Search results for: variational inference

Authors: Azeddine El-Hassouny, Chandrashekhar Meshram, Geraldin Nanfack

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In recent years, learning from data with noisy labels (Label Noise) has been a major concern in supervised learning. This problem has become even more worrying in Deep Learning, where the generalization capabilities have been questioned lately. Indeed, deep learning requires a large amount of data that is generally collected by search engines, which frequently return data with unreliable labels. In this paper, we investigate the Label Noise in Deep Learning using variational inference. Our contributions are : (1) exploiting Label Noise concept where the true labels are learnt using reparameterization variational inference, while observed labels are learnt discriminatively. (2) the noise transition matrix is learnt during the training without any particular process, neither heuristic nor preliminary phases. The theoretical results shows how true label distribution can be learned by variational inference in any discriminate neural network, and the effectiveness of our approach is proved in several target datasets, such as MNIST and CIFAR32.

Keywords: label noise, deep learning, discrete latent variable, variational inference, MNIST, CIFAR32

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Authors: Zhen Cheng, Xinyu Dai, Shujian Huang, Jiajun Chen

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Recently, explanatory natural language inference has attracted much attention for the interpretability of logic relationship prediction, which is also known as explanation generation for Natural Language Inference (NLI). Existing explanation generators based on discriminative Encoder-Decoder architecture have achieved noticeable results. However, we find that these discriminative generators usually generate explanations with correct evidence but incorrect logic semantic. It is due to that logic information is implicitly encoded in the premise-hypothesis pairs and difficult to model. Actually, logic information identically exists between premise-hypothesis pair and explanation. And it is easy to extract logic information that is explicitly contained in the target explanation. Hence we assume that there exists a latent space of logic information while generating explanations. Specifically, we propose a generative model called Variational Explanation Generator (VariationalEG) with a latent variable to model this space. Training with the guide of explicit logic information in target explanations, latent variable in VariationalEG could capture the implicit logic information in premise-hypothesis pairs effectively. Additionally, to tackle the problem of posterior collapse while training VariaztionalEG, we propose a simple yet effective approach called Logic Supervision on the latent variable to force it to encode logic information. Experiments on explanation generation benchmark—explanation-Stanford Natural Language Inference (e-SNLI) demonstrate that the proposed VariationalEG achieves significant improvement compared to previous studies and yields a state-of-the-art result. Furthermore, we perform the analysis of generated explanations to demonstrate the effect of the latent variable.

Keywords: natural language inference, explanation generation, variational auto-encoder, generative model

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Authors: Wanhyun Cho, Soonja Kang, Sangkyoon Kim, Soonyoung Park

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In this paper, we present the human action recognition method using the variational Bayesian HMM with the Dirichlet process mixture (DPM) of the Gaussian-Wishart emission model (GWEM). First, we define the Bayesian HMM based on the Dirichlet process, which allows an infinite number of Gaussian-Wishart components to support continuous emission observations. Second, we have considered an efficient variational Bayesian inference method that can be applied to drive the posterior distribution of hidden variables and model parameters for the proposed model based on training data. And then we have derived the predictive distribution that may be used to classify new action. Third, the paper proposes a process of extracting appropriate spatial-temporal feature vectors that can be used to recognize a wide range of human behaviors from input video image. Finally, we have conducted experiments that can evaluate the performance of the proposed method. The experimental results show that the method presented is more efficient with human action recognition than existing methods.

Keywords: human action recognition, Bayesian HMM, Dirichlet process mixture model, Gaussian-Wishart emission model, Variational Bayesian inference, prior distribution and approximate posterior distribution, KTH dataset

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Authors: Alberto Hananel

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The aim of this work is to modelize the occlusion of a person with temporomandibular disorders as an evolutionary equation and approach its solution by the construction and characterizing of discrete variational splines. To formulate the problem, certain boundary conditions have been considered. After showing the existence and the uniqueness of the solution of such a problem, a convergence result of a discrete variational evolutionary spline is shown. A stress analysis of the occlusion of a human jaw with temporomandibular disorders by finite elements is carried out in FreeFem++ in order to prove the validity of the presented method.

Keywords: approximation, evolutionary PDE, Finite Element Method, temporomandibular disorders, variational spline

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Authors: C. Juntarasaid, T. Pulngern, S. Chucheepsakul

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A formulation of postbuckling analysis of end supported rods under self-weight has been presented by the variational method. The variational formulation involving the strain energy due to bending and the potential energy of the self-weight, are expressed in terms of the intrinsic coordinates. The variational formulation is accomplished by introducing the Lagrange multiplier technique to impose the boundary conditions. The finite element method is used to derive a system of nonlinear equations resulting from the stationary of the total potential energy and then Newton-Raphson iterative procedure is applied to solve this system of equations. The numerical results demonstrate the postbluckled configurations of end supported rods under self-weight. This finite element method based on variational formulation expressed in term of intrinsic coordinate is highly recommended for postbuckling analysis of end-supported rods under self-weight.

Keywords: postbuckling, finite element method, variational method, intrinsic coordinate

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Authors: Wanhyun Cho, Soonja Kang, Sangkyoon Kim, Soonyoung Park

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In this paper, we propose a novel inference algorithm for the multi-class Gaussian process classification model that can be used in the field of human behavior recognition. This algorithm can drive simultaneously both a posterior distribution of a latent function and estimators of hyper-parameters in a Gaussian process classification model with multi-class. Our algorithm is based on the Laplace approximation (LA) technique and variational EM framework. This is performed in two steps: called expectation and maximization steps. First, in the expectation step, using the Bayesian formula and LA technique, we derive approximately the posterior distribution of the latent function indicating the possibility that each observation belongs to a certain class in the Gaussian process classification model. Second, in the maximization step, using a derived posterior distribution of latent function, we compute the maximum likelihood estimator for hyper-parameters of a covariance matrix necessary to define prior distribution for latent function. These two steps iteratively repeat until a convergence condition satisfies. Moreover, we apply the proposed algorithm with human action classification problem using a public database, namely, the KTH human action data set. Experimental results reveal that the proposed algorithm shows good performance on this data set.

Keywords: bayesian rule, gaussian process classification model with multiclass, gaussian process prior, human action classification, laplace approximation, variational EM algorithm

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Authors: M. O. Olayiwola

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Numerical solutions of the generalized Burger-Fisher are obtained using a Modified Variational Iteration Method (MVIM) with minimal computational efforts. The computed results with this technique have been compared with other results. The present method is seen to be a very reliable alternative method to some existing techniques for such nonlinear problems.

Keywords: burger-fisher, modified variational iteration method, lagrange multiplier, Taylor’s series, partial differential equation

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Authors: Athmane Bakhta, Sebastien Leclaire, David Vidal, Francois Bertrand, Mohamed Cheriet

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This work presents a new three-dimensional variational model proposed for the simulation of ink seepage into paper sheets at the fiber level. The model, inspired by the Hising model, takes into account a finite volume of ink and describes the system state through gravity, cohesion, and adhesion force interactions. At the mesoscopic scale, the paper substrate is modeled using a discretized fiber structure generated using a numerical deposition procedure. A modified Monte Carlo method is introduced for the simulation of the ink dynamics. Besides, a multiphase lattice Boltzmann method is suggested to fine-tune the mesoscopic variational model parameters, and it is shown that the ink seepage behaviors predicted by the proposed model can resemble those predicted by a method relying on first principles.

Keywords: fibrous media, lattice Boltzmann, modelling and simulation, Monte Carlo, variational model

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Authors: May George

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Inference plays an important role in the learning process and it can lead to a rapid acquisition of a second language. When learning a non-native language, i.e., a critical language like Arabic, the students depend on the teacher’s support most of the time to learn new concepts. The students focus on memorizing the new vocabulary and stress on learning all the grammatical rules. Hence, the students became mechanical and cannot produce the language easily. As a result, they are unable to predict the meaning of words in the context by relying heavily on the teacher, in that they cannot link their prior knowledge or even identify the meaning of the words without the support of the teacher. This study explores how the teacher guides students learning during the inference process and what are the processes of learning that can direct student’s inference.

Keywords: inference, reading, Arabic, language acquisition

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Authors: Kholod Mohammad Abualnaja

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A new algorithm is presented to find some new iterative methods for solving nonlinear equations F(x)=0 by using the variational iteration method. The efficiency of the considered method is illustrated by example. The results show that the proposed iteration technique, without linearization or small perturbation, is very effective and convenient.

Keywords: variational iteration method, nonlinear equations, Lagrange multiplier, algorithms

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Authors: Olayiwola Moruf Oyedunsi

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This paper discusses the Modified Variational Iteration Method (MVIM) for the solution of nonlinear Burgers’ equation arising in longitudinal dispersion phenomena in fluid flow through porous media. The method is an elegant combination of Taylor’s series and the variational iteration method (VIM). Using Maple 18 for implementation, it is observed that the procedure provides rapidly convergent approximation with less computational efforts. The result shows that the concentration C(x,t) of the contaminated water decreases as distance x increases for the given time t.

Keywords: modified variational iteration method, Burger’s equation, porous media, partial differential equation

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Authors: Jiangyong Liu, Xiangxiang Xu, Bote Luo, Xiaoxue Luo, Jiang Zhu, Lingzhi Yi

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To address the problems of non-linearity and high randomness of the original power load sequence causing the degradation of power load forecasting accuracy, a short-term load forecasting method is proposed. The method is based on the Least Square Support Vector Machine optimized by an Improved Sparrow Search Algorithm combined with the Variational Mode Decomposition proposed in this paper. The application of the variational mode decomposition technique decomposes the raw power load data into a series of Intrinsic Mode Functions components, which can reduce the complexity and instability of the raw data while overcoming modal confounding; the proposed improved sparrow search algorithm can solve the problem of difficult selection of learning parameters in the least Square Support Vector Machine. Finally, through comparison experiments, the results show that the method can effectively improve prediction accuracy.

Keywords: load forecasting, variational mode decomposition, improved sparrow search algorithm, least square support vector machine

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Authors: Yihao Kuang, Bowen Ding

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With the increasing scale and complexity of knowledge graph, modern knowledge graph contains more and more types of entity, relationship, and attribute information. Therefore, in recent years, it has been a trend for knowledge graph inference to use reinforcement learning to deal with large-scale, incomplete, and noisy knowledge graphs and improve the inference effect and interpretability. The Proximal Policy Optimization (PPO) algorithm utilizes a near-end strategy optimization approach. This allows for more extensive updates of policy parameters while constraining the update extent to maintain training stability. This characteristic enables PPOs to converge to improved strategies more rapidly, often demonstrating enhanced performance early in the training process. Furthermore, PPO has the advantage of offline learning, effectively utilizing historical experience data for training and enhancing sample utilization. This means that even with limited resources, PPOs can efficiently train for reinforcement learning tasks. Based on these characteristics, this paper aims to obtain a better and more efficient inference effect by introducing PPO into knowledge inference technology.

Keywords: reinforcement learning, PPO, knowledge inference

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Authors: Yihao Kuang, Bowen Ding

Abstract:

With the increasing scale and complexity of knowledge graph, modern knowledge graph contains more and more types of entity, relationship, and attribute information. Therefore, in recent years, it has been a trend for knowledge graph inference to use reinforcement learning to deal with large-scale, incomplete, and noisy knowledge graph and improve the inference effect and interpretability. The Proximal Policy Optimization (PPO) algorithm utilizes a near-end strategy optimization approach. This allows for more extensive updates of policy parameters while constraining the update extent to maintain training stability. This characteristic enables PPOs to converge to improve strategies more rapidly, often demonstrating enhanced performance early in the training process. Furthermore, PPO has the advantage of offline learning, effectively utilizing historical experience data for training and enhancing sample utilization. This means that even with limited resources, PPOs can efficiently train for reinforcement learning tasks. Based on these characteristics, this paper aims to obtain better and more efficient inference effect by introducing PPO into knowledge inference technology.

Keywords: reinforcement learning, PPO, knowledge inference, supervised learning

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Authors: Yas Barzegaar, Atrin Barzegar

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The aim of this research is to develop an intelligent system to analyze the risk level of wheat flour product manufacturing system. The model consists of five Fuzzy Inference Systems in two different layers to analyse the risk of a wheat flour product manufacturing system. The first layer of the model consists of four Fuzzy Inference Systems with three criteria. The output of each one of the Physical, Chemical, Biological and Environmental Failures will be the input of the final manufacturing systems. The proposed model based on Mamdani Fuzzy Inference Systems gives a performance ranking of wheat flour products manufacturing systems. The first step is obtaining data to identify the failure modes from expert’s opinions. The second step is the fuzzification process to convert crisp input to a fuzzy set., then the IF-then fuzzy rule applied through inference engine, and in the final step, the defuzzification process is applied to convert the fuzzy output into real numbers.

Keywords: failure modes, fuzzy rules, fuzzy inference system, risk assessment

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Authors: A. W. Gbolagade, M. O. Olayiwola, K. O. Kareem

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In this paper, further to our result on recent paper on the solution of nonlinear advection equations, we present further results on the nonlinear nonhomogeneous advection equations using a modified variational iteration method.

Keywords: lagrange multiplier, non-homogeneous equations, advection equations, mathematics

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Authors: Purnima Pandit

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Malaria remains one of the world’s most deadly infectious disease and arguably, the greatest menace to modern society in terms of morbidity and mortality. To choose the right treatment and to ensure a quality of life suitable for a specific patient condition, early and accurate diagnosis of malaria is essential. It reduces transmission of disease and prevents deaths. Our work focuses on designing an efficient, accurate fuzzy inference system for malaria diagnosis.

Keywords: fuzzy inference system, fuzzy logic, malaria disease, triangular fuzzy number

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Authors: Atrin Barzegar, Yas Barzegar, Stefano Marrone, Francesco Bellini, Laura Verde

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The aim of this research is to develop an intelligent system to analyze the risk level of wheat flour product manufacturing system. The model consists of five Fuzzy Inference Systems in two different layers to analyse the risk of a wheat flour product manufacturing system. The first layer of the model consists of four Fuzzy Inference Systems with three criteria. The output of each one of the Physical, Chemical, Biological and Environmental Failures will be the input of the final manufacturing systems. The proposed model based on Mamdani Fuzzy Inference Systems gives a performance ranking of wheat flour products manufacturing systems. The first step is obtaining data to identify the failure modes from expert’s opinions. The second step is the fuzzification process to convert crisp input to a fuzzy set., then the IF-then fuzzy rule applied through inference engine, and in the final step, the defuzzification process is applied to convert the fuzzy output into real numbers.

Keywords: failure modes, fuzzy rules, fuzzy inference system, risk assessment

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Authors: Desmond Adair, Kairat Ismailov, Martin Jaeger

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Modelling of Timoshenko beams on elastic foundations has been widely used in the analysis of buildings, geotechnical problems, and, railway and aerospace structures. For the elastic foundation, the most widely used models are one-parameter mechanical models or two-parameter models to include continuity and cohesion of typical foundations, with the two-parameter usually considered the better of the two. Knowledge of free vibration characteristics of beams on an elastic foundation is considered necessary for optimal design solutions in many engineering applications, and in this work, the efficient and accurate variational iteration method is developed and used to calculate natural frequencies of a Timoshenko beam on a two-parameter foundation. The variational iteration method is a technique capable of dealing with some linear and non-linear problems in an easy and efficient way. The calculations are compared with those using a finite-element method and other analytical solutions, and it is shown that the results are accurate and are obtained efficiently. It is found that the effect of the presence of the two-parameter foundation is to increase the beam’s natural frequencies and this is thought to be because of the shear-layer stiffness, which has an effect on the elastic stiffness. By setting the two-parameter model’s stiffness parameter to zero, it is possible to obtain a one-parameter foundation model, and so, comparison between the two foundation models is also made.

Keywords: Timoshenko beam, variational iteration method, two-parameter elastic foundation model

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Authors: Jack R. McKenzie, Peter A. Appleby, Thomas House, Neil Walton

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Cold-start is a notoriously difficult problem which can occur in recommendation systems, and arises when there is insufficient information to draw inferences for users or items. To address this challenge, a contextual bandit algorithm – the Fast Approximate Bayesian Contextual Cold Start Learning algorithm (FAB-COST) – is proposed, which is designed to provide improved accuracy compared to the traditionally used Laplace approximation in the logistic contextual bandit, while controlling both algorithmic complexity and computational cost. To this end, FAB-COST uses a combination of two moment projection variational methods: Expectation Propagation (EP), which performs well at the cold start, but becomes slow as the amount of data increases; and Assumed Density Filtering (ADF), which has slower growth of computational cost with data size but requires more data to obtain an acceptable level of accuracy. By switching from EP to ADF when the dataset becomes large, it is able to exploit their complementary strengths. The empirical justification for FAB-COST is presented, and systematically compared to other approaches on simulated data. In a benchmark against the Laplace approximation on real data consisting of over 670, 000 impressions from autotrader.co.uk, FAB-COST demonstrates at one point increase of over 16% in user clicks. On the basis of these results, it is argued that FAB-COST is likely to be an attractive approach to cold-start recommendation systems in a variety of contexts.

Keywords: cold-start learning, expectation propagation, multi-armed bandits, Thompson Sampling, variational inference

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Authors: Harendra Singh, Rajesh Pandey

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The paper presents a numerical method based on operational matrix of integration and Ryleigh method for the solution of a class of non-linear fractional variational problems (NLFVPs). Chebyshev first kind polynomials are used for the construction of operational matrix. Using operational matrix and Ryleigh method the NLFVP is converted into a system of non-linear algebraic equations, and solving these equations we obtained approximate solution for NLFVPs. Convergence analysis of the proposed method is provided. Numerical experiment is done to show the applicability of the proposed numerical method. The obtained numerical results are compared with exact solution and solution obtained from Chebyshev third kind. Further the results are shown graphically for different fractional order involved in the problems.

Keywords: non-linear fractional variational problems, Rayleigh-Ritz method, convergence analysis, error analysis

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Authors: Nazanin Pilevari, Kamyar Mahmoodi

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The purpose of this research is to provide a model based on fuzzy inference system for evaluating empowerment of Knowledge management. The first prototype of the research was developed based on the study of literature. In the next step, experts were provided with these models and after implementing consensus-based reform, the views of Fuzzy Delphi experts and techniques, components and Index research model were finalized. Culture, structure, IT and leadership were considered as dimensions of empowerment. Then, In order to collect and extract data for fuzzy inference system based on knowledge and Experience, the experts were interviewed. The values obtained from designed fuzzy inference system, made review and assessment of the organization's empowerment of Knowledge management possible. After the design and validation of systems to measure indexes ,empowerment of Knowledge management and inputs into fuzzy inference) in the AYANDEH Bank, a questionnaire was used. In the case of this bank, the system output indicates that the status of empowerment of Knowledge management, culture, organizational structure and leadership are at the moderate level and information technology empowerment are relatively high. Based on these results, the status of knowledge management empowerment in AYANDE Bank, was moderate. Eventually, some suggestions for improving the current situation of banks were provided. According to studies of research history, the use of powerful tools in Fuzzy Inference System for assessment of Knowledge management and knowledge management empowerment such an assessment in the field of banking, are the innovation of this Research.

Keywords: knowledge management, knowledge management empowerment, fuzzy inference system, fuzzy Delphi

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Authors: Mikhail Zarechnev, Bora I. Kumova

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A syllogism is a deductive inference scheme used to derive a conclusion from a set of premises. In a categorical syllogisms, there are only two premises and every premise and conclusion is given in form of a quantified relationship between two objects. The different order of objects in premises give classification known as figures. We have shown that the ordered combinations of 3 generalized quantifiers with certain figure provide in total of 108 syllogistic moods which can be considered as different inference rules. The classical syllogistic system allows to model human thought and reasoning with syllogistic structures always attracted the attention of cognitive scientists. Since automated reasoning is considered as part of learning subsystem of AI agents, syllogistic system can be applied for this approach. Another application of syllogistic system is related to inference mechanisms on the Semantic Web applications. In this paper we proposed the mathematical model and algorithm for syllogistic reasoning. Also the model of iterative syllogistic reasoning in case of continuous flows of incoming data based on case–based reasoning and possible applications of proposed system were discussed.

Keywords: categorical syllogism, case-based reasoning, cognitive architecture, inference on the semantic web, syllogistic reasoning

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Authors: Sung Hyun Yoo, In Hwan Choi, Jun Ho Jung, Choon Ki Ahn, Myo Taeg Lim

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Home energy management system (HEMS) has been issued to reduce the power consumption. The HEMS performs electric power control for the indoor electric device. However, HEMS commonly treats the smart devices. In this paper, we suggest the output estimation of home legacy device using the artificial neural fuzzy inference system (ANFIS). This paper discusses the overview and the architecture of the system. In addition, accurate performance of the output estimation using the ANFIS inference system is shown via a numerical example.

Keywords: artificial neural fuzzy inference system (ANFIS), home energy management system (HEMS), smart device, legacy device

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Authors: Pushpendra Kumar, Sanjeev Kumar, R. Balasubramanian

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Estimation of optical flow from a sequence of images using variational methods is one of the most successful approach. Discontinuity between different motions is one of the challenging problem in flow estimation. In this paper, we design a new anisotropic diffusion operator, which is able to provide smooth flow over a region and efficiently preserve discontinuity in optical flow. This operator is designed on the basis of intensity differences of the pixels and isotropic operator using exponential function. The combination of these are used to control the propagation of flow. Experimental results on the different datasets verify the robustness and accuracy of the algorithm and also validate the effect of anisotropic operator in the discontinuity preserving.

Keywords: optical flow, variational methods, computer vision, anisotropic operator

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Authors: Surendra Mund

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At the beginning, the physical entity force was defined mathematically by Sir Isaac Newton in his Principia Mathematica as F ⃗=(dp ⃗)/dt in form of his second law of motion. Newton also defines his Universal law of Gravitational force exist in same outstanding book, but at the end of 20th century and beginning of 21st century, we have tried a lot to specify and unify four or five Fundamental forces or Interaction exist in universe, but we failed every time. Usually, Gravity creates problems in this unification every single time, but in my previous papers and presentations, I defined and derived Field and force equations for Gravitational like Interactions for each and every kind of central systems. This force is named as Variational Force by me, and this force is generated by variation in the scalar field density around the body. In this particular paper, at first, I am specifying which type of Interactions are Fundamental in Universal sense (or in all type of central systems or bodies predicted by my N-time Inflationary Model of Universe) and then unify them in Universal framework (defined and derived by me as Universal Mechanics in a separate paper) as well. This will also be valid in Universal dynamical sense which includes inflations and deflations of universe, central system relativity, Universal relativity, ϕ-ψ transformation and transformation of spin, physical perception principle, Generalized Fundamental Dynamical Law and many other important Generalized Principles of Generalized Quantum Mechanics (GQM) and Central System Theory (CST). So, In this article, at first, I am Generalizing some Fundamental Principles, and then Unifying Variational Forces (General form of Gravitation like Interactions) and Flow Generated Force (General form of EM like Interactions), and then Unify all Fundamental Forces by specifying Weak and Strong Interactions in form of more basic terms - Variational, Flow Generated and Transformational Interactions.

Keywords: Central System Force, Disturbance Force, Flow Generated Forces, Generalized Nuclear Force, Generalized Weak Interactions, Generalized EM-Like Interactions, Imbalance Force, Spin Generated Forces, Transformation Generated Force, Unified Force, Universal Mechanics, Uniform And Non-Uniform Variational Interactions, Variational Interactions

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Authors: Md Yeasin, Ranjit Kumar Paul

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In recent years, recommendation systems have become indispensable tools for agricultural system. The accurate and timely recommendations can significantly impact crop yield and overall productivity. Causal inference modeling aims to establish cause-and-effect relationships by identifying the impact of variables or factors on outcomes, enabling more accurate and reliable recommendations. New advancements in causal inference models have been found in the literature. With the advent of the modern era, deep learning and machine learning models have emerged as efficient tools for modeling. This study proposed an innovative approach to enhance recommendation systems-based machine learning based casual inference model. By considering the causal effect and opportunity cost of covariates, the proposed system can provide more reliable and actionable recommendations for cereal farmers. To validate the effectiveness of the proposed approach, experiments are conducted using cereal cultivation data of eastern India. Comparative evaluations are performed against existing correlation-based recommendation systems, demonstrating the superiority of the advanced causal inference modeling approach in terms of recommendation accuracy and impact on crop yield. Overall, it empowers farmers with personalized recommendations tailored to their specific circumstances, leading to optimized decision-making and increased crop productivity.

Keywords: agriculture, casual inference, machine learning, recommendation system

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Authors: Shael Brown, Reza Farivar

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Persistence diagrams capture valuable topological features of datasets that other methods cannot uncover. Still, their adoption in data pipelines has been limited due to the lack of publicly available tools in R (and python) for analyzing groups of them with machine learning and statistical inference. In an easy-to-use and scalable R package called TDApplied, we implement several applied analysis methods tailored to groups of persistence diagrams. The two main contributions of our package are comprehensiveness (most functions do not have implementations elsewhere) and speed (shown through benchmarking against other R packages). We demonstrate applications of the tools on simulated data to illustrate how easily practical analyses of any dataset can be enhanced with topological information.

Keywords: machine learning, persistence diagrams, R, statistical inference

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Authors: Orhun Aydin, Mark V. Janikas, Rodrigo Alves, Renato Assuncao

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In this paper, a tree-based perturbation methodology for regionalization inference is presented. Regionalization is a constrained optimization problem that aims to create groups with similar attributes while satisfying spatial contiguity constraints. Similar to any constrained optimization problem, the spatial constraint may hinder convergence to some global minima, resulting in spatially contiguous members of a group with dissimilar attributes. This paper presents a general methodology for rigorously perturbing spatial constraints through the use of random spanning trees. The general framework presented can be used to quantify the effect of the spatial constraints in the overall regionalization result. We compare several types of stochastic spanning trees used in inference problems such as fuzzy regionalization and determining the number of regions. Performance of stochastic spanning trees is juxtaposed against the traditional permutation-based hypothesis testing frequently used in spatial statistics. Inference results for fuzzy regionalization and determining the number of regions is presented on the Local Area Personal Incomes for Texas Counties provided by the Bureau of Economic Analysis.

Keywords: regionalization, constrained clustering, probabilistic inference, fuzzy clustering

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Authors: Eva L. Sanjuán, Jacinto Martín, M. Isabel Parra, Mario M. Pizarro

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In Extreme Value Theory, inference estimation for the parameters of the distribution is made employing a small part of the observation values. When block maxima values are taken, many data are discarded. We developed a new Bayesian inference model to seize all the information provided by the data, introducing informative priors and using the relations between baseline and limit parameters. Firstly, we studied the accuracy of the new model for three baseline distributions that lead to a Gumbel extreme distribution: Exponential, Normal and Gumbel. Secondly, we considered mixtures of Normal variables, to simulate practical situations when data do not adjust to pure distributions, because of perturbations (noise).

Keywords: bayesian inference, extreme value theory, Gumbel distribution, highly informative prior

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