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Title: Contextual Bandit Algorithms with Supervised Learning Guarantees
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Abstract: We address the problem of learning in an online, bandit setting where the learner must repeatedly select among $K$ actions, but only receives partial feedback based on its choices. We establish two new facts: First, using a new algorithm called Exp4.P, we show that it is possible to compete with the best in a set of $N$ experts with probability $1-\delta$ while incurring regret at most $O()$ over $T$ time steps. The new algorithm is tested empirically in a large-scale, real-world dataset. Second, we give a new algorithm called VE that competes with a possibly infinite set of policies of VC-dimension $d$ while incurring regret at most $O(\sqrtT(d\ln(T) + \ln (1/\delta)))$ with probability $1-\delta$. These guarantees improve on those of all previous algorithms, whether in a stochastic or adversarial environment, and bring us closer to providing supervised learning type guarantees for the contextual bandit setting.
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Title: The Degrees of Freedom of Partial Least Squares Regression
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Abstract: The derivation of statistical properties for Partial Least Squares regression can be a challenging task. The reason is that the construction of latent components from the predictor variables also depends on the response variable. While this typically leads to good performance and interpretable models in practice, it makes the statistical analysis more involved. In this work, we study the intrinsic complexity of Partial Least Squares Regression. Our contribution is an unbiased estimate of its Degrees of Freedom. It is defined as the trace of the first derivative of the fitted values, seen as a function of the response. We establish two equivalent representations that rely on the close connection of Partial Least Squares to matrix decompositions and Krylov subspace techniques. We show that the Degrees of Freedom depend on the collinearity of the predictor variables: The lower the collinearity is, the higher the Degrees of Freedom are. In particular, they are typically higher than the naive approach that defines the Degrees of Freedom as the number of components. Further, we illustrate how the Degrees of Freedom approach can be used for the comparison of different regression methods. In the experimental section, we show that our Degrees of Freedom estimate in combination with information criteria is useful for model selection.
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Title: Design of a Smart Unmanned Ground Vehicle for Hazardous Environments
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Abstract: A smart Unmanned Ground Vehicle (UGV) is designed and developed for some application specific missions to operate predominantly in hazardous environments. In our work, we have developed a small and lightweight vehicle to operate in general cross-country terrains in or without daylight. The UGV can send visual feedbacks to the operator at a remote location. Onboard infrared sensors can detect the obstacles around the UGV and sends signals to the operator.
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Title: Redundancy, Deduction Schemes, and Minimum-Size Bases for Association Rules
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Abstract: Association rules are among the most widely employed data analysis methods in the field of Data Mining. An association rule is a form of partial implication between two sets of binary variables. In the most common approach, association rules are parameterized by a lower bound on their confidence, which is the empirical conditional probability of their consequent given the antecedent, and/or by some other parameter bounds such as "support" or deviation from independence. We study here notions of redundancy among association rules from a fundamental perspective. We see each transaction in a dataset as an interpretation (or model) in the propositional logic sense, and consider existing notions of redundancy, that is, of logical entailment, among association rules, of the form "any dataset in which this first rule holds must obey also that second rule, therefore the second is redundant". We discuss several existing alternative definitions of redundancy between association rules and provide new characterizations and relationships among them. We show that the main alternatives we discuss correspond actually to just two variants, which differ in the treatment of full-confidence implications. For each of these two notions of redundancy, we provide a sound and complete deduction calculus, and we show how to construct complete bases (that is, axiomatizations) of absolutely minimum size in terms of the number of rules. We explore finally an approach to redundancy with respect to several association rules, and fully characterize its simplest case of two partial premises.
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Title: CLD-shaped Brushstrokes in Non-Photorealistic Rendering
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Abstract: Rendering techniques based on a random grid can be improved by adapting brushstrokes to the shape of different areas of the original picture. In this paper, the concept of Coherence Length Diagram is applied to determine the adaptive brushstrokes, in order to simulate an impressionist painting. Some examples are provided to instance the proposed algorithm.
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Title: The distribution and quantiles of functionals of weighted empirical distributions when observations have different distributions
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Abstract: This paper extends Edgeworth-Cornish-Fisher expansions for the distribution and quantiles of nonparametric estimates in two ways. Firstly it allows observations to have different distributions. Secondly it allows the observations to be weighted in a predetermined way. The use of weighted estimates has a long history including applications to regression, rank statistics and Bayes theory. However, asymptotic results have generally been only first order (the CLT and weak convergence). We give third order asymptotics for the distribution and percentiles of any smooth functional of a weighted empirical distribution, thus allowing a considerable increase in accuracy over earlier CLT results. Consider independent non-identically distributed (\it non-iid) observations $X_1n, ..., X_nn$ in $R^s$. Let $(x)$ be their \it weighted empirical distribution with weights $w_1n, ..., w_nn$. We obtain cumulant expansions and hence Edgeworth-Cornish-Fisher expansions for $T()$ for any smooth functional $T(\cdot)$ by extending the concepts of von Mises derivatives to signed measures of total measure 1. As an example we give the cumulant coefficients needed for Edgeworth-Cornish-Fisher expansions to $O(n^-3/2)$ for the sample variance when observations are non-iid.
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Title: Nonparametric Estimation and On-Line Prediction for General Stationary Ergodic Sources
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Abstract: We proposed a learning algorithm for nonparametric estimation and on-line prediction for general stationary ergodic sources. We prepare histograms each of which estimates the probability as a finite distribution, and mixture them with weights to construct an estimator. The whole analysis is based on measure theory. The estimator works whether the source is discrete or continuous. If it is stationary ergodic, then the measure theoretically given Kullback-Leibler information divided by the sequence length $n$ converges to zero as $n$ goes to infinity. In particular, for continuous sources, the method does not require existence of a probability density function.
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Title: Feature Importance in Bayesian Assessment of Newborn Brain Maturity from EEG
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Abstract: The methodology of Bayesian Model Averaging (BMA) is applied for assessment of newborn brain maturity from sleep EEG. In theory this methodology provides the most accurate assessments of uncertainty in decisions. However, the existing BMA techniques have been shown providing biased assessments in the absence of some prior information enabling to explore model parameter space in details within a reasonable time. The lack in details leads to disproportional sampling from the posterior distribution. In case of the EEG assessment of brain maturity, BMA results can be biased because of the absence of information about EEG feature importance. In this paper we explore how the posterior information about EEG features can be used in order to reduce a negative impact of disproportional sampling on BMA performance. We use EEG data recorded from sleeping newborns to test the efficiency of the proposed BMA technique.
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Title: Principal Component Analysis with Contaminated Data: The High Dimensional Case
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Abstract: We consider the dimensionality-reduction problem (finding a subspace approximation of observed data) for contaminated data in the high dimensional regime, where the number of observations is of the same magnitude as the number of variables of each observation, and the data set contains some (arbitrarily) corrupted observations. We propose a High-dimensional Robust Principal Component Analysis (HR-PCA) algorithm that is tractable, robust to contaminated points, and easily kernelizable. The resulting subspace has a bounded deviation from the desired one, achieves maximal robustness -- a breakdown point of 50% while all existing algorithms have a breakdown point of zero, and unlike ordinary PCA algorithms, achieves optimality in the limit case where the proportion of corrupted points goes to zero.
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Title: Syntactic Topic Models
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Abstract: The syntactic topic model (STM) is a Bayesian nonparametric model of language that discovers latent distributions of words (topics) that are both semantically and syntactically coherent. The STM models dependency parsed corpora where sentences are grouped into documents. It assumes that each word is drawn from a latent topic chosen by combining document-level features and the local syntactic context. Each document has a distribution over latent topics, as in topic models, which provides the semantic consistency. Each element in the dependency parse tree also has a distribution over the topics of its children, as in latent-state syntax models, which provides the syntactic consistency. These distributions are convolved so that the topic of each word is likely under both its document and syntactic context. We derive a fast posterior inference algorithm based on variational methods. We report qualitative and quantitative studies on both synthetic data and hand-parsed documents. We show that the STM is a more predictive model of language than current models based only on syntax or only on topics.
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Title: Non-Central Limit Theorem Statistical Analysis for the "Long-tailed" Internet Society
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Abstract: This article presents a statistical analysis method and introduces the corresponding software package "tailstat," which is believed to be widely applicable to today's internet society. The proposed method facilitates statistical analyses with small sample sets from given populations, which render the central limit theorem inapplicable. A large-scale case study demonstrates the effectiveness of the method and provides implications for applying similar analyses to other cases.
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Title: A copula based approach to adaptive sampling
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Abstract: Our article is concerned with adaptive sampling schemes for Bayesian inference that update the proposal densities using previous iterates. We introduce a copula based proposal density which is made more efficient by combining it with antithetic variable sampling. We compare the copula based proposal to an adaptive proposal density based on a multivariate mixture of normals and an adaptive random walk Metropolis proposal. We also introduce a refinement of the random walk proposal which performs better for multimodal target distributions. We compare the sampling schemes using challenging but realistic models and priors applied to real data examples. The results show that for the examples studied, the adaptive independent proposals are much more efficient than the adaptive random walk proposals and that in general the copula based proposal has the best acceptance rates and lowest inefficiencies.
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Title: Gaussian Process Structural Equation Models with Latent Variables
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Abstract: In a variety of disciplines such as social sciences, psychology, medicine and economics, the recorded data are considered to be noisy measurements of latent variables connected by some causal structure. This corresponds to a family of graphical models known as the structural equation model with latent variables. While linear non-Gaussian variants have been well-studied, inference in nonparametric structural equation models is still underdeveloped. We introduce a sparse Gaussian process parameterization that defines a non-linear structure connecting latent variables, unlike common formulations of Gaussian process latent variable models. The sparse parameterization is given a full Bayesian treatment without compromising Markov chain Monte Carlo efficiency. We compare the stability of the sampling procedure and the predictive ability of the model against the current practice.
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Title: SLAM : Solutions lexicales automatique pour m\'etaphores
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Abstract: This article presents SLAM, an Automatic Solver for Lexical Metaphors like ?d\'eshabiller* une pomme? (to undress* an apple). SLAM calculates a conventional solution for these productions. To carry on it, SLAM has to intersect the paradigmatic axis of the metaphorical verb ?d\'eshabiller*?, where ?peler? (?to peel?) comes closer, with a syntagmatic axis that comes from a corpus where ?peler une pomme? (to peel an apple) is semantically and syntactically regular. We test this model on DicoSyn, which is a ?small world? network of synonyms, to compute the paradigmatic axis and on Frantext.20, a French corpus, to compute the syntagmatic axis. Further, we evaluate the model with a sample of an experimental corpus of the database of Flexsem
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Title: Less Regret via Online Conditioning
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Abstract: We analyze and evaluate an online gradient descent algorithm with adaptive per-coordinate adjustment of learning rates. Our algorithm can be thought of as an online version of batch gradient descent with a diagonal preconditioner. This approach leads to regret bounds that are stronger than those of standard online gradient descent for general online convex optimization problems. Experimentally, we show that our algorithm is competitive with state-of-the-art algorithms for large scale machine learning problems.
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Title: Adaptive Bound Optimization for Online Convex Optimization
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Abstract: We introduce a new online convex optimization algorithm that adaptively chooses its regularization function based on the loss functions observed so far. This is in contrast to previous algorithms that use a fixed regularization function such as L2-squared, and modify it only via a single time-dependent parameter. Our algorithm's regret bounds are worst-case optimal, and for certain realistic classes of loss functions they are much better than existing bounds. These bounds are problem-dependent, which means they can exploit the structure of the actual problem instance. Critically, however, our algorithm does not need to know this structure in advance. Rather, we prove competitive guarantees that show the algorithm provides a bound within a constant factor of the best possible bound (of a certain functional form) in hindsight.
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Title: Asymptotic Analysis of Generative Semi-Supervised Learning
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Abstract: Semisupervised learning has emerged as a popular framework for improving modeling accuracy while controlling labeling cost. Based on an extension of stochastic composite likelihood we quantify the asymptotic accuracy of generative semi-supervised learning. In doing so, we complement distribution-free analysis by providing an alternative framework to measure the value associated with different labeling policies and resolve the fundamental question of how much data to label and in what manner. We demonstrate our approach with both simulation studies and real world experiments using naive Bayes for text classification and MRFs and CRFs for structured prediction in NLP.
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Title: A New Understanding of Prediction Markets Via No-Regret Learning
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Abstract: We explore the striking mathematical connections that exist between market scoring rules, cost function based prediction markets, and no-regret learning. We show that any cost function based prediction market can be interpreted as an algorithm for the commonly studied problem of learning from expert advice by equating trades made in the market with losses observed by the learning algorithm. If the loss of the market organizer is bounded, this bound can be used to derive an O(sqrt(T)) regret bound for the corresponding learning algorithm. We then show that the class of markets with convex cost functions exactly corresponds to the class of Follow the Regularized Leader learning algorithms, with the choice of a cost function in the market corresponding to the choice of a regularizer in the learning problem. Finally, we show an equivalence between market scoring rules and prediction markets with convex cost functions. This implies that market scoring rules can also be interpreted naturally as Follow the Regularized Leader algorithms, and may be of independent interest. These connections provide new insight into how it is that commonly studied markets, such as the Logarithmic Market Scoring Rule, can aggregate opinions into accurate estimates of the likelihood of future events.
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Title: Comment on "Fastest learning in small-world neural networks"
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Abstract: This comment reexamines Simard et al.'s work in [D. Simard, L. Nadeau, H. Kroger, Phys. Lett. A 336 (2005) 8-15]. We found that Simard et al. calculated mistakenly the local connectivity lengths Dlocal of networks. The right results of Dlocal are presented and the supervised learning performance of feedforward neural networks (FNNs) with different rewirings are re-investigated in this comment. This comment discredits Simard et al's work by two conclusions: 1) Rewiring connections of FNNs cannot generate networks with small-world connectivity; 2) For different training sets, there do not exist networks with a certain number of rewirings generating reduced learning errors than networks with other numbers of rewiring.
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Title: Security Analysis of Online Centroid Anomaly Detection
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Abstract: Security issues are crucial in a number of machine learning applications, especially in scenarios dealing with human activity rather than natural phenomena (e.g., information ranking, spam detection, malware detection, etc.). It is to be expected in such cases that learning algorithms will have to deal with manipulated data aimed at hampering decision making. Although some previous work addressed the handling of malicious data in the context of supervised learning, very little is known about the behavior of anomaly detection methods in such scenarios. In this contribution we analyze the performance of a particular method -- online centroid anomaly detection -- in the presence of adversarial noise. Our analysis addresses the following security-related issues: formalization of learning and attack processes, derivation of an optimal attack, analysis of its efficiency and constraints. We derive bounds on the effectiveness of a poisoning attack against centroid anomaly under different conditions: bounded and unbounded percentage of traffic, and bounded false positive rate. Our bounds show that whereas a poisoning attack can be effectively staged in the unconstrained case, it can be made arbitrarily difficult (a strict upper bound on the attacker's gain) if external constraints are properly used. Our experimental evaluation carried out on real HTTP and exploit traces confirms the tightness of our theoretical bounds and practicality of our protection mechanisms.
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Title: Non-Sparse Regularization for Multiple Kernel Learning
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Abstract: Learning linear combinations of multiple kernels is an appealing strategy when the right choice of features is unknown. Previous approaches to multiple kernel learning (MKL) promote sparse kernel combinations to support interpretability and scalability. Unfortunately, this 1-norm MKL is rarely observed to outperform trivial baselines in practical applications. To allow for robust kernel mixtures, we generalize MKL to arbitrary norms. We devise new insights on the connection between several existing MKL formulations and develop two efficient interleaved optimization strategies for arbitrary norms, like p-norms with p>1. Empirically, we demonstrate that the interleaved optimization strategies are much faster compared to the commonly used wrapper approaches. A theoretical analysis and an experiment on controlled artificial data experiment sheds light on the appropriateness of sparse, non-sparse and $\ell_\infty$-norm MKL in various scenarios. Empirical applications of p-norm MKL to three real-world problems from computational biology show that non-sparse MKL achieves accuracies that go beyond the state-of-the-art.
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Title: Learning from Logged Implicit Exploration Data
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Abstract: We provide a sound and consistent foundation for the use of exploration data in "contextual bandit" or "partially labeled" settings where only the value of a chosen action is learned. The primary challenge in a variety of settings is that the exploration policy, in which "offline" data is logged, is not explicitly known. Prior solutions here require either control of the actions during the learning process, recorded random exploration, or actions chosen obliviously in a repeated manner. The techniques reported here lift these restrictions, allowing the learning of a policy for choosing actions given features from historical data where no randomization occurred or was logged. We empirically verify our solution on two reasonably sized sets of real-world data obtained from Yahoo!.
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Title: A Contextual-Bandit Approach to Personalized News Article Recommendation
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Abstract: Personalized web services strive to adapt their services (advertisements, news articles, etc) to individual users by making use of both content and user information. Despite a few recent advances, this problem remains challenging for at least two reasons. First, web service is featured with dynamically changing pools of content, rendering traditional collaborative filtering methods inapplicable. Second, the scale of most web services of practical interest calls for solutions that are both fast in learning and computation. In this work, we model personalized recommendation of news articles as a contextual bandit problem, a principled approach in which a learning algorithm sequentially selects articles to serve users based on contextual information about the users and articles, while simultaneously adapting its article-selection strategy based on user-click feedback to maximize total user clicks. The contributions of this work are three-fold. First, we propose a new, general contextual bandit algorithm that is computationally efficient and well motivated from learning theory. Second, we argue that any bandit algorithm can be reliably evaluated offline using previously recorded random traffic. Finally, using this offline evaluation method, we successfully applied our new algorithm to a Yahoo! Front Page Today Module dataset containing over 33 million events. Results showed a 12.5% click lift compared to a standard context-free bandit algorithm, and the advantage becomes even greater when data gets more scarce.
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Title: Product-limit estimators of the gap time distribution of a renewal process under different sampling patterns
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Abstract: Nonparametric estimation of the gap time distribution in a simple renewal process may be considered a problem in survival analysis under particular sampling frames corresponding to how the renewal process is observed. This note describes several such situations where simple product limit estimators, though inefficient, may still be useful.
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Title: History of applications of martingales in survival analysis
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Abstract: The paper traces the development of the use of martingale methods in survival analysis from the mid 1970's to the early 1990's. This development was initiated by Aalen's Berkeley PhD-thesis in 1975, progressed through the work on estimation of Markov transition probabilities, non-parametric tests and Cox's regression model in the late 1970's and early 1980's, and it was consolidated in the early 1990's with the publication of the monographs by Fleming and Harrington (1991) and Andersen, Borgan, Gill and Keiding (1993). The development was made possible by an unusually fast technology transfer of pure mathematical concepts, primarily from French probability, into practical biostatistical methodology, and we attempt to outline some of the personal relationships that helped this happen. We also point out that survival analysis was ready for this development since the martingale ideas inherent in the deep understanding of temporal development so intrinsic to the French theory of processes were already quite close to the surface in survival analysis.
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Title: Detecting Weak but Hierarchically-Structured Patterns in Networks
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Abstract: The ability to detect weak distributed activation patterns in networks is critical to several applications, such as identifying the onset of anomalous activity or incipient congestion in the Internet, or faint traces of a biochemical spread by a sensor network. This is a challenging problem since weak distributed patterns can be invisible in per node statistics as well as a global network-wide aggregate. Most prior work considers situations in which the activation/non-activation of each node is statistically independent, but this is unrealistic in many problems. In this paper, we consider structured patterns arising from statistical dependencies in the activation process. Our contributions are three-fold. First, we propose a sparsifying transform that succinctly represents structured activation patterns that conform to a hierarchical dependency graph. Second, we establish that the proposed transform facilitates detection of very weak activation patterns that cannot be detected with existing methods. Third, we show that the structure of the hierarchical dependency graph governing the activation process, and hence the network transform, can be learnt from very few (logarithmic in network size) independent snapshots of network activity.
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Title: Why has (reasonably accurate) Automatic Speech Recognition been so hard to achieve?
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Abstract: Hidden Markov models (HMMs) have been successfully applied to automatic speech recognition for more than 35 years in spite of the fact that a key HMM assumption -- the statistical independence of frames -- is obviously violated by speech data. In fact, this data/model mismatch has inspired many attempts to modify or replace HMMs with alternative models that are better able to take into account the statistical dependence of frames. However it is fair to say that in 2010 the HMM is the consensus model of choice for speech recognition and that HMMs are at the heart of both commercially available products and contemporary research systems. In this paper we present a preliminary exploration aimed at understanding how speech data depart from HMMs and what effect this departure has on the accuracy of HMM-based speech recognition. Our analysis uses standard diagnostic tools from the field of statistics -- hypothesis testing, simulation and resampling -- which are rarely used in the field of speech recognition. Our main result, obtained by novel manipulations of real and resampled data, demonstrates that real data have statistical dependency and that this dependency is responsible for significant numbers of recognition errors. We also demonstrate, using simulation and resampling, that if we `remove' the statistical dependency from data, then the resulting recognition error rates become negligible. Taken together, these results suggest that a better understanding of the structure of the statistical dependency in speech data is a crucial first step towards improving HMM-based speech recognition.
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Title: Perfect simulation using dominated coupling from the past with application to area-interaction point processes and wavelet thresholding
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Abstract: We consider perfect simulation algorithms for locally stable point processes based on dominated coupling from the past, and apply these methods in two different contexts. A new version of the algorithm is developed which is feasible for processes which are neither purely attractive nor purely repulsive. Such processes include multiscale area-interaction processes, which are capable of modelling point patterns whose clustering structure varies across scales. The other topic considered is nonparametric regression using wavelets, where we use a suitable area-interaction process on the discrete space of indices of wavelet coefficients to model the notion that if one wavelet coefficient is non-zero then it is more likely that neighbouring coefficients will be also. A method based on perfect simulation within this model shows promising results compared to the standard methods which threshold coefficients independently.
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Title: Statistical inference for time-changed L\'evy processes via composite characteristic function estimation
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Abstract: In this article, the problem of semi-parametric inference on the parameters of a multidimensional L\'evy process $L_t$ with independent components based on the low-frequency observations of the corresponding time-changed L\'evy process $L_(t)$, where $$ is a nonnegative, nondecreasing real-valued process independent of $L_t$, is studied. We show that this problem is closely related to the problem of composite function estimation that has recently gotten much attention in statistical literature. Under suitable identifiability conditions, we propose a consistent estimate for the L\'evy density of $L_t$ and derive the uniform as well as the pointwise convergence rates of the estimate proposed. Moreover, we prove that the rates obtained are optimal in a minimax sense over suitable classes of time-changed L\'evy models. Finally, we present a simulation study showing the performance of our estimation algorithm in the case of time-changed Normal Inverse Gaussian (NIG) L\'evy processes.
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Title: Kernel methods and minimum contrast estimators for empirical deconvolution
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Abstract: We survey classical kernel methods for providing nonparametric solutions to problems involving measurement error. In particular we outline kernel-based methodology in this setting, and discuss its basic properties. Then we point to close connections that exist between kernel methods and much newer approaches based on minimum contrast techniques. The connections are through use of the sinc kernel for kernel-based inference. This `infinite order' kernel is not often used explicitly for kernel-based deconvolution, although it has received attention in more conventional problems where measurement error is not an issue. We show that in a comparison between kernel methods for density deconvolution, and their counterparts based on minimum contrast, the two approaches give identical results on a grid which becomes increasingly fine as the bandwidth decreases. In consequence, the main numerical differences between these two techniques are arguably the result of different approaches to choosing smoothing parameters.
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Title: Further Exploration of the Dendritic Cell Algorithm: Antigen Multiplier and Time Windows
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Abstract: As an immune-inspired algorithm, the Dendritic Cell Algorithm (DCA), produces promising performances in the field of anomaly detection. This paper presents the application of the DCA to a standard data set, the KDD 99 data set. The results of different implementation versions of the DXA, including the antigen multiplier and moving time windows are reported. The real-valued Negative Selection Algorithm (NSA) using constant-sized detectors and the C4.5 decision tree algorithm are used, to conduct a baseline comparison. The results suggest that the DCA is applicable to KDD 99 data set, and the antigen multiplier and moving time windows have the same effect on the DCA for this particular data set. The real-valued NSA with constant-sized detectors is not applicable to the data set, and the C4.5 decision tree algorithm provides a benchmark of the classification performance for this data set.
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Title: Change of word types to word tokens ratio in the course of translation (based on Russian translations of K. Vonnegut novels)
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Abstract: The article provides lexical statistical analysis of K. Vonnegut's two novels and their Russian translations. It is found out that there happen some changes between the speed of word types and word tokens ratio change in the source and target texts. The author hypothesizes that these changes are typical for English-Russian translations, and moreover, they represent an example of Baker's translation feature of levelling out.
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Title: libtissue - implementing innate immunity
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Abstract: In a previous paper the authors argued the case for incorporating ideas from innate immunity into articficial immune systems (AISs) and presented an outline for a conceptual framework for such systems. A number of key general properties observed in the biological innate and adaptive immune systems were hughlighted, and how such properties might be instantiated in artificial systems was discussed in detail. The next logical step is to take these ideas and build a software system with which AISs with these properties can be implemented and experimentally evaluated. This paper reports on the results of that step - the libtissue system.
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Title: Deep Big Simple Neural Nets Excel on Handwritten Digit Recognition
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