media along with some descriptions, an attempt to show relevancy - why they are being shown. For example, Twitter search for a topical keyword shows expert twitterers on the side for 'whom to follow'. Google+ and Facebook also recommend users to follow or add to friend circle. Popular Internet newspaper- The Huffington Post shows Twitter influencers/ experts on the side of an article for authoritative relevant tweets. The state of the art shows user profile bios as summary for Twitter experts, but it has issues with length constraint imposed by user interface (UI) design, missing bio and sometimes funny profile bio. Alternatively, applications can use human generated user summary, but it will not scale. Therefore, we study the problem of automatic generation of informative expertise summary or taglines for Twitter experts in space constraint imposed by UI design. We propose three methods for expertise summary generation- Occupation-Pattern based, Link-Triangulation based and User-Classification based, with use of knowledge-enhanced computing approaches. We also propose methods for final summary selection for users with multiple candidates of generated summaries. We evaluate the proposed approaches by user-study using a number of experiments. Our results show promising quality of 92.8% good summaries with majority agreement in the best case and 70% with majority agreement in the worst case. Our approaches also outperform the state of the art up to 88%. This study has implications in the area of expert profiling, user presentation and application design for engaging user experience.
1212.1936
High-dimensional sequence transduction
cs.LG
We investigate the problem of transforming an input sequence into a high-dimensional output sequence in order to transcribe polyphonic audio music into symbolic notation. We introduce a probabilistic model based on a recurrent neural network that is able to learn realistic output distributions given the input and we devise an efficient algorithm to search for the global mode of that distribution. The resulting method produces musically plausible transcriptions even under high levels of noise and drastically outperforms previous state-of-the-art approaches on five datasets of synthesized sounds and real recordings, approximately halving the test error rate.
1212.1940
Consensus Formation on Simplicial Complex of Opinions
physics.soc-ph cs.SI
Geometric realization of opinion is considered as a simplex and the opinion space of a group of individuals is a simplicial complex whose topological features are monitored in the process of opinion formation. The agents are physically located on the nodes of the scale-free network. Social interactions include all concepts of social dynamics present in the mainstream models augmented by four additional interaction mechanisms which depend on the local properties of opinions and their overlapping properties. The results pertaining to the formation of consensus are of particular interest. An analogy with quantum mechanical pure states is established through the application of the high dimensional combinatorial Laplacian.
1212.1942
Balanced K-SAT and Biased random K-SAT on trees
cond-mat.stat-mech cs.AI cs.CC
We study and solve some variations of the random K-satisfiability problem - balanced K-SAT and biased random K-SAT - on a regular tree, using techniques we have developed earlier(arXiv:1110.2065). In both these problems, as well as variations of these that we have looked at, we find that the SAT-UNSAT transition obtained on the Bethe lattice matches the exact threshold for the same model on a random graph for K=2 and is very close to the numerical value obtained for K=3. For higher K it deviates from the numerical estimates of the solvability threshold on random graphs, but is very close to the dynamical 1-RSB threshold as obtained from the first non-trivial fixed point of the survey propagation algorithm.
1212.1969
Joint Secured and Robust Technique for OFDM Systems
cs.IT math.IT
This work presents a novel technique for joint secured and robust transmission of orthogonal frequency division multiplexing (OFDM) based communication systems. The proposed system is implemented by developing a new OFDM symbol structure based on symmetric key cryptography. At the receiver side, data detection becomes infeasible without the knowledge of the secret key. For an intruder who tries to detect the data without the knowledge of the key, the signal will be a noise-like signal. In addition to the system security, theoretical and simulation results demonstrated that the proposed system provides time and frequency diversity, which makes the system highly robust against severe frequency-selective fading as well as other impairments such as impulsive noise and multiple access interference. For particular frequency-selective fading channels, the bit error rate (BER) improvements was about 15 dB at BER of 10E-4.
1212.2002
A simpler approach to obtaining an O(1/t) convergence rate for the projected stochastic subgradient method
cs.LG math.OC stat.ML
In this note, we present a new averaging technique for the projected stochastic subgradient method. By using a weighted average with a weight of t+1 for each iterate w_t at iteration t, we obtain the convergence rate of O(1/t) with both an easy proof and an easy implementation. The new scheme is compared empirically to existing techniques, with similar performance behavior.
1212.2005
The Dynamic Controllability of Conditional STNs with Uncertainty
cs.AI cs.SY
Recent attempts to automate business processes and medical-treatment processes have uncovered the need for a formal framework that can accommodate not only temporal constraints, but also observations and actions with uncontrollable durations. To meet this need, this paper defines a Conditional Simple Temporal Network with Uncertainty (CSTNU) that combines the simple temporal constraints from a Simple Temporal Network (STN) with the conditional nodes from a Conditional Simple Temporal Problem (CSTP) and the contingent links from a Simple Temporal Network with Uncertainty (STNU). A notion of dynamic controllability for a CSTNU is defined that generalizes the dynamic consistency of a CTP and the dynamic controllability of an STNU. The paper also presents some sound constraint-propagation rules for dynamic controllability that are expected to form the backbone of a dynamic-controllability-checking algorithm for CSTNUs.
1212.2006
A Novel Feature-based Bayesian Model for Query Focused Multi-document Summarization
cs.CL cs.IR
Both supervised learning methods and LDA based topic model have been successfully applied in the field of query focused multi-document summarization. In this paper, we propose a novel supervised approach that can incorporate rich sentence features into Bayesian topic models in a principled way, thus taking advantages of both topic model and feature based supervised learning methods. Experiments on TAC2008 and TAC2009 demonstrate the effectiveness of our approach.
1212.2036
Query-focused Multi-document Summarization: Combining a Novel Topic Model with Graph-based Semi-supervised Learning
cs.CL cs.IR
Graph-based semi-supervised learning has proven to be an effective approach for query-focused multi-document summarization. The problem of previous semi-supervised learning is that sentences are ranked without considering the higher level information beyond sentence level. Researches on general summarization illustrated that the addition of topic level can effectively improve the summary quality. Inspired by previous researches, we propose a two-layer (i.e. sentence layer and topic layer) graph-based semi-supervised learning approach. At the same time, we propose a novel topic model which makes full use of the dependence between sentences and words. Experimental results on DUC and TAC data sets demonstrate the effectiveness of our proposed approach.
1212.2044
Macro-Economic Time Series Modeling and Interaction Networks
cs.NE stat.AP
Macro-economic models describe the dynamics of economic quantities. The estimations and forecasts produced by such models play a substantial role for financial and political decisions. In this contribution we describe an approach based on genetic programming and symbolic regression to identify variable interactions in large datasets. In the proposed approach multiple symbolic regression runs are executed for each variable of the dataset to find potentially interesting models. The result is a variable interaction network that describes which variables are most relevant for the approximation of each variable of the dataset. This approach is applied to a macro-economic dataset with monthly observations of important economic indicators in order to identify potentially interesting dependencies of these indicators. The resulting interaction network of macro-economic indicators is briefly discussed and two of the identified models are presented in detail. The two models approximate the help wanted index and the CPI inflation in the US.
1212.2056
Soft Constraint Logic Programming for Electric Vehicle Travel Optimization
cs.AI
Soft Constraint Logic Programming is a natural and flexible declarative programming formalism, which allows to model and solve real-life problems involving constraints of different types. In this paper, after providing a slightly more general and elegant presentation of the framework, we show how we can apply it to the e-mobility problem of coordinating electric vehicles in order to overcome both energetic and temporal constraints and so to reduce their running cost. In particular, we focus on the journey optimization sub-problem, considering sequences of trips from a user's appointment to another one. Solutions provide the best alternatives in terms of time and energy consumption, including route sequences and possible charging events.
1212.2065
A Survey on Information Retrieval, Text Categorization, and Web Crawling
cs.IR
This paper is a survey discussing Information Retrieval concepts, methods, and applications. It goes deep into the document and query modelling involved in IR systems, in addition to pre-processing operations such as removing stop words and searching by synonym techniques. The paper also tackles text categorization along with its application in neural networks and machine learning. Finally, the architecture of web crawlers is to be discussed shedding the light on how internet spiders index web documents and how they allow users to search for items on the web.
1212.2071
A Data Warehouse Design for a Typical University Information System
cs.DB
Presently, large enterprises rely on database systems to manage their data and information. These databases are useful for conducting daily business transactions. However, the tight competition in the marketplace has led to the concept of data mining in which data are analyzed to derive effective business strategies and discover better ways in carrying out business. In order to perform data mining, regular databases must be converted into what so called informational databases also known as data warehouse. This paper presents a design model for building data warehouse for a typical university information system. It is based on transforming an operational database into an informational warehouse useful for decision makers to conduct data analysis, predication, and forecasting. The proposed model is based on four stages of data migration: Data extraction, data cleansing, data transforming, and data indexing and loading. The complete system is implemented under MS Access 2010 and is meant to serve as a repository of data for data mining operations.
1212.2094
Secondary Access to Spectrum with SINR Requirements Through Constraint Transformation
cs.NI cs.IT math.IT
In this paper we investigate the problem of allocating spectrum among radio nodes under SINR requirements. This problem is of special interest in dynamic spectrum access networks where topology and spectral resources differ with time and location. The problem is to determine the number of radio nodes that can transmit simultaneously while still achieving their SINR requirements and then decide which channels these nodes should transmit on. Previous work have shown how this can be done for a large spectrum pool where nodes allocate multiple channels from that pool which renders a linear programming approach feasible when the pool is large enough. In this paper we extend their work by considering arbitrary individual pool sizes and allow nodes to only transmit on one channel. Due to the accumulative nature of interference this problem is a non-convex integer problem which is NP-hard. However, we introduce a constraint transformation that transforms the problem to a binary quadratic constraint problem. Although this problem is still NP-hard, well known heuristic algorithms for solving this problem are known in the literature. We implement a heuristic algorithm based on Lagrange relaxation which bounds the solution value of the heuristic to the optimal value of the constraint transformed problem. Simulation results show that this approach provides solutions within an average gap of 10% of solutions obtained by a genetic algorithm for the original non-convex integer problem.
1212.2125
Sparse Regression Codes for Multi-terminal Source and Channel Coding
cs.IT math.IT
We study a new class of codes for Gaussian multi-terminal source and channel coding. These codes are designed using the statistical framework of high-dimensional linear regression and are called Sparse Superposition or Sparse Regression codes. Codewords are linear combinations of subsets of columns of a design matrix. These codes were recently introduced by Barron and Joseph and shown to achieve the channel capacity of AWGN channels with computationally feasible decoding. They have also recently been shown to achieve the optimal rate-distortion function for Gaussian sources. In this paper, we demonstrate how to implement random binning and superposition coding using sparse regression codes. In particular, with minimum-distance encoding/decoding it is shown that sparse regression codes attain the optimal information-theoretic limits for a variety of multi-terminal source and channel coding problems.
1212.2129
Online Portfolio Selection: A Survey
q-fin.CP cs.AI cs.CE q-fin.PM
Online portfolio selection is a fundamental problem in computational finance, which has been extensively studied across several research communities, including finance, statistics, artificial intelligence, machine learning, and data mining, etc. This article aims to provide a comprehensive survey and a structural understanding of published online portfolio selection techniques. From an online machine learning perspective, we first formulate online portfolio selection as a sequential decision problem, and then survey a variety of state-of-the-art approaches, which are grouped into several major categories, including benchmarks, "Follow-the-Winner" approaches, "Follow-the-Loser" approaches, "Pattern-Matching" based approaches, and "Meta-Learning Algorithms". In addition to the problem formulation and related algorithms, we also discuss the relationship of these algorithms with the Capital Growth theory in order to better understand the similarities and differences of their underlying trading ideas. This article aims to provide a timely and comprehensive survey for both machine learning and data mining researchers in academia and quantitative portfolio managers in the financial industry to help them understand the state-of-the-art and facilitate their research and practical applications. We also discuss some open issues and evaluate some emerging new trends for future research directions.
1212.2136
A class of random fields on complete graphs with tractable partition function
cs.LG stat.ML
The aim of this short note is to draw attention to a method by which the partition function and marginal probabilities for a certain class of random fields on complete graphs can be computed in polynomial time. This class includes Ising models with homogeneous pairwise potentials but arbitrary (inhomogeneous) unary potentials. Similarly, the partition function and marginal probabilities can be computed in polynomial time for random fields on complete bipartite graphs, provided they have homogeneous pairwise potentials. We expect that these tractable classes of large scale random fields can be very useful for the evaluation of approximation algorithms by providing exact error estimates.
1212.2142
Universality in voting behavior: an empirical analysis
physics.soc-ph cs.SI physics.data-an
Election data represent a precious source of information to study human behavior at a large scale. In proportional elections with open lists, the number of votes received by a candidate, rescaled by the average performance of all competitors in the same party list, has the same distribution regardless of the country and the year of the election. Here we provide the first thorough assessment of this claim. We analyzed election datasets of 15 countries with proportional systems. We confirm that a class of nations with similar election rules fulfill the universality claim. Discrepancies from this trend in other countries with open-lists elections are always associated with peculiar differences in the election rules, which matter more than differences between countries and historical periods. Our analysis shows that the role of parties in the electoral performance of candidates is crucial: alternative scalings not taking into account party affiliations lead to poor results.
1212.2144
Design of companding quantizer for Laplacian source using the approximation of probability density function
math.OC cs.IT math.IT
In this paper both piecewise linear and piecewise uniform approximation of probability density function are performed. For the probability density function approximated in these ways, a compressor function is formed. On the basis of compressor function formed in this way, piecewise linear and piecewise uniform companding quantizer are designed. Design of these companding quantizer models is performed for the Laplacian source at the entrance of the quantizer. The performance estimate of the proposed companding quantizer models is done by determining the values of signal to quantization noise ratio (SQNR) and approximation error for the both of proposed models and also by their mutual comparison.
1212.2145
A Scale-Space Theory for Text
cs.IR cs.CL
Scale-space theory has been established primarily by the computer vision and signal processing communities as a well-founded and promising framework for multi-scale processing of signals (e.g., images). By embedding an original signal into a family of gradually coarsen signals parameterized with a continuous scale parameter, it provides a formal framework to capture the structure of a signal at different scales in a consistent way. In this paper, we present a scale space theory for text by integrating semantic and spatial filters, and demonstrate how natural language documents can be understood, processed and analyzed at multiple resolutions, and how this scale-space representation can be used to facilitate a variety of NLP and text analysis tasks.
1212.2150
Collaborative Competitive filtering II: Optimal Recommendation and Collaborative Games
cs.IR
Recommender systems have emerged as a new weapon to help online firms to realize many of their strategic goals (e.g., to improve sales, revenue, customer experience etc.). However, many existing techniques commonly approach these goals by seeking to recover preference (e.g., estimating ratings) in a matrix completion framework. This paper aims to bridge this significant gap between the clearly-defined strategic objectives and the not-so-well-justified proxy. We show it is advantageous to think of a recommender system as an analogy to a monopoly economic market with the system as the sole seller, users as the buyers and items as the goods. This new perspective motivates a game-theoretic formulation for recommendation that enables us to identify the optimal recommendation policy by explicit optimizing certain strategic goals. In this paper, we revisit and extend our prior work, the Collaborative-Competitive Filtering preference model, towards a game-theoretic framework. The proposed framework consists of two components. First, a conditional preference model that characterizes how a user would respond to a recommendation action; Second, knowing in advance how the user would respond, how a recommender system should act (i.e., recommend) strategically to maximize its goals. We show how objectives such as click-through rate, sales revenue and consumption diversity can be optimized explicitly in this framework. Experiments are conducted on a commercial recommender system and demonstrate promising results.
1212.2153
Emergence of network features from multiplexity
physics.soc-ph cs.SI
Many biological and man-made networked systems are characterized by the simultaneous presence of different sub-networks organized in separate layers, with links and nodes of qualitatively different types. While during the past few years theoretical studies have examined a variety of structural features of complex networks, the outstanding question is whether such features are characterizing all single layers, or rather emerge as a result of coarse-graining, i.e. when going from the multilayered to the aggregate network representation. Here we address this issue with the help of real data. We analyze the structural properties of an intrinsically multilayered real network, the European Air Transportation Multiplex Network in which each commercial airline defines a network layer. We examine how several structural measures evolve as layers are progressively merged together. In particular, we discuss how the topology of each layer affects the emergence of structural properties in the aggregate network.
1212.2170
Stochastic Perron's method for Hamilton-Jacobi-Bellman equations
math.PR cs.SY math.AP math.OC
We show that the value function of a stochastic control problem is the unique solution of the associated Hamilton-Jacobi-Bellman (HJB) equation, completely avoiding the proof of the so-called dynamic programming principle (DPP). Using Stochastic Perron's method we construct a super-solution lying below the value function and a sub-solution dominating it. A comparison argument easily closes the proof. The program has the precise meaning of verification for viscosity-solutions, obtaining the DPP as a conclusion. It also immediately follows that the weak and strong formulations of the stochastic control problem have the same value. Using this method we also capture the possible face-lifting phenomenon in a straightforward manner.
1212.2245
Fast and Robust Linear Motion Deblurring
cs.CV
We investigate efficient algorithmic realisations for robust deconvolution of grey-value images with known space-invariant point-spread function, with emphasis on 1D motion blur scenarios. The goal is to make deconvolution suitable as preprocessing step in automated image processing environments with tight time constraints. Candidate deconvolution methods are selected for their restoration quality, robustness and efficiency. Evaluation of restoration quality and robustness on synthetic and real-world test images leads us to focus on a combination of Wiener filtering with few iterations of robust and regularised Richardson-Lucy deconvolution. We discuss algorithmic optimisations for specific scenarios. In the case of uniform linear motion blur in coordinate direction, it is possible to achieve real-time performance (less than 50 ms) in single-threaded CPU computation on images of $256\times256$ pixels. For more general space-invariant blur settings, still favourable computation times are obtained. Exemplary parallel implementations demonstrate that the proposed method also achieves real-time performance for general 1D motion blurs in a multi-threaded CPU setting, and for general 2D blurs on a GPU.
1212.2251
A Propagation Model for Provenance Views of Public/Private Workflows
cs.DB
We study the problem of concealing functionality of a proprietary or private module when provenance information is shown over repeated executions of a workflow which contains both `public' and `private' modules. Our approach is to use `provenance views' to hide carefully chosen subsets of data over all executions of the workflow to ensure G-privacy: for each private module and each input x, the module's output f(x) is indistinguishable from G -1 other possible values given the visible data in the workflow executions. We show that G-privacy cannot be achieved simply by combining solutions for individual private modules; data hiding must also be `propagated' through public modules. We then examine how much additional data must be hidden and when it is safe to stop propagating data hiding. The answer depends strongly on the workflow topology as well as the behavior of public modules on the visible data. In particular, for a class of workflows (which include the common tree and chain workflows), taking private solutions for each private module, augmented with a `public closure' that is `upstream-downstream safe', ensures G-privacy. We define these notions formally and show that the restrictions are necessary. We also study the related optimization problems of minimizing the amount of hidden data.
1212.2262
Bag-of-Words Representation for Biomedical Time Series Classification
cs.LG cs.AI
Automatic analysis of biomedical time series such as electroencephalogram (EEG) and electrocardiographic (ECG) signals has attracted great interest in the community of biomedical engineering due to its important applications in medicine. In this work, a simple yet effective bag-of-words representation that is able to capture both local and global structure similarity information is proposed for biomedical time series representation. In particular, similar to the bag-of-words model used in text document domain, the proposed method treats a time series as a text document and extracts local segments from the time series as words. The biomedical time series is then represented as a histogram of codewords, each entry of which is the count of a codeword appeared in the time series. Although the temporal order of the local segments is ignored, the bag-of-words representation is able to capture high-level structural information because both local and global structural information are well utilized. The performance of the bag-of-words model is validated on three datasets extracted from real EEG and ECG signals. The experimental results demonstrate that the proposed method is not only insensitive to parameters of the bag-of-words model such as local segment length and codebook size, but also robust to noise.
1212.2264
A space efficient streaming algorithm for triangle counting using the birthday paradox
cs.DS cs.DM cs.SI
We design a space efficient algorithm that approximates the transitivity (global clustering coefficient) and total triangle count with only a single pass through a graph given as a stream of edges. Our procedure is based on the classic probabilistic result, the birthday paradox. When the transitivity is constant and there are more edges than wedges (common properties for social networks), we can prove that our algorithm requires $O(\sqrt{n})$ space ($n$ is the number of vertices) to provide accurate estimates. We run a detailed set of experiments on a variety of real graphs and demonstrate that the memory requirement of the algorithm is a tiny fraction of the graph. For example, even for a graph with 200 million edges, our algorithm stores just 60,000 edges to give accurate results. Being a single pass streaming algorithm, our procedure also maintains a real-time estimate of the transitivity/number of triangles of a graph, by storing a minuscule fraction of edges.
1212.2278
Inverting and Visualizing Features for Object Detection
cs.CV
We introduce algorithms to visualize feature spaces used by object detectors. The tools in this paper allow a human to put on `HOG goggles' and perceive the visual world as a HOG based object detector sees it. We found that these visualizations allow us to analyze object detection systems in new ways and gain new insight into the detector's failures. For example, when we visualize the features for high scoring false alarms, we discovered that, although they are clearly wrong in image space, they do look deceptively similar to true positives in feature space. This result suggests that many of these false alarms are caused by our choice of feature space, and indicates that creating a better learning algorithm or building bigger datasets is unlikely to correct these errors. By visualizing feature spaces, we can gain a more intuitive understanding of our detection systems.
1212.2287
Runtime Optimizations for Prediction with Tree-Based Models
cs.DB cs.IR cs.LG
Tree-based models have proven to be an effective solution for web ranking as well as other problems in diverse domains. This paper focuses on optimizing the runtime performance of applying such models to make predictions, given an already-trained model. Although exceedingly simple conceptually, most implementations of tree-based models do not efficiently utilize modern superscalar processor architectures. By laying out data structures in memory in a more cache-conscious fashion, removing branches from the execution flow using a technique called predication, and micro-batching predictions using a technique called vectorization, we are able to better exploit modern processor architectures and significantly improve the speed of tree-based models over hard-coded if-else blocks. Our work contributes to the exploration of architecture-conscious runtime implementations of machine learning algorithms.
1212.2309
Low Rank Mechanism for Optimizing Batch Queries under Differential Privacy
cs.DB cs.CR
Differential privacy is a promising privacy-preserving paradigm for statistical query processing over sensitive data. It works by injecting random noise into each query result, such that it is provably hard for the adversary to infer the presence or absence of any individual record from the published noisy results. The main objective in differentially private query processing is to maximize the accuracy of the query results, while satisfying the privacy guarantees. Previous work, notably \cite{LHR+10}, has suggested that with an appropriate strategy, processing a batch of correlated queries as a whole achieves considerably higher accuracy than answering them individually. However, to our knowledge there is currently no practical solution to find such a strategy for an arbitrary query batch; existing methods either return strategies of poor quality (often worse than naive methods) or require prohibitively expensive computations for even moderately large domains. Motivated by this, we propose the \emph{Low-Rank Mechanism} (LRM), the first practical differentially private technique for answering batch queries with high accuracy, based on a \emph{low rank approximation} of the workload matrix. We prove that the accuracy provided by LRM is close to the theoretical lower bound for any mechanism to answer a batch of queries under differential privacy. Extensive experiments using real data demonstrate that LRM consistently outperforms state-of-the-art query processing solutions under differential privacy, by large margins.
1212.2314
Tree Projections and Structural Decomposition Methods: Minimality and Game-Theoretic Characterization
cs.DM cs.AI
Tree projections provide a mathematical framework that encompasses all the various (purely) structural decomposition methods that have been proposed in the literature to single out classes of nearly-acyclic (hyper)graphs, such as the tree decomposition method, which is the most powerful decomposition method on graphs, and the (generalized) hypertree decomposition method, which is its natural counterpart on arbitrary hypergraphs. The paper analyzes this framework, by focusing in particular on "minimal" tree projections, that is, on tree projections without useless redundancies. First, it is shown that minimal tree projections enjoy a number of properties that are usually required for normal form decompositions in various structural decomposition methods. In particular, they enjoy the same kind of connection properties as (minimal) tree decompositions of graphs, with the result being tight in the light of the negative answer that is provided to the open question about whether they enjoy a slightly stronger notion of connection property, defined to speed-up the computation of hypertree decompositions. Second, it is shown that tree projections admit a natural game-theoretic characterization in terms of the Captain and Robber game. In this game, as for the Robber and Cops game characterizing tree decompositions, the existence of winning strategies implies the existence of monotone ones. As a special case, the Captain and Robber game can be used to characterize the generalized hypertree decomposition method, where such a game-theoretic characterization was missing and asked for. Besides their theoretical interest, these results have immediate algorithmic applications both for the general setting and for structural decomposition methods that can be recast in terms of tree projections.
1212.2316
Asymptotic Optimality of Equal Power Allocation for Linear Estimation of WSS Random Processes
cs.IT math.IT
This letter establishes the asymptotic optimality of equal power allocation for measurements of a continuous wide-sense stationary (WSS) random process with a square-integrable autocorrelation function when linear estimation is used on equally-spaced measurements with periodicity meeting the Nyquist criterion and with the variance of the noise on any sample inversely proportional to the power expended by the user to obtain that measurement.
1212.2338
Controlled conflict resolution for replicated document
cs.DB
Collaborative working is increasingly popular, but it presents challenges due to the need for high responsiveness and disconnected work support. To address these challenges the data is optimistically replicated at the edges of the network, i.e. personal computers or mobile devices. This replication requires a merge mechanism that preserves the consistency and structure of the shared data subject to concurrent modifications. In this paper, we propose a generic design to ensure eventual consistency (every replica will eventually view the same data) and to maintain the specific constraints of the replicated data. Our layered design provides to the application engineer the complete control over system scalability and behavior of the replicated data in face of concurrent modifications. We show that our design allows replication of complex data types with acceptable performances.
1212.2340
PAC-Bayesian Learning and Domain Adaptation
stat.ML cs.LG
In machine learning, Domain Adaptation (DA) arises when the distribution gen- erating the test (target) data differs from the one generating the learning (source) data. It is well known that DA is an hard task even under strong assumptions, among which the covariate-shift where the source and target distributions diverge only in their marginals, i.e. they have the same labeling function. Another popular approach is to consider an hypothesis class that moves closer the two distributions while implying a low-error for both tasks. This is a VC-dim approach that restricts the complexity of an hypothesis class in order to get good generalization. Instead, we propose a PAC-Bayesian approach that seeks for suitable weights to be given to each hypothesis in order to build a majority vote. We prove a new DA bound in the PAC-Bayesian context. This leads us to design the first DA-PAC-Bayesian algorithm based on the minimization of the proposed bound. Doing so, we seek for a \rho-weighted majority vote that takes into account a trade-off between three quantities. The first two quantities being, as usual in the PAC-Bayesian approach, (a) the complexity of the majority vote (measured by a Kullback-Leibler divergence) and (b) its empirical risk (measured by the \rho-average errors on the source sample). The third quantity is (c) the capacity of the majority vote to distinguish some structural difference between the source and target samples.
1212.2342
Distributed MIMO coding scheme with low decoding complexity for future mobile TV broadcasting
cs.NI cs.IT math.IT
A novel distributed space-time block code (STBC) for the next generation mobile TV broadcasting is proposed. The new code provides efficient performance within a wide range of power imbalance showing strong adaptivity to the single frequency network (SFN) broadcasting deployments. The new code outperforms existing STBCs with equivalent decoding complexity and approaches those with much higher complexities.
1212.2343
Improved Channel Estimation Methods based on PN sequence for TDS-OFDM
cs.IT cs.NI math.IT
An accurate channel estimation is crucial for the novel time domain synchronous orthogonal frequency-division multiplexing (TDS-OFDM) scheme in which pseudo noise (PN) sequences serve as both guard intervals (GI) for OFDM data symbols and training sequences for synchronization/channel estimation. This paper studies the channel estimation method based on the cross-correlation of PN sequences. A theoretical analysis of this estimator is conducted and several improved estimators are then proposed to reduce the estimation error floor encountered by the PN-correlation-based estimator. It is shown through mathematical derivations and simulations that the new estimators approach or even achieve the Cramer-Rao bound.
1212.2345
Enhanced Mobile Digital Video Broadcasting with Distributed Space-Time Coding
cs.IT cs.MM math.IT
This paper investigates the distributed space-time (ST) coding proposals for the future Digital Video Broadcasting--Next Generation Handheld (DVB-NGH) standard. We first theoretically show that the distributed MIMO scheme is the best broadcasting scenario in terms of channel capacity. Consequently we evaluate the performance of several ST coding proposals for DVB-NGH with practical system specifications and channel conditions. Simulation results demonstrate that the 3D code is the best ST coding solution for broadcasting in the distributed MIMO scenario.
1212.2390
On the complexity of learning a language: An improvement of Block's algorithm
cs.CL cs.LG
Language learning is thought to be a highly complex process. One of the hurdles in learning a language is to learn the rules of syntax of the language. Rules of syntax are often ordered in that before one rule can applied one must apply another. It has been thought that to learn the order of n rules one must go through all n! permutations. Thus to learn the order of 27 rules would require 27! steps or 1.08889x10^{28} steps. This number is much greater than the number of seconds since the beginning of the universe! In an insightful analysis the linguist Block ([Block 86], pp. 62-63, p.238) showed that with the assumption of transitivity this vast number of learning steps reduces to a mere 377 steps. We present a mathematical analysis of the complexity of Block's algorithm. The algorithm has a complexity of order n^2 given n rules. In addition, we improve Block's results exponentially, by introducing an algorithm that has complexity of order less than n log n.
1212.2396
Source Coding Problems with Conditionally Less Noisy Side Information
cs.IT math.IT
A computable expression for the rate-distortion (RD) function proposed by Heegard and Berger has eluded information theory for nearly three decades. Heegard and Berger's single-letter achievability bound is well known to be optimal for \emph{physically degraded} side information; however, it is not known whether the bound is optimal for arbitrarily correlated side information (general discrete memoryless sources). In this paper, we consider a new setup in which the side information at one receiver is \emph{conditionally less noisy} than the side information at the other. The new setup includes degraded side information as a special case, and it is motivated by the literature on degraded and less noisy broadcast channels. Our key contribution is a converse proving the optimality of Heegard and Berger's achievability bound in a new setting. The converse rests upon a certain \emph{single-letterization} lemma, which we prove using an information theoretic telescoping identity {recently presented by Kramer}. We also generalise the above ideas to two different successive-refinement problems.
1212.2398
An Information Theoretic Algorithm for Finding Periodicities in Stellar Light Curves
astro-ph.IM cs.IT math.IT
We propose a new information theoretic metric for finding periodicities in stellar light curves. Light curves are astronomical time series of brightness over time, and are characterized as being noisy and unevenly sampled. The proposed metric combines correntropy (generalized correlation) with a periodic kernel to measure similarity among samples separated by a given period. The new metric provides a periodogram, called Correntropy Kernelized Periodogram (CKP), whose peaks are associated with the fundamental frequencies present in the data. The CKP does not require any resampling, slotting or folding scheme as it is computed directly from the available samples. CKP is the main part of a fully-automated pipeline for periodic light curve discrimination to be used in astronomical survey databases. We show that the CKP method outperformed the slotted correntropy, and conventional methods used in astronomy for periodicity discrimination and period estimation tasks, using a set of light curves drawn from the MACHO survey. The proposed metric achieved 97.2% of true positives with 0% of false positives at the confidence level of 99% for the periodicity discrimination task; and 88% of hits with 11.6% of multiples and 0.4% of misses in the period estimation task.
1212.2414
Mining Techniques in Network Security to Enhance Intrusion Detection Systems
cs.CR cs.LG
In intrusion detection systems, classifiers still suffer from several drawbacks such as data dimensionality and dominance, different network feature types, and data impact on the classification. In this paper two significant enhancements are presented to solve these drawbacks. The first enhancement is an improved feature selection using sequential backward search and information gain. This, in turn, extracts valuable features that enhance positively the detection rate and reduce the false positive rate. The second enhancement is transferring nominal network features to numeric ones by exploiting the discrete random variable and the probability mass function to solve the problem of different feature types, the problem of data dominance, and data impact on the classification. The latter is combined to known normalization methods to achieve a significant hybrid normalization approach. Finally, an intensive and comparative study approves the efficiency of these enhancements and shows better performance comparing to other proposed methods.
1212.2415
Robust Face Recognition using Local Illumination Normalization and Discriminant Feature Point Selection
cs.LG cs.CV
Face recognition systems must be robust to the variation of various factors such as facial expression, illumination, head pose and aging. Especially, the robustness against illumination variation is one of the most important problems to be solved for the practical use of face recognition systems. Gabor wavelet is widely used in face detection and recognition because it gives the possibility to simulate the function of human visual system. In this paper, we propose a method for extracting Gabor wavelet features which is stable under the variation of local illumination and show experiment results demonstrating its effectiveness.
1212.2425
Multi-layered Social Networks
cs.SI physics.soc-ph
It is quite obvious that in the real world, more than one kind of relationship can exist between two actors and that those ties can be so intertwined that it is impossible to analyse them separately [Fienberg 85], [Minor 83], [Szell 10]. Social networks with more than one type of relation are not a completely new concept [Wasserman 94] but they were analysed mainly at the small scale, e.g. in [McPherson 01], [Padgett 93], and [Entwisle 07]. Just like in the case of regular single-layered social network there is no widely accepted definition or even common name. At the beginning such networks have been called multiplex network [Haythornthwaite 99], [Monge 03]. The term is derived from communications theory which defines multiplex as combining multiple signals into one in such way that it is possible to separate them if needed [Hamill 06]. Recently, the area of multi-layered social network has started attracting more and more attention in research conducted within different domains [Kazienko 11a], [Szell 10], [Rodriguez 07], [Rodriguez 09], and the meaning of multiplex network has expanded and covers not only social relationships but any kind of connection, e.g. based on geography, occupation, kinship, hobbies, etc. [Abraham 12]. This essay aims to summarize existing knowledge about one concept which has many different names i.e. the concept of Multi-layered Social Network also known as Layered social network, Multi-relational social network, Multidimensional social network, Multiplex social network
1212.2438
Model-order reduction of biochemical reaction networks
cs.SY cs.SE math.DS physics.chem-ph q-bio.MN
In this paper we propose a model-order reduction method for chemical reaction networks governed by general enzyme kinetics, including the mass-action and Michaelis-Menten kinetics. The model-order reduction method is based on the Kron reduction of the weighted Laplacian matrix which describes the graph structure of complexes in the chemical reaction network. We apply our method to a yeast glycolysis model, where the simulation result shows that the transient behaviour of a number of key metabolites of the reduced-order model is in good agreement with those of the full-order model.
1212.2442
Active Collaborative Filtering
cs.IR cs.LG stat.ML
Collaborative filtering (CF) allows the preferences of multiple users to be pooled to make recommendations regarding unseen products. We consider in this paper the problem of online and interactive CF: given the current ratings associated with a user, what queries (new ratings) would most improve the quality of the recommendations made? We cast this terms of expected value of information (EVOI); but the online computational cost of computing optimal queries is prohibitive. We show how offline prototyping and computation of bounds on EVOI can be used to dramatically reduce the required online computation. The framework we develop is general, but we focus on derivations and empirical study in the specific case of the multiple-cause vector quantization model.
1212.2444
On revising fuzzy belief bases
cs.AI
We look at the problem of revising fuzzy belief bases, i.e., belief base revision in which both formulas in the base as well as revision-input formulas can come attached with varying truth-degrees. Working within a very general framework for fuzzy logic which is able to capture a variety of types of inference under uncertainty, such as truth-functional fuzzy logics and certain types of probabilistic inference, we show how the idea of rational change from 'crisp' base revision, as embodied by the idea of partial meet revision, can be faithfully extended to revising fuzzy belief bases. We present and axiomatise an operation of partial meet fuzzy revision and illustrate how the operation works in several important special instances of the framework.
1212.2445
Upgrading Ambiguous Signs in QPNs
cs.AI
WA qualitative probabilistic network models the probabilistic relationships between its variables by means of signs. Non-monotonic influences have associated an ambiguous sign. These ambiguous signs typically lead to uninformative results upon inference. A non-monotonic influence can, however, be associated with a, more informative, sign that indicates its effect in the current state of the network. To capture this effect, we introduce the concept of situational sign. Furthermore, if the network converts to a state in which all variables that provoke the non-monotonicity have been observed, a non-monotonic influence reduces to a monotonic influence. We study the persistence and propagation of situational signs upon inference and give a method to establish the sign of a reduced influence.
1212.2446
Parametric Dependability Analysis through Probabilistic Horn Abduction
cs.AI
Dependability modeling and evaluation is aimed at investigating that a system performs its function correctly in time. A usual way to achieve a high reliability, is to design redundant systems that contain several replicas of the same subsystem or component. State space methods for dependability analysis may suffer of the state space explosion problem in such a kind of situation. Combinatorial models, on the other hand, require the simplified assumption of statistical independence; however, in case of redundant systems, this does not guarantee a reduced number of modeled elements. In order to provide a more compact system representation, parametric system modeling has been investigated in the literature, in such a way that a set of replicas of a given subsystem is parameterized so that only one representative instance is explicitly included. While modeling aspects can be suitably addressed by these approaches, analytical tools working on parametric characterizations are often more difficult to be defined and the standard approach is to 'unfold' the parametric model, in order to exploit standard analysis algorithms working at the unfolded 'ground' level. Moreover, parameterized combinatorial methods still require the statistical independence assumption. In the present paper we consider the formalism of Parametric Fault Tree (PFT) and we show how it can be related to Probabilistic Horn Abduction (PHA). Since PHA is a framework where both modeling and analysis can be performed in a restricted first-order language, we aim at showing that converting a PFT into a PHA knowledge base will allow an approach to dependability analysis directly exploiting parametric representation. We will show that classical qualitative and quantitative dependability measures can be characterized within PHA. Furthermore, additional modeling aspects (such as noisy gates and local dependencies) as well as additional reliability measures (such as posterior probability analysis) can be naturally addressed by this conversion. A simple example of a multi-processor system with several replicated units is used to illustrate the approach.
1212.2447
Bayesian Hierarchical Mixtures of Experts
cs.LG stat.ML
The Hierarchical Mixture of Experts (HME) is a well-known tree-based model for regression and classification, based on soft probabilistic splits. In its original formulation it was trained by maximum likelihood, and is therefore prone to over-fitting. Furthermore the maximum likelihood framework offers no natural metric for optimizing the complexity and structure of the tree. Previous attempts to provide a Bayesian treatment of the HME model have relied either on ad-hoc local Gaussian approximations or have dealt with related models representing the joint distribution of both input and output variables. In this paper we describe a fully Bayesian treatment of the HME model based on variational inference. By combining local and global variational methods we obtain a rigourous lower bound on the marginal probability of the data under the model. This bound is optimized during the training phase, and its resulting value can be used for model order selection. We present results using this approach for a data set describing robot arm kinematics.
1212.2448
On Triangulating Dynamic Graphical Models
cs.AI
This paper introduces new methodology to triangulate dynamic Bayesian networks (DBNs) and dynamic graphical models (DGMs). While most methods to triangulate such networks use some form of constrained elimination scheme based on properties of the underlying directed graph, we find it useful to view triangulation and elimination using properties only of the resulting undirected graph, obtained after the moralization step. We first briefly introduce the Graphical model toolkit (GMTK) and its notion of dynamic graphical models, one that slightly extends the standard notion of a DBN. We next introduce the 'boundary algorithm', a method to find the best boundary between partitions in a dynamic model. We find that using this algorithm, the notions of forward- and backward-interface become moot - namely, the size and fill-in of the best forward- and backward- interface are identical. Moreover, we observe that finding a good partition boundary allows for constrained elimination orders (and therefore graph triangulations) that are not possible using standard slice-by-slice constrained eliminations. More interestingly, with certain boundaries it is possible to obtain constrained elimination schemes that lie outside the space of possible triangulations using only unconstrained elimination. Lastly, we report triangulation results on invented graphs, standard DBNs from the literature, novel DBNs used in speech recognition research systems, and also random graphs. Using a number of different triangulation quality measures (max clique size, state-space, etc.), we find that with our boundary algorithm the triangulation quality can dramatically improve.
1212.2449
An Empirical Study of w-Cutset Sampling for Bayesian Networks
cs.AI
The paper studies empirically the time-space trade-off between sampling and inference in a sl cutset sampling algorithm. The algorithm samples over a subset of nodes in a Bayesian network and applies exact inference over the rest. Consequently, while the size of the sampling space decreases, requiring less samples for convergence, the time for generating each single sample increases. The w-cutset sampling selects a sampling set such that the induced-width of the network when the sampling set is observed is bounded by w, thus requiring inference whose complexity is exponential in w. In this paper, we investigate performance of w-cutset sampling over a range of w values and measure the accuracy of w-cutset sampling as a function of w. Our experiments demonstrate that the cutset sampling idea is quite powerful showing that an optimal balance between inference and sampling benefits substantially from restricting the cutset size, even at the cost of more complex inference.
1212.2450
A possibilistic handling of partially ordered information
cs.AI
In a standard possibilistic logic, prioritized information are encoded by means of weighted knowledge base. This paper proposes an extension of possibilistic logic for dealing with partially ordered information. We Show that all basic notions of standard possibilitic logic (sumbsumption, syntactic and semantic inference, etc.) have natural couterparts when dealing with partially ordered information. We also propose an algorithm which computes possibilistic conclusions of a partial knowledge base of a partially ordered knowlege base.
1212.2452
Value Elimination: Bayesian Inference via Backtracking Search
cs.AI
Backtracking search is a powerful algorithmic paradigm that can be used to solve many problems. It is in a certain sense the dual of variable elimination; but on many problems, e.g., SAT, it is vastly superior to variable elimination in practice. Motivated by this we investigate the application of backtracking search to the problem of Bayesian inference (Bayes). We show that natural generalizations of known techniques allow backtracking search to achieve performance guarantees similar to standard algorithms for Bayes, and that there exist problems on which backtracking can in fact do much better. We also demonstrate that these ideas can be applied to implement a Bayesian inference engine whose performance is competitive with standard algorithms. Since backtracking search can very naturally take advantage of context specific structure, the potential exists for performance superior to standard algorithms on many problems.
1212.2453
Web-Based Question Answering: A Decision-Making Perspective
cs.IR cs.CL
We describe an investigation of the use of probabilistic models and cost-benefit analyses to guide resource-intensive procedures used by a Web-based question answering system. We first provide an overview of research on question-answering systems. Then, we present details on AskMSR, a prototype web-based question answering system. We discuss Bayesian analyses of the quality of answers generated by the system and show how we can endow the system with the ability to make decisions about the number of queries issued to a search engine, given the cost of queries and the expected value of query results in refining an ultimate answer. Finally, we review the results of a set of experiments.
1212.2455
New Advances in Inference by Recursive Conditioning
cs.AI
Recursive Conditioning (RC) was introduced recently as the first any-space algorithm for inference in Bayesian networks which can trade time for space by varying the size of its cache at the increment needed to store a floating point number. Under full caching, RC has an asymptotic time and space complexity which is comparable to mainstream algorithms based on variable elimination and clustering (exponential in the network treewidth and linear in its size). We show two main results about RC in this paper. First, we show that its actual space requirements under full caching are much more modest than those needed by mainstream methods and study the implications of this finding. Second, we show that RC can effectively deal with determinism in Bayesian networks by employing standard logical techniques, such as unit resolution, allowing a significant reduction in its time requirements in certain cases. We illustrate our results using a number of benchmark networks, including the very challenging ones that arise in genetic linkage analysis.
1212.2456
Incremental Compilation of Bayesian networks
cs.AI
Most methods of exact probability propagation in Bayesian networks do not carry out the inference directly over the network, but over a secondary structure known as a junction tree or a join tree (JT). The process of obtaining a JT is usually termed {sl compilation}. As compilation is usually viewed as a whole process; each time the network is modified, a new compilation process has to be carried out. The possibility of reusing an already existing JT, in order to obtain the new one regarding only the modifications in the network has received only little attention in the literature. In this paper we present a method for incremental compilation of a Bayesian network, following the classical scheme in which triangulation plays the key role. In order to perform incremental compilation we propose to recompile only those parts of the JT which can have been affected by the networks modifications. To do so, we exploit the technique OF maximal prime subgraph decomposition in determining the minimal subgraph(s) that have to be recompiled, and thereby the minimal subtree(s) of the JT that should be replaced by new subtree(s).We focus on structural modifications : addition and deletion of links and variables.
1212.2457
Structure-Based Causes and Explanations in the Independent Choice Logic
cs.AI
This paper is directed towards combining Pearl's structural-model approach to causal reasoning with high-level formalisms for reasoning about actions. More precisely, we present a combination of Pearl's structural-model approach with Poole's independent choice logic. We show how probabilistic theories in the independent choice logic can be mapped to probabilistic causal models. This mapping provides the independent choice logic with appealing concepts of causality and explanation from the structural-model approach. We illustrate this along Halpern and Pearl's sophisticated notions of actual cause, explanation, and partial explanation. This mapping also adds first-order modeling capabilities and explicit actions to the structural-model approach.
1212.2458
Inference in Polytrees with Sets of Probabilities
cs.AI stat.CO
Inferences in directed acyclic graphs associated with probability sets and probability intervals are NP-hard, even for polytrees. In this paper we focus on such inferences, and propose: 1) a substantial improvement on Tessems A / R algorithm FOR polytrees WITH probability intervals; 2) a new algorithm FOR direction - based local search(IN sets OF probability) that improves ON existing methods; 3) a collection OF branch - AND - bound algorithms that combine the previous techniques.The first two techniques lead TO approximate solutions, WHILE branch - AND - bound procedures can produce either exact OR approximate solutions.We report ON dramatic improvements ON existing techniques FOR inference WITH probability sets AND intervals, IN SOME cases reducing the computational effort BY many orders OF magnitude.
1212.2459
Symbolic Generalization for On-line Planning
cs.AI
Symbolic representations have been used successfully in off-line planning algorithms for Markov decision processes. We show that they can also improve the performance of on-line planners. In addition to reducing computation time, symbolic generalization can reduce the amount of costly real-world interactions required for convergence. We introduce Symbolic Real-Time Dynamic Programming (or sRTDP), an extension of RTDP. After each step of on-line interaction with an environment, sRTDP uses symbolic model-checking techniques to generalizes its experience by updating a group of states rather than a single state. We examine two heuristic approaches to dynamic grouping of states and show that they accelerate the planning process significantly in terms of both CPU time and the number of steps of interaction with the environment.
1212.2460
The Information Bottleneck EM Algorithm
cs.LG stat.ML
Learning with hidden variables is a central challenge in probabilistic graphical models that has important implications for many real-life problems. The classical approach is using the Expectation Maximization (EM) algorithm. This algorithm, however, can get trapped in local maxima. In this paper we explore a new approach that is based on the Information Bottleneck principle. In this approach, we view the learning problem as a tradeoff between two information theoretic objectives. The first is to make the hidden variables uninformative about the identity of specific instances. The second is to make the hidden variables informative about the observed attributes. By exploring different tradeoffs between these two objectives, we can gradually converge on a high-scoring solution. As we show, the resulting, Information Bottleneck Expectation Maximization (IB-EM) algorithm, manages to find solutions that are superior to standard EM methods.
1212.2461
Probabilistic Reasoning about Actions in Nonmonotonic Causal Theories
cs.AI
We present the language {m P}{cal C}+ for probabilistic reasoning about actions, which is a generalization of the action language {cal C}+ that allows to deal with probabilistic as well as nondeterministic effects of actions. We define a formal semantics of {m P}{cal C}+ in terms of probabilistic transitions between sets of states. Using a concept of a history and its belief state, we then show how several important problems in reasoning about actions can be concisely formulated in our formalism.
1212.2462
A New Algorithm for Maximum Likelihood Estimation in Gaussian Graphical Models for Marginal Independence
stat.ME cs.LG stat.ML
Graphical models with bi-directed edges (<->) represent marginal independence: the absence of an edge between two vertices indicates that the corresponding variables are marginally independent. In this paper, we consider maximum likelihood estimation in the case of continuous variables with a Gaussian joint distribution, sometimes termed a covariance graph model. We present a new fitting algorithm which exploits standard regression techniques and establish its convergence properties. Moreover, we contrast our procedure to existing estimation methods.
1212.2463
A Simple Insight into Iterative Belief Propagation's Success
cs.AI
In Non - ergodic belief networks the posterior belief OF many queries given evidence may become zero.The paper shows that WHEN belief propagation IS applied iteratively OVER arbitrary networks(the so called, iterative OR loopy belief propagation(IBP)) it IS identical TO an arc - consistency algorithm relative TO zero - belief queries(namely assessing zero posterior probabilities). This implies that zero - belief conclusions derived BY belief propagation converge AND are sound.More importantly it suggests that the inference power OF IBP IS AS strong AND AS weak, AS that OF arc - consistency.This allows the synthesis OF belief networks FOR which belief propagation IS useless ON one hand, AND focuses the investigation OF classes OF belief network FOR which belief propagation may be zero - complete.Finally, ALL the above conclusions apply also TO Generalized belief propagation algorithms that extend loopy belief propagation AND allow a crisper understanding OF their power.
1212.2464
A Robust Independence Test for Constraint-Based Learning of Causal Structure
cs.AI cs.LG stat.ML
Constraint-based (CB) learning is a formalism for learning a causal network with a database D by performing a series of conditional-independence tests to infer structural information. This paper considers a new test of independence that combines ideas from Bayesian learning, Bayesian network inference, and classical hypothesis testing to produce a more reliable and robust test. The new test can be calculated in the same asymptotic time and space required for the standard tests such as the chi-squared test, but it allows the specification of a prior distribution over parameters and can be used when the database is incomplete. We prove that the test is correct, and we demonstrate empirically that, when used with a CB causal discovery algorithm with noninformative priors, it recovers structural features more reliably and it produces networks with smaller KL-Divergence, especially as the number of nodes increases or the number of records decreases. Another benefit is the dramatic reduction in the probability that a CB algorithm will stall during the search, providing a remedy for an annoying problem plaguing CB learning when the database is small.
1212.2465
Loopy Belief Propagation as a Basis for Communication in Sensor Networks
cs.AI cs.NI
Sensor networks are an exciting new kind of computer system. Consisting of a large number of tiny, cheap computational devices physically distributed in an environment, they gather and process data about the environment in real time. One of the central questions in sensor networks is what to do with the data, i.e., how to reason with it and how to communicate it. This paper argues that the lessons of the UAI community, in particular that one should produce and communicate beliefs rather than raw sensor values, are highly relevant to sensor networks. We contend that loopy belief propagation is particularly well suited to communicating beliefs in sensor networks, due to its compact implementation and distributed nature. We investigate the ability of loopy belief propagation to function under the stressful conditions likely to prevail in sensor networks. Our experiments show that it performs well and degrades gracefully. It converges to appropriate beliefs even in highly asynchronous settings where some nodes communicate far less frequently than others; it continues to function if some nodes fail to participate in the propagation process; and it can track changes in the environment that occur while beliefs are propagating. As a result, we believe that sensor networks present an important application opportunity for UAI.
1212.2466
On Information Regularization
cs.LG stat.ML
We formulate a principle for classification with the knowledge of the marginal distribution over the data points (unlabeled data). The principle is cast in terms of Tikhonov style regularization where the regularization penalty articulates the way in which the marginal density should constrain otherwise unrestricted conditional distributions. Specifically, the regularization penalty penalizes any information introduced between the examples and labels beyond what is provided by the available labeled examples. The work extends Szummer and Jaakkola's information regularization (NIPS 2002) to multiple dimensions, providing a regularizer independent of the covering of the space used in the derivation. We show in addition how the information regularizer can be used as a measure of complexity of the classification task with unlabeled data and prove a relevant sample-complexity bound. We illustrate the regularization principle in practice by restricting the class of conditional distributions to be logistic regression models and constructing the regularization penalty from a finite set of unlabeled examples.
1212.2468
Large-Sample Learning of Bayesian Networks is NP-Hard
cs.LG cs.AI stat.ML
In this paper, we provide new complexity results for algorithms that learn discrete-variable Bayesian networks from data. Our results apply whenever the learning algorithm uses a scoring criterion that favors the simplest model able to represent the generative distribution exactly. Our results therefore hold whenever the learning algorithm uses a consistent scoring criterion and is applied to a sufficiently large dataset. We show that identifying high-scoring structures is hard, even when we are given an independence oracle, an inference oracle, and/or an information oracle. Our negative results also apply to the learning of discrete-variable Bayesian networks in which each node has at most k parents, for all k > 3.
1212.2469
Using the structure of d-connecting paths as a qualitative measure of the strength of dependence
cs.AI
Pearls concept OF a d - connecting path IS one OF the foundations OF the modern theory OF graphical models : the absence OF a d - connecting path IN a DAG indicates that conditional independence will hold IN ANY distribution factorising according TO that graph. IN this paper we show that IN singly - connected Gaussian DAGs it IS possible TO USE the form OF a d - connection TO obtain qualitative information about the strength OF conditional dependence.More precisely, the squared partial correlations BETWEEN two given variables, conditioned ON different subsets may be partially ordered BY examining the relationship BETWEEN the d - connecting path AND the SET OF variables conditioned upon.
1212.2470
Reasoning about Bayesian Network Classifiers
cs.LG cs.AI stat.ML
Bayesian network classifiers are used in many fields, and one common class of classifiers are naive Bayes classifiers. In this paper, we introduce an approach for reasoning about Bayesian network classifiers in which we explicitly convert them into Ordered Decision Diagrams (ODDs), which are then used to reason about the properties of these classifiers. Specifically, we present an algorithm for converting any naive Bayes classifier into an ODD, and we show theoretically and experimentally that this algorithm can give us an ODD that is tractable in size even given an intractable number of instances. Since ODDs are tractable representations of classifiers, our algorithm allows us to efficiently test the equivalence of two naive Bayes classifiers and characterize discrepancies between them. We also show a number of additional results including a count of distinct classifiers that can be induced by changing some CPT in a naive Bayes classifier, and the range of allowable changes to a CPT which keeps the current classifier unchanged.
1212.2471
Monte Carlo Matrix Inversion Policy Evaluation
cs.LG cs.AI cs.NA
In 1950, Forsythe and Leibler (1950) introduced a statistical technique for finding the inverse of a matrix by characterizing the elements of the matrix inverse as expected values of a sequence of random walks. Barto and Duff (1994) subsequently showed relations between this technique and standard dynamic programming and temporal differencing methods. The advantage of the Monte Carlo matrix inversion (MCMI) approach is that it scales better with respect to state-space size than alternative techniques. In this paper, we introduce an algorithm for performing reinforcement learning policy evaluation using MCMI. We demonstrate that MCMI improves on runtime over a maximum likelihood model-based policy evaluation approach and on both runtime and accuracy over the temporal differencing (TD) policy evaluation approach. We further improve on MCMI policy evaluation by adding an importance sampling technique to our algorithm to reduce the variance of our estimator. Lastly, we illustrate techniques for scaling up MCMI to large state spaces in order to perform policy improvement.
1212.2472
Budgeted Learning of Naive-Bayes Classifiers
cs.LG stat.ML
Frequently, acquiring training data has an associated cost. We consider the situation where the learner may purchase data during training, subject TO a budget. IN particular, we examine the CASE WHERE each feature label has an associated cost, AND the total cost OF ALL feature labels acquired during training must NOT exceed the budget.This paper compares methods FOR choosing which feature label TO purchase next, given the budget AND the CURRENT belief state OF naive Bayes model parameters.Whereas active learning has traditionally focused ON myopic(greedy) strategies FOR query selection, this paper presents a tractable method FOR incorporating knowledge OF the budget INTO the decision making process, which improves performance.
1212.2473
A Linear Belief Function Approach to Portfolio Evaluation
cs.AI q-fin.ST
By elaborating on the notion of linear belief functions (Dempster 1990; Liu 1996), we propose an elementary approach to knowledge representation for expert systems using linear belief functions. We show how to use basic matrices to represent market information and financial knowledge, including complete ignorance, statistical observations, subjective speculations, distributional assumptions, linear relations, and empirical asset pricing models. We then appeal to Dempster's rule of combination to integrate the knowledge for assessing an overall belief of portfolio performance, and updating the belief by incorporating additional information. We use an example of three gold stocks to illustrate the approach.
1212.2474
Learning Riemannian Metrics
cs.LG stat.ML
We propose a solution to the problem of estimating a Riemannian metric associated with a given differentiable manifold. The metric learning problem is based on minimizing the relative volume of a given set of points. We derive the details for a family of metrics on the multinomial simplex. The resulting metric has applications in text classification and bears some similarity to TFIDF representation of text documents.
1212.2475
Efficient Gradient Estimation for Motor Control Learning
cs.LG cs.SY
The task of estimating the gradient of a function in the presence of noise is central to several forms of reinforcement learning, including policy search methods. We present two techniques for reducing gradient estimation errors in the presence of observable input noise applied to the control signal. The first method extends the idea of a reinforcement baseline by fitting a local linear model to the function whose gradient is being estimated; we show how to find the linear model that minimizes the variance of the gradient estimate, and how to estimate the model from data. The second method improves this further by discounting components of the gradient vector that have high variance. These methods are applied to the problem of motor control learning, where actuator noise has a significant influence on behavior. In particular, we apply the techniques to learn locally optimal controllers for a dart-throwing task using a simulated three-link arm; we demonstrate that proposed methods significantly improve the reward function gradient estimate and, consequently, the learning curve, over existing methods.
1212.2476
Approximate Decomposition: A Method for Bounding and Estimating Probabilistic and Deterministic Queries
cs.AI
In this paper, we introduce a method for approximating the solution to inference and optimization tasks in uncertain and deterministic reasoning. Such tasks are in general intractable for exact algorithms because of the large number of dependency relationships in their structure. Our method effectively maps such a dense problem to a sparser one which is in some sense "closest". Exact methods can be run on the sparser problem to derive bounds on the original answer, which can be quite sharp. We present empirical results demonstrating that our method works well on the tasks of belief inference and finding the probability of the most probable explanation in belief networks, and finding the cost of the solution that violates the smallest number of constraints in constraint satisfaction problems. On one large CPCS network, for example, we were able to calculate upper and lower bounds on the conditional probability of a variable, given evidence, that were almost identical in the average case.
1212.2477
1 Billion Pages = 1 Million Dollars? Mining the Web to Play "Who Wants to be a Millionaire?"
cs.IR cs.CL
We exploit the redundancy and volume of information on the web to build a computerized player for the ABC TV game show 'Who Wants To Be A Millionaire?' The player consists of a question-answering module and a decision-making module. The question-answering module utilizes question transformation techniques, natural language parsing, multiple information retrieval algorithms, and multiple search engines; results are combined in the spirit of ensemble learning using an adaptive weighting scheme. Empirically, the system correctly answers about 75% of questions from the Millionaire CD-ROM, 3rd edition - general-interest trivia questions often about popular culture and common knowledge. The decision-making module chooses from allowable actions in the game in order to maximize expected risk-adjusted winnings, where the estimated probability of answering correctly is a function of past performance and confidence in in correctly answering the current question. When given a six question head start (i.e., when starting from the $2,000 level), we find that the system performs about as well on average as humans starting at the beginning. Our system demonstrates the potential of simple but well-chosen techniques for mining answers from unstructured information such as the web.
1212.2478
Preference-based Graphic Models for Collaborative Filtering
cs.IR
Collaborative filtering is a very useful general technique for exploiting the preference patterns of a group of users to predict the utility of items to a particular user. Previous research has studied several probabilistic graphic models for collaborative filtering with promising results. However, while these models have succeeded in capturing the similarity among users and items in one way or the other, none of them has considered the fact that users with similar interests in items can have very different rating patterns; some users tend to assign a higher rating to all items than other users. In this paper, we propose and study of two new graphic models that address the distinction between user preferences and ratings. In one model, called the decoupled model, we introduce two different variables to decouple a users preferences FROM his ratings. IN the other, called the preference model, we model the orderings OF items preferred BY a USER, rather than the USERs numerical ratings of items. Empirical study over two datasets of movie ratings shows that appropriate modeling of the distinction between user preferences and ratings improves the performance substantially and consistently. Specifically, the proposed decoupled model outperforms all five existing approaches that we compare with significantly, but the preference model is not very successful. These results suggest that explicit modeling of the underlying user preferences is very important for collaborative filtering, but we can not afford ignoring the rating information completely.
1212.2479
LAYERWIDTH: Analysis of a New Metric for Directed Acyclic Graphs
cs.DS cs.AI cs.DM
We analyze a new property of directed acyclic graphs (DAGs), called layerwidth, arising from a class of DAGs proposed by Eiter and Lukasiewicz. This class of DAGs permits certain problems of structural model-based causality and explanation to be tractably solved. In this paper, we first address an open question raised by Eiter and Lukasiewicz - the computational complexity of deciding whether a given graph has a bounded layerwidth. After proving that this problem is NP-complete, we proceed by proving numerous important properties of layerwidth that are helpful in efficiently computing the optimal layerwidth. Finally, we compare this new DAG property to two other important DAG properties: treewidth and bandwidth.
1212.2480
Approximate Inference and Constrained Optimization
cs.LG cs.AI stat.ML
Loopy and generalized belief propagation are popular algorithms for approximate inference in Markov random fields and Bayesian networks. Fixed points of these algorithms correspond to extrema of the Bethe and Kikuchi free energy. However, belief propagation does not always converge, which explains the need for approaches that explicitly minimize the Kikuchi/Bethe free energy, such as CCCP and UPS. Here we describe a class of algorithms that solves this typically nonconvex constrained minimization of the Kikuchi free energy through a sequence of convex constrained minimizations of upper bounds on the Kikuchi free energy. Intuitively one would expect tighter bounds to lead to faster algorithms, which is indeed convincingly demonstrated in our simulations. Several ideas are applied to obtain tight convex bounds that yield dramatic speed-ups over CCCP.
1212.2481
Monte-Carlo optimizations for resource allocation problems in stochastic network systems
cs.AI
Real-world distributed systems and networks are often unreliable and subject to random failures of its components. Such a stochastic behavior affects adversely the complexity of optimization tasks performed routinely upon such systems, in particular, various resource allocation tasks. In this work we investigate and develop Monte Carlo solutions for a class of two-stage optimization problems in stochastic networks in which the expected value of resource allocations before and after stochastic failures needs to be optimized. The limitation of these problems is that their exact solutions are exponential in the number of unreliable network components: thus, exact methods do not scale-up well to large networks often seen in practice. We first prove that Monte Carlo optimization methods can overcome the exponential bottleneck of exact methods. Next we support our theoretical findings on resource allocation experiments and show a very good scale-up potential of the new methods to large stochastic networks.
1212.2482
Implementation and Comparison of Solution Methods for Decision Processes with Non-Markovian Rewards
cs.AI
This paper examines a number of solution methods for decision processes with non-Markovian rewards (NMRDPs). They all exploit a temporal logic specification of the reward function to automatically translate the NMRDP into an equivalent Markov decision process (MDP) amenable to well-known MDP solution methods. They differ however in the representation of the target MDP and the class of MDP solution methods to which they are suited. As a result, they adopt different temporal logics and different translations. Unfortunately, no implementation of these methods nor experimental let alone comparative results have ever been reported. This paper is the first step towards filling this gap. We describe an integrated system for solving NMRDPs which implements these methods and several variants under a common interface; we use it to compare the various approaches and identify the problem features favoring one over the other.
1212.2483
Sufficient Dimensionality Reduction with Irrelevant Statistics
cs.LG stat.ML
The problem of finding a reduced dimensionality representation of categorical variables while preserving their most relevant characteristics is fundamental for the analysis of complex data. Specifically, given a co-occurrence matrix of two variables, one often seeks a compact representation of one variable which preserves information about the other variable. We have recently introduced ``Sufficient Dimensionality Reduction' [GT-2003], a method that extracts continuous reduced dimensional features whose measurements (i.e., expectation values) capture maximal mutual information among the variables. However, such measurements often capture information that is irrelevant for a given task. Widely known examples are illumination conditions, which are irrelevant as features for face recognition, writing style which is irrelevant as a feature for content classification, and intonation which is irrelevant as a feature for speech recognition. Such irrelevance cannot be deduced apriori, since it depends on the details of the task, and is thus inherently ill defined in the purely unsupervised case. Separating relevant from irrelevant features can be achieved using additional side data that contains such irrelevant structures. This approach was taken in [CT-2002], extending the information bottleneck method, which uses clustering to compress the data. Here we use this side-information framework to identify features whose measurements are maximally informative for the original data set, but carry as little information as possible on a side data set. In statistical terms this can be understood as extracting statistics which are maximally sufficient for the original dataset, while simultaneously maximally ancillary for the side dataset. We formulate this tradeoff as a constrained optimization problem and characterize its solutions. We then derive a gradient descent algorithm for this problem, which is based on the Generalized Iterative Scaling method for finding maximum entropy distributions. The method is demonstrated on synthetic data, as well as on real face recognition datasets, and is shown to outperform standard methods such as oriented PCA.
1212.2484
Decision Making with Partially Consonant Belief Functions
cs.AI
This paper studies decision making for Walley's partially consonant belief functions (pcb). In a pcb, the set of foci are partitioned. Within each partition, the foci are nested. The pcb class includes probability functions and possibility functions as extreme cases. Unlike earlier proposals for a decision theory with belief functions, we employ an axiomatic approach. We adopt an axiom system similar in spirit to von Neumann - Morgenstern's linear utility theory for a preference relation on pcb lotteries. We prove a representation theorem for this relation. Utility for a pcb lottery is a combination of linear utility for probabilistic lottery and binary utility for possibilistic lottery.
1212.2485
Phase Transition of Tractability in Constraint Satisfaction and Bayesian Network Inference
cs.AI cs.DS
There has been great interest in identifying tractable subclasses of NP complete problems and designing efficient algorithms for these tractable classes. Constraint satisfaction and Bayesian network inference are two examples of such problems that are of great importance in AI and algorithms. In this paper we study, under the frameworks of random constraint satisfaction problems and random Bayesian networks, a typical tractable subclass characterized by the treewidth of the problems. We show that the property of having a bounded treewidth for CSPs and Bayesian network inference problem has a phase transition that occurs while the underlying structures of problems are still sparse. This implies that algorithms making use of treewidth based structural knowledge only work efficiently in a limited range of random instance.
1212.2486
Extending Factor Graphs so as to Unify Directed and Undirected Graphical Models
cs.AI
The two most popular types of graphical model are directed models (Bayesian networks) and undirected models (Markov random fields, or MRFs). Directed and undirected models offer complementary properties in model construction, expressing conditional independencies, expressing arbitrary factorizations of joint distributions, and formulating message-passing inference algorithms. We show that the strengths of these two representations can be combined in a single type of graphical model called a 'factor graph'. Every Bayesian network or MRF can be easily converted to a factor graph that expresses the same conditional independencies, expresses the same factorization of the joint distribution, and can be used for probabilistic inference through application of a single, simple message-passing algorithm. In contrast to chain graphs, where message-passing is implemented on a hypergraph, message-passing can be directly implemented on the factor graph. We describe a modified 'Bayes-ball' algorithm for establishing conditional independence in factor graphs, and we show that factor graphs form a strict superset of Bayesian networks and MRFs. In particular, we give an example of a commonly-used 'mixture of experts' model fragment, whose independencies cannot be represented in a Bayesian network or an MRF, but can be represented in a factor graph. We finish by giving examples of real-world problems that are not well suited to representation in Bayesian networks and MRFs, but are well-suited to representation in factor graphs.
1212.2487
Locally Weighted Naive Bayes
cs.LG stat.ML
Despite its simplicity, the naive Bayes classifier has surprised machine learning researchers by exhibiting good performance on a variety of learning problems. Encouraged by these results, researchers have looked to overcome naive Bayes primary weakness - attribute independence - and improve the performance of the algorithm. This paper presents a locally weighted version of naive Bayes that relaxes the independence assumption by learning local models at prediction time. Experimental results show that locally weighted naive Bayes rarely degrades accuracy compared to standard naive Bayes and, in many cases, improves accuracy dramatically. The main advantage of this method compared to other techniques for enhancing naive Bayes is its conceptual and computational simplicity.
1212.2488
A Distance-Based Branch and Bound Feature Selection Algorithm
cs.LG stat.ML
There is no known efficient method for selecting k Gaussian features from n which achieve the lowest Bayesian classification error. We show an example of how greedy algorithms faced with this task are led to give results that are not optimal. This motivates us to propose a more robust approach. We present a Branch and Bound algorithm for finding a subset of k independent Gaussian features which minimizes the naive Bayesian classification error. Our algorithm uses additive monotonic distance measures to produce bounds for the Bayesian classification error in order to exclude many feature subsets from evaluation, while still returning an optimal solution. We test our method on synthetic data as well as data obtained from gene expression profiling.
1212.2490
On the Convergence of Bound Optimization Algorithms
cs.LG stat.ML
Many practitioners who use the EM algorithm complain that it is sometimes slow. When does this happen, and what can be done about it? In this paper, we study the general class of bound optimization algorithms - including Expectation-Maximization, Iterative Scaling and CCCP - and their relationship to direct optimization algorithms such as gradient-based methods for parameter learning. We derive a general relationship between the updates performed by bound optimization methods and those of gradient and second-order methods and identify analytic conditions under which bound optimization algorithms exhibit quasi-Newton behavior, and conditions under which they possess poor, first-order convergence. Based on this analysis, we consider several specific algorithms, interpret and analyze their convergence properties and provide some recipes for preprocessing input to these algorithms to yield faster convergence behavior. We report empirical results supporting our analysis and showing that simple data preprocessing can result in dramatically improved performance of bound optimizers in practice.
1212.2491
Automated Analytic Asymptotic Evaluation of the Marginal Likelihood for Latent Models
cs.LG stat.ML
We present and implement two algorithms for analytic asymptotic evaluation of the marginal likelihood of data given a Bayesian network with hidden nodes. As shown by previous work, this evaluation is particularly hard for latent Bayesian network models, namely networks that include hidden variables, where asymptotic approximation deviates from the standard BIC score. Our algorithms solve two central difficulties in asymptotic evaluation of marginal likelihood integrals, namely, evaluation of regular dimensionality drop for latent Bayesian network models and computation of non-standard approximation formulas for singular statistics for these models. The presented algorithms are implemented in Matlab and Maple and their usage is demonstrated for marginal likelihood approximations for Bayesian networks with hidden variables.
1212.2493
Decentralized Sensor Fusion With Distributed Particle Filters
cs.AI cs.RO
This paper presents a scalable Bayesian technique for decentralized state estimation from multiple platforms in dynamic environments. As has long been recognized, centralized architectures impose severe scaling limitations for distributed systems due to the enormous communication overheads. We propose a strictly decentralized approach in which only nearby platforms exchange information. They do so through an interactive communication protocol aimed at maximizing information flow. Our approach is evaluated in the context of a distributed surveillance scenario that arises in a robotic system for playing the game of laser tag. Our results, both from simulation and using physical robots, illustrate an unprecedented scaling capability to large teams of vehicles.
1212.2494
Learning Generative Models of Similarity Matrices
cs.LG stat.ML
We describe a probabilistic (generative) view of affinity matrices along with inference algorithms for a subclass of problems associated with data clustering. This probabilistic view is helpful in understanding different models and algorithms that are based on affinity functions OF the data. IN particular, we show how(greedy) inference FOR a specific probabilistic model IS equivalent TO the spectral clustering algorithm.It also provides a framework FOR developing new algorithms AND extended models. AS one CASE, we present new generative data clustering models that allow us TO infer the underlying distance measure suitable for the clustering problem at hand. These models seem to perform well in a larger class of problems for which other clustering algorithms (including spectral clustering) usually fail. Experimental evaluation was performed in a variety point data sets, showing excellent performance.
1212.2495
Policy-contingent abstraction for robust robot control
cs.RO cs.AI cs.SY
This paper presents a scalable control algorithm that enables a deployed mobile robot system to make high-level decisions under full consideration of its probabilistic belief. Our approach is based on insights from the rich literature of hierarchical controllers and hierarchical MDPs. The resulting controller has been successfully deployed in a nursing facility near Pittsburgh, PA. To the best of our knowledge, this work is a unique instance of applying POMDPs to high-level robotic control problems.
1212.2496
An Axiomatic Approach to Robustness in Search Problems with Multiple Scenarios
cs.AI
This paper is devoted to the search of robust solutions in state space graphs when costs depend on scenarios. We first present axiomatic requirements for preference compatibility with the intuitive idea of robustness.This leads us to propose the Lorenz dominance rule as a basis for robustness analysis. Then, after presenting complexity results about the determination of robust solutions, we propose a new sophistication of A* specially designed to determine the set of robust paths in a state space graph. The behavior of the algorithm is illustrated on a small example. Finally, an axiomatic justification of the refinement of robustness by an OWA criterion is provided.