Bayesian invariant measurements of generalisation for discrete distributions

Neural network learning rules can be viewed as statistical estimators. They should be studied in Bayesian framework even if they are not Bayesian estimators. Generalisation should be measured by the divergence between the true distribution and the estimated distribution. Information divergences are invariant measurements of the divergence between two distributions. The posterior average information divergence is used to measure the generalisation ability of a network. The optimal estimators for multinomial distributions with Dirichlet priors are studied in detail. This confirms that the definition is compatible with intuition. The results also show that many commonly used methods can be put under this unified framework, by assume special priors and special divergences.

Fast reconstruction of harmonic functions from Cauchy data using the Dirichlet-to-Neumann map and integral equations

We propose and investigate a method for the stable determination of a harmonic function from knowledge of its value and its normal derivative on a part of the boundary of the (bounded) solution domain (Cauchy problem). We reformulate the Cauchy problem as an operator equation on the boundary using the Dirichlet-to-Neumann map. To discretize the obtained operator, we modify and employ a method denoted as Classic II given in [J. Helsing, Faster convergence and higher accuracy for the Dirichlet–Neumann map, J. Comput. Phys. 228 (2009), pp. 2578–2576, Section 3], which is based on Fredholm integral equations and Nyström discretization schemes. Then, for stability reasons, to solve the discretized integral equation we use the method of smoothing projection introduced in [J. Helsing and B.T. Johansson, Fast reconstruction of harmonic functions from Cauchy data using integral equation techniques, Inverse Probl. Sci. Eng. 18 (2010), pp. 381–399, Section 7], which makes it possible to solve the discretized operator equation in a stable way with minor computational cost and high accuracy. With this approach, for sufficiently smooth Cauchy data, the normal derivative can also be accurately computed on the part of the boundary where no data is initially given.

Numerical solution of the Dirichlet initial boundary value problem for the heat equation in exterior 3-dimensional domains using integral equations

A numerical method for the Dirichlet initial boundary value problem for the heat equation in the exterior and unbounded region of a smooth closed simply connected 3-dimensional domain is proposed and investigated. This method is based on a combination of a Laguerre transformation with respect to the time variable and an integral equation approach in the spatial variables. Using the Laguerre transformation in time reduces the parabolic problem to a sequence of stationary elliptic problems which are solved by a boundary layer approach giving a sequence of boundary integral equations of the first kind to solve. Under the assumption that the boundary surface of the solution domain has a one-to-one mapping onto the unit sphere, these integral equations are transformed and rewritten over this sphere. The numerical discretisation and solution are obtained by a discrete projection method involving spherical harmonic functions. Numerical results are included.

Simple approximate MAP inference for Dirichlet processes mixtures

The Dirichlet process mixture model (DPMM) is a ubiquitous, flexible Bayesian nonparametric statistical model. However, full probabilistic inference in this model is analytically intractable, so that computationally intensive techniques such as Gibbs sampling are required. As a result, DPMM-based methods, which have considerable potential, are restricted to applications in which computational resources and time for inference is plentiful. For example, they would not be practical for digital signal processing on embedded hardware, where computational resources are at a serious premium. Here, we develop a simplified yet statistically rigorous approximate maximum a-posteriori (MAP) inference algorithm for DPMMs. This algorithm is as simple as DP-means clustering, solves the MAP problem as well as Gibbs sampling, while requiring only a fraction of the computational effort. (For freely available code that implements the MAP-DP algorithm for Gaussian mixtures see http://www.maxlittle.net/.) Unlike related small variance asymptotics (SVA), our method is non-degenerate and so inherits the “rich get richer” property of the Dirichlet process. It also retains a non-degenerate closed-form likelihood which enables out-of-sample calculations and the use of standard tools such as cross-validation. We illustrate the benefits of our algorithm on a range of examples and contrast it to variational, SVA and sampling approaches from both a computational complexity perspective as well as in terms of clustering performance. We demonstrate the wide applicabiity of our approach by presenting an approximate MAP inference method for the infinite hidden Markov model whose performance contrasts favorably with a recently proposed hybrid SVA approach. Similarly, we show how our algorithm can applied to a semiparametric mixed-effects regression model where the random effects distribution is modelled using an infinite mixture model, as used in longitudinal progression modelling in population health science. Finally, we propose directions for future research on approximate MAP inference in Bayesian nonparametrics.

Evaluating service quality and customer satisfaction evaluation in an emerging markets

Developing economies offer tremendous potential for future growth and organizations appreciating these consumers’ requirements stand to reap considerable returns. However, compared with more developed economies published consumer studies are few. In particular, there is a dearth of service quality research and hardly any from Africa. Furthermore, the little available research tends to apply Western methodologies, which may not be entirely appropriate. This research investigates East African consumer perceptions of retail banking using an approach that takes account of the research context. Qualitative research was undertaken to define the relevant service attributes. Performance along these was then investigated through a survey with over 2000 respondents. Principal component analysis identifies 13 core service dimensions and multinomial logistic regression reveals which are the key drivers of customer satisfaction. Comparison of the results with studies from other regions confirms that established standardized research instruments are likely to miss or under-represent service attributes important in developing countries.

Higher-order co-occurrences for exploratory point pattern analysis and decision tree clustering on spatial data

Analyzing geographical patterns by collocating events, objects or their attributes has a long history in surveillance and monitoring, and is particularly applied in environmental contexts, such as ecology or epidemiology. The identification of patterns or structures at some scales can be addressed using spatial statistics, particularly marked point processes methodologies. Classification and regression trees are also related to this goal of finding "patterns" by deducing the hierarchy of influence of variables on a dependent outcome. Such variable selection methods have been applied to spatial data, but, often without explicitly acknowledging the spatial dependence. Many methods routinely used in exploratory point pattern analysis are2nd-order statistics, used in a univariate context, though there is also a wide literature on modelling methods for multivariate point pattern processes. This paper proposes an exploratory approach for multivariate spatial data using higher-order statistics built from co-occurrences of events or marks given by the point processes. A spatial entropy measure, derived from these multinomial distributions of co-occurrences at a given order, constitutes the basis of the proposed exploratory methods. © 2010 Elsevier Ltd.

Higher-order co-occurrences for exploratory point pattern analysis and decision tree clustering on spatial data

Analyzing geographical patterns by collocating events, objects or their attributes has a long history in surveillance and monitoring, and is particularly applied in environmental contexts, such as ecology or epidemiology. The identification of patterns or structures at some scales can be addressed using spatial statistics, particularly marked point processes methodologies. Classification and regression trees are also related to this goal of finding "patterns" by deducing the hierarchy of influence of variables on a dependent outcome. Such variable selection methods have been applied to spatial data, but, often without explicitly acknowledging the spatial dependence. Many methods routinely used in exploratory point pattern analysis are2nd-order statistics, used in a univariate context, though there is also a wide literature on modelling methods for multivariate point pattern processes. This paper proposes an exploratory approach for multivariate spatial data using higher-order statistics built from co-occurrences of events or marks given by the point processes. A spatial entropy measure, derived from these multinomial distributions of co-occurrences at a given order, constitutes the basis of the proposed exploratory methods. © 2010 Elsevier Ltd.

Weakly supervised joint sentiment-topic detection from text

Sentiment analysis or opinion mining aims to use automated tools to detect subjective information such as opinions, attitudes, and feelings expressed in text. This paper proposes a novel probabilistic modeling framework called joint sentiment-topic (JST) model based on latent Dirichlet allocation (LDA), which detects sentiment and topic simultaneously from text. A reparameterized version of the JST model called Reverse-JST, obtained by reversing the sequence of sentiment and topic generation in the modeling process, is also studied. Although JST is equivalent to Reverse-JST without a hierarchical prior, extensive experiments show that when sentiment priors are added, JST performs consistently better than Reverse-JST. Besides, unlike supervised approaches to sentiment classification which often fail to produce satisfactory performance when shifting to other domains, the weakly supervised nature of JST makes it highly portable to other domains. This is verified by the experimental results on data sets from five different domains where the JST model even outperforms existing semi-supervised approaches in some of the data sets despite using no labeled documents. Moreover, the topics and topic sentiment detected by JST are indeed coherent and informative. We hypothesize that the JST model can readily meet the demand of large-scale sentiment analysis from the web in an open-ended fashion.

Incorporating sentiment prior knowledge for weakly supervised sentiment analysis

This article presents two novel approaches for incorporating sentiment prior knowledge into the topic model for weakly supervised sentiment analysis where sentiment labels are considered as topics. One is by modifying the Dirichlet prior for topic-word distribution (LDA-DP), the other is by augmenting the model objective function through adding terms that express preferences on expectations of sentiment labels of the lexicon words using generalized expectation criteria (LDA-GE). We conducted extensive experiments on English movie review data and multi-domain sentiment dataset as well as Chinese product reviews about mobile phones, digital cameras, MP3 players, and monitors. The results show that while both LDA-DP and LDAGE perform comparably to existing weakly supervised sentiment classification algorithms, they are much simpler and computationally efficient, rendering themmore suitable for online and real-time sentiment classification on the Web. We observed that LDA-GE is more effective than LDA-DP, suggesting that it should be preferred when considering employing the topic model for sentiment analysis. Moreover, both models are able to extract highly domain-salient polarity words from text.

Automatically extracting polarity-bearing topics for cross-domain sentiment classification

Joint sentiment-topic (JST) model was previously proposed to detect sentiment and topic simultaneously from text. The only supervision required by JST model learning is domain-independent polarity word priors. In this paper, we modify the JST model by incorporating word polarity priors through modifying the topic-word Dirichlet priors. We study the polarity-bearing topics extracted by JST and show that by augmenting the original feature space with polarity-bearing topics, the in-domain supervised classifiers learned from augmented feature representation achieve the state-of-the-art performance of 95% on the movie review data and an average of 90% on the multi-domain sentiment dataset. Furthermore, using feature augmentation and selection according to the information gain criteria for cross-domain sentiment classification, our proposed approach performs either better or comparably compared to previous approaches. Nevertheless, our approach is much simpler and does not require difficult parameter tuning.

Feature LDA:a supervised topic model for automatic detection of web API documentations from the web

Web APIs have gained increasing popularity in recent Web service technology development owing to its simplicity of technology stack and the proliferation of mashups. However, efficiently discovering Web APIs and the relevant documentations on the Web is still a challenging task even with the best resources available on the Web. In this paper we cast the problem of detecting the Web API documentations as a text classification problem of classifying a given Web page as Web API associated or not. We propose a supervised generative topic model called feature latent Dirichlet allocation (feaLDA) which offers a generic probabilistic framework for automatic detection of Web APIs. feaLDA not only captures the correspondence between data and the associated class labels, but also provides a mechanism for incorporating side information such as labelled features automatically learned from data that can effectively help improving classification performance. Extensive experiments on our Web APIs documentation dataset shows that the feaLDA model outperforms three strong supervised baselines including naive Bayes, support vector machines, and the maximum entropy model, by over 3% in classification accuracy. In addition, feaLDA also gives superior performance when compared against other existing supervised topic models.

Entrepreneurs, expectations and business expansion:lessons from Lithuania

This article applies a multinomial logit estimator to investigate which factors affect SME owners' expectations to grow their businesses in Lithuania. Our findings provide evidence that SME owners' human capital (education) matters and that growth expectations are positively related to exporting. In addition, we analyse the link between the perceptions of business constraints and growth expectations and find that the factors, which are perceived as main business barriers, are not necessarily those which are associated with reduced growth expectations. However, perceptions of corruption seem to affect growth expectations the most.

Joint sentiment/topic model for sentiment analysis

Sentiment analysis or opinion mining aims to use automated tools to detect subjective information such as opinions, attitudes, and feelings expressed in text. This paper proposes a novel probabilistic modeling framework based on Latent Dirichlet Allocation (LDA), called joint sentiment/topic model (JST), which detects sentiment and topic simultaneously from text. Unlike other machine learning approaches to sentiment classification which often require labeled corpora for classifier training, the proposed JST model is fully unsupervised. The model has been evaluated on the movie review dataset to classify the review sentiment polarity and minimum prior information have also been explored to further improve the sentiment classification accuracy. Preliminary experiments have shown promising results achieved by JST.

Relaxation procedures for an iterative MFS algorithm for the stable reconstruction of elastic fields from Cauchy data in two-dimensional isotropic linear elasticity

We investigate two numerical procedures for the Cauchy problem in linear elasticity, involving the relaxation of either the given boundary displacements (Dirichlet data) or the prescribed boundary tractions (Neumann data) on the over-specified boundary, in the alternating iterative algorithm of Kozlov et al. (1991). The two mixed direct (well-posed) problems associated with each iteration are solved using the method of fundamental solutions (MFS), in conjunction with the Tikhonov regularization method, while the optimal value of the regularization parameter is chosen via the generalized cross-validation (GCV) criterion. An efficient regularizing stopping criterion which ceases the iterative procedure at the point where the accumulation of noise becomes dominant and the errors in predicting the exact solutions increase, is also presented. The MFS-based iterative algorithms with relaxation are tested for Cauchy problems for isotropic linear elastic materials in various geometries to confirm the numerical convergence, stability, accuracy and computational efficiency of the proposed method.

Relaxation of alternating iterative algorithms for the Cauchy problem associated with the modified Helmholtz equation

We propose two algorithms involving the relaxation of either the given Dirichlet data or the prescribed Neumann data on the over-specified boundary, in the case of the alternating iterative algorithm of ` 12 ` 12 `$12 `&12 `#12 `^12 `_12 `%12 `~12 *Kozlov91 applied to Cauchy problems for the modified Helmholtz equation. A convergence proof of these relaxation methods is given, along with a stopping criterion. The numerical results obtained using these procedures, in conjunction with the boundary element method (BEM), show the numerical stability, convergence, consistency and computational efficiency of the proposed methods.