Mixture Model

Supervised learning, while deployed in real-life scenarios, often encounters instances of unknown classes. Conventional algorithms for training a supervised learning model do not provide an option to detect such instances, so they miss-classify such instances with 100% probability. Open Set Recognition (OSR) and Non-Exhaustive Learning (NEL) are potential solutions to overcome this problem. Most existing methods of OSR first classify members of existing classes and then identify instances of new classes. However, many of the existing methods of OSR only makes a binary decision, i.e., they only identify the existence of the unknown class. Hence, such methods cannot distinguish test instances belonging to incremental unseen classes. On the other hand, the majority of NEL methods often make a parametric assumption over the data distribution, which either fail to return good results, due to the reason that real-life complex datasets may not follow a well-known data distribution. In this paper, we propose a new online non-exhaustive learning model, namely, Non-Exhaustive Gaussian Mixture Generative Adversarial Networks (NE-GM-GAN) to address these issues. Our proposed model synthesizes Gaussian mixture based latent representation over a deep generative model, such as GAN, for incremental detection of instances of emerging classes in the test data. Extensive experimental results on several benchmark datasets show that NE-GM-GAN significantly outperforms the state-of-the-art methods in detecting instances of novel classes in streaming data.

CLUSTERING is one of the fundamental data mining tasks. Many different clustering paradigms have been developed over the years, which include partitional, hierarchical, mixture model based, density-based, spectral, subspace, and so on. The focus of this paper is on fulldimensional, arbitrary shaped clusters. Existing methods for this problem suffer either in terms of the memory or time complexity (quadratic or even cubic). This shortcoming has restricted these algorithms to datasets of moderate sizes. In this paper we propose SPARCL, a simple and scalable algorithm for finding clusters with arbitrary shapes and sizes, and it has linear space and time complexity. SPARCL consists of two stages -the first stage runs a carefully initialized version of the Kmeans algorithm to generate many small seed clusters. The second stage iteratively merges the generated clusters to obtain the final shape-based clusters. Experiments were conducted on a variety of datasets to highlight the effectiveness, efficiency, and scalability of our approach. On the large datasets SPARCL is an order of magnitude faster than the best existing approaches.

A sponge subjected to an increase of the outside flui pressure expands its volume but nearly mantains its true density and thus gives way to an increase of the interstitial volume. This behaviour, not yet properly described by solid-flui mixture theories, is studied here by using the Principle of Virtual Power with the most simple dependence of the free energy as a function of the partial apparent densities of the solid and the fluid The model is capable of accounting for the above mentioned dilatational behaviour, but in order to isolate its essential features more clearly we compromise on the other aspects of deformation. Specifically the following questions are addressed: (i) The boundary pressure is divided between the solid and flui pressures with a dividing coefficien which depends on the constituent apparent densities regarded as state parameters. The work performed by these tractions should vanish in any cyclic process over this parameter space. This condition severely restricts the permissible constitutive relations for the dividing coefficient which results to be characterized by a single material parameter. (ii) A stability analysis is performed for homogeneous, pressurized reference states of the mixture by postulating a quadratic form for the free energy and using the afore mentioned permissible constitutive relations. It is shown that such reference states become always unstable if only the external pressure is sufficientl large, but the exact value depends on the interaction terms in the free energy. The larger this interaction is, the smaller will be the critical (smallest unstable) external pressure. (iii) It will be shown that within the stable regime of behaviour an increase of the external pressure will lead to a decrease of the solid density and correspondingly an increase of the specifi volume, thus proving the wanted dilatation effects. (iv) We close by presenting a formulation of mixture theory involving second gradients of the displacement as a further deformation measure ; this allows for the regularization of the otherwise singular boundary effects (dell'Isola and Guarascio 1999).

A two-stage stepup procedure is defined and an explicit formula for the FDR of this procedure is derived under any distributional setting. Sets of critical values are determined that provide a control of the FDR of a two-stage stepup procedure under iid mixture model. A class of two-stage FDR procedures modifying the Benjamini-Hochberg (BH) procedure and containing the one given in Strong control, conservative point estimation and simultanaeous conservative consistency of false discovery rates: a unified approach. J. Roy. Statist. Soc. Ser. B 66, 187-205] is obtained. The FDR controlling property of the Storey-Taylor-Siegmund procedure is proved only under the independence, which is different from that presented by these authors. A single-stage stepup procedure controlling the FDR under any form of dependence, which is different from and in some situations performs better than the Benjamini-Yekutieli (BY) procedure, is given before discussing how to obtain two-stage versions of the BY and this new procedures. Simulations reveal that procedures proposed in this article under the mixture model can perform quite well in terms of improving the FDR control of the BH procedure. However, the similar idea of improving the FDR control of a stepup procedure under any form dependence does not seem to work.

In this note, we focus on estimating the false discovery rate (FDR) of a multiple testing method with a common, non-random rejection threshold under a mixture model. We develop a new class of estimates of the FDR and prove that it is less conservatively biased than what is traditionally used. Numerical evidence is presented to show that the mean squared error (MSE) is also often smaller for the present class of estimates, especially in small-scale multiple testings. A similar class of estimates of the positive false discovery rate (pFDR) less conservatively biased than what is usually used is then proposed. When modified using our estimate of the pFDR and applied to a gene-expression data, Storey's q-value method identifies a few more significant genes than his original q-value method at certain thresholds. The BH method of controlling the FDR is modified using our estimate of the FDR. The modified BH method is more powerful and controls the FDR in situations where the p-values have the same dependence structure as required by the BH method and, for lack of information about the proportion π 0 of true null hypotheses, it is reasonable to assume that π 0 is uniformly distributed over (0,1).

Identifying source objects in astronomical observations, in particular with reliable algorithms, is extremely important in large-area surveys. It is of great importance for any source detection algorithm to limit the number of false detections since follow up investigations are timely and costly. In this paper, we consider two new statistical procedures to control the false discovery rate (FDR) for group-dependent data -the two-stage BH method and adaptive two-stage BH method. Motivated by the belief that the spatial dependencies among the hypotheses occur more locally than globally, these procedures test hypotheses in groups that incorporate the local, unknown dependencies. If a group is found significant, further investigation is done to the individual hypotheses within that group. Importantly, these methodologies make no dependence assumption for hypotheses within each group. The properties of the two procedures are examined through simulation studies as well as astronomical source detection data.

The concept of k-FWER has received much attention lately as an appropriate error rate for multiple testing when one seeks to control at least k false rejections, for some fixed k ≥ 1. A less conservative notion, the k-FDR, has been introduced very recently by Sarkar [Ann. Statist. 34 (2006) 394-415], generalizing the false discovery rate of Benjamini and Hochberg [J. Roy. Statist. Soc. Ser. B 57 (1995) 289-300]. In this article, we bring newer insight to the k-FDR considering a mixture model involving independent p-values before motivating the developments of some new procedures that control it. We prove the k-FDR control of the proposed methods under a slightly weaker condition than in the mixture model. We provide numerical evidence of the proposed methods' superior power performance over some k-FWER and k-FDR methods. Finally, we apply our methods to a real data set.

Results on the false discovery rate (FDR) and the false nondiscovery rate (FNR) are developed for single-step multiple testing procedures. In addition to verifying desirable properties of FDR and FNR as measures of error rates, these results extend previously known results, providing further insights, particularly under dependence, into the notions of FDR and FNR and related measures. First, considering fixed configurations of true and false null hypotheses, inequalities are obtained to explain how an FDR-or FNR-controlling single-step procedure, such as a Bonferroni or Sidák procedure, can potentially be improved. Two families of procedures are then constructed, one that modifies the FDR-controlling and the other that modifies the FNR-controlling Sidák procedure. These are proved to control FDR or FNR under independence less conservatively than the corresponding families that modify the FDR-or FNR-controlling Bonferroni procedure. Results of numerical investigations of the performance of the modified Sidák FDR procedure over its competitors are presented. Second, considering a mixture model where different configurations of true and false null hypotheses are assumed to have certain probabilities, results are also derived that extend some of Storey's work to the dependence case.

The success of process design in chemical engineering and energy technology depends on the availability and accuracy of thermodynamic properties. In recent years, molecular modeling and simulation has become a promising tool to accurately predict thermodynamic properties of fluids. Thermodynamic data can accurately be predicted with molecular models that are based on quantum chemical calculations and are optimized to vapor-liquid equilibrium (VLE) data only. This approach is applied to ammonia here, studying a wide range of properties and thermodynamic conditions. In addition to static properties, the self-diffusion coefficient, shear viscosity and the thermal conductivity are determined. The employed molecular model is based on one Lennard-Jones site and four point charges. Furthermore, the influence of the intramolecular degrees of freedom on the VLE is studied, showing that angle bending plays an unexpectedly large role in the liquid state, because of a significantly enhanced dip...

An insurance claim is a demand made by the insured, which becomes the obligation of the insurance company (insurer) according to the contract of insurance between policyholders and the insurer. The calculation of estimated claim severity is necessary so that the company can build claim reserves appropriately and accurately. One of the methods for calculating the estimated claim severity is by using statistical distributions. The author wants to calculate the estimated claim severity using this method to find out which distribution is best for modeling insurance claims data, where the results will later be compared with the initial claim for reserves in the settlement process (initial reserves) PT XYZ. This was done by the author to find out that the claim estimation calculation method using this statistical distribution could be more accurate. In this research, the author used claim data for property all risk insurance product for years of 2017 2021 at PT XYZ and data on the initial reserve value determined by PT XYZ is IDR 100.000.000. Based on the results of the research, the Lognormal distribution is a good statistical distribution for modeling the estimation of claim severity. This can be seen from the Kolmogorov Smirnov test which was carried out with a significance level of 5% and considering the smallest Akaike's Information Criterion (AIC) value. The estimated total value of property all risk insurance product claims using the Lognormal distribution is IDR 103.244.948. This shows that this value is not significantly different from the initial reserve set by PT XYZ. However, the estimated claim severity obtained from this research can be more accurate because it describes the actual value by looking at the entire distribution of the data.

This paper is concerned with a class of exponential dispersion distributions. We particularly focused on the mixture models, which represent an extension of the Gaussian distribution. It should be noted that the parameters estimation of mixture distributions is an important task in statistical processing. In order to estimate the parameters vector, we proposed a formulation of the Expectation-Maximization algorithm (EM) under exponential dispersion mixture distributions. Also, we developed a hybrid algorithm called Expectation-Maximization and Method of moments algorithm (EMM). Under mild regularity, several convergence results of the EMM algorithm were obtained. Through simulation studies, the robustness of the EMM was proved and the strong consistency of the EMM sequence appeared when the data set size and the number of iterations tend to infinity.

In this paper, we introduced the infinite continuous mixture of Dirichlet distributions as a generalization of the infinite mixture of Dirichlet ones, in order to avoid the limitation of choosing the a priori sample size for the expectation \textit{a posteriori} estimator. Monte-Carlo sampling was used in order to obtain the \textit{posterior} distributions mixture, since this mixture is difficult to get analytically. A new parametrization of this proposed distribution was achieved. Then, we suggested a mixture expectation \textit{a posteriori} estimator of the unknown parameters. The proposed estimator solves the problem of how to construct a Bayesian estimation of proportions without specifying particular parameters and sample size of the prior knowledge. Some asymptotic properties of this estimator were derived, specifically, its bias and variance. The consistency and asymptotic normality of the estimator were also established when the sample size tends to infinity and its credib...

Supervised speech segregation for cochannel speech signal can be made easier if we use predetermined speaker's models instead of taking models for all the population. Here we propose a signal to signal ratio (SSR) independent method to detect speaker identities from a cochannel speech signal with unique speaker specific features for speaker identification. Proposed Kekre's Transform Cepstral Coefficient (KTCC) features are the robust acoustic features for speaker identification. A text independent speaker identification system is utilized for identifying speakers in short segments of test signal. Gaussian mixture modeling (GMM) classifier is used for the identification task. We compare the proposed method with a system utilizing conventional features called Mel Frequency Cepstral Coefficient (MFCC) features. Spontaneous speech utterances from candidates are taken for experimentation instead of utterances that follow a command like structure with a unique grammatical structure and have a limited word list in speech separation challenge (SSC) corpus. Identification is performed on short segments of the cochannel mixture. Two Speakers who have been identified for most of segments of the cochannel mixture are selected as two speakers detected for the same cochannel mixture. Average speaker detection accuracy of 93.56% is achieved in case of two speaker cochannel mixture for of KTCC features. This method produces best results for cochannel speaker identification even being text independent. Speaker identification performance is also checked for various test segment lengths. KTCC features outperform in speaker identification task even the length of speech segment is very short.

Childhood sexual abuse (CSA) has been associated with HIV/AIDS risk behavior; however, much of this work is retrospective and focuses on women. The current study used semiparametric mixture modeling with youth (n = 844; 48.8% boys) from the Longitudinal Studies of Child Abuse and Neglect (LONGSCAN) to examine the link between trajectories of CSA (2 to 12 y.o.) and HIV/AIDS risk behavior at age 14 (i.e., sexual intercourse & alcohol use). Trajectory analyses revealed a link between a history of CSA and the development of risky behavior. In addition,

Motivation: Most genotyping technologies for single nucleotide polymorphism (SNP) markers use standard clustering methods to ‘call’ the SNP genotypes. These methods are not always optimal in distinguishing the genotype clusters of a SNP because they do not take advantage of specific features of the genotype calling problem. In particular, when family data are available, pedigree information is ignored. Furthermore, prior information about the distribution of the measurements for each cluster can be used to choose an appropriate model-based clustering method and can significantly improve the genotype calls. One special genotyping problem that has never been discussed in the literature is that of genotyping of trisomic individuals, such as individuals with Down syndrome. Calling trisomic genotypes is a more complicated problem, and the addition of external information becomes very important. Results: In this article, we discuss the impact of incorporating external information into clu...

In this paper, a co-channel multi-pitch detection algorithm is described. We suggest the importance of this when prosodic information is need to be extracted separately from respective F 0 patterns of concurrent utterances. Though temporal continuity of speech prosody should be considered, we discuss a process done independently on each single frame as the first step. A model of multiple harmonic structures is constructed with a mixture of tied Gaussian mixtures with which a single harmonic structure is modeled. Our algorithm enables to detect both a number of concurrent speakers, and each spectral envelope of underlying harmonic structure based on a maximum likelihood estimation of the model parameters using EM algorithm and an information criterion. It operates without a priori information of F 0 contours and a restriction of a number of speakers, and it also extracts accurate F 0 s as continuous values with simple procedures in spectral domain. Experiments showed our algorithm outperformed well-known cepstrum for both speech signals of a single speaker and simultaneous two speakers.

The purpose of the present study is to compare nonnormal distributions (i.e., t, skew-normal, skew-t with equal skew and skew-t with unequal skew) in growth mixture models (GMMs) based on diverse conditions of a number of time points, sample sizes, and skewness for intercepts. To carry out this research, two simulation studies were conducted with two different models: an unconditional GMM and a GMM with a continuous distal outcome variable. For the simulation, data were generated under the conditions of a different number of time points (4, 8), sample size (300, 800, 1,500), and skewness for intercept (1.2, 2, 4). Results demonstrate that it is not appropriate to fit nonnormal data to normal, t, or skew-normal distributions other than the skew-t distribution. It was also found that if there is skewness over time, it is necessary to model skewness in the slope as well.

The purpose of the present study is to compare nonnormal distributions (i.e., t, skew-normal, skew- t with equal skew and skew- t with unequal skew) in growth mixture models (GMMs) based on diverse conditions of a number of time points, sample sizes, and skewness for intercepts. To carry out this research, two simulation studies were conducted with two different models: an unconditional GMM and a GMM with a continuous distal outcome variable. For the simulation, data were generated under the conditions of a different number of time points (4, 8), sample size (300, 800, 1,500), and skewness for intercept (1.2, 2, 4). Results demonstrate that it is not appropriate to fit nonnormal data to normal, t, or skew-normal distributions other than the skew- t distribution. It was also found that if there is skewness over time, it is necessary to model skewness in the slope as well.

ost current speech recognition systems use hidden Markov models (HMMs) to deal with the temporal variability of speech and Gaussian mixture models (GMMs) to determine how well each state of each HMM fits a frame or a short window of frames of coefficients that represents the acoustic input. An alternative way to evaluate the fit is to use a feed-forward neural network that takes several frames of coefficients as input and produces posterior proba-bilities over HMM states as output. Deep neural networks (DNNs) that have many hidden layers and are trained using new methods have been shown to outperform GMMs on a variety of speech recognition benchmarks, sometimes by a large margin. This article provides an overview of this progress and represents the shared views of four research groups that have had recent successes in using DNNs for acoustic modeling in speech recognition.

Two bagging approaches, say \(\frac{1}{2}n\)-out-of-\(n\) without replacement (subagging) and \(n\)-out-of-\(n\) with replacement (bagging) have been applied in the problem of estimation of the parameters in a multivariate mixture model. It has been observed by Monte Carlo simulations and a real data example, that both bagging methods have improved the standard deviation of the maximum likelihood estimator of the mixing proportion, whilst the absolute bias increased slightly. In estimating the component distributions, bagging could increase the root mean integrated squared error when estimating the most probable component.

Voice conversion is an important problem in audio signal processing. The goal of voice conversion is to transform the speech signal of a source speaker such that it sounds as if it had been uttered by a target speaker. Our contribution in this paper includes a new methodology for designing the relationship between two sets of spectral envelopes. Our systems perform by: (1) cascading deep neural networks and Gaussian mixture model to construct DNN-GMM and GMM-DNN-GMM models in order to find a global mapping relationship between the cepstral vectors of the two speakers; (2) using a new spectral synthesis process with cascaded cepstrum predictors and excitation and phase extracted from the target training space encoded as a KD-tree. Experimental results of the proposed methods exhibit a great improvement of the intelligibility, the quality and naturalness of the converted speech signals when compared with stimuli obtained by baseline conversion methods. The extraction of excitation and phase from the target training space, permits the preservation of target speaker's identity.

Bayesian methodology is an important technique in statistics, and especially in mathematical statistics. It consists of the sample information along with the prior information available about the parameter before the sample has been observed. This paper exhibits the estimation of the parameters of queueing model with inter-arrival time and service time which follows Gumbel distribution. Bayesian procedure is applied to obtain the estimation of the model parameters and the trac intensity of queueing model based on the informative and the non-informative prior knowledges. In this paper, the Bayesian estimates are carried out by numerically and graphically with the help of Markov Chain Monte Carlo (MCMC) simulation technique, particularly in Gibbs sampling algorithm.

This study presents a response-spectral Ground Motion Model (GMM) for Israel, called KYB22 herein and derived with practical applications in mind. This model is based on the former work by , which derived a suite of nine Fourier amplitude spectra GMMs, based on both empirical data and calibrated point-source simulations. In this study, a weighted average of the Maiti et al. ( ) FAS models is computed and a synthetic database is created. Next, this database is converted to the Response spectral domain using the random vibration theory and a new GMM is regressed, constraining the magnitude and distance scaling on the synthetic response-spectral data. Site scaling is represented by VS30 and is a combination of empirical scaling with other considerations which are discussed in the text. Nonlinear site response is constrained from a global model, as are finite-fault effects, such as hanging-wall, mechanism and top of rupturewhich cannot be constrained from the data because it does not contain enough large magnitude data. State-wide hazard is then computed using KYB22, comparing results with other GMM combinations. It is found that the hazard results obtained by using KYB22 as a backbone model are comparable to results obtained using other popular combinations of GMMs in the logic tree. Therefore, we recommend using the new GMM as one of the branches within the ground-motion logic tree when conducting seismic hazard calculations for Israel.

In this research paper, we delve into the topics of Speech Diarization and Automatic Speech Recognition (ASR). Speech diarization involves the separation of individual speakers within an audio stream. By employing the ASR transcript, the diarization process aims to segregate each speaker's utterances, grouping them based on their unique audio characteristics. On the other hand, Automatic Speech Recognition refers to the capability of a machine or program to identify and convert spoken words and phrases into a machine-readable format. In our speech diarization approach, we utilize the Gaussian Mixer Model (GMM) to represent speech segments. The inter-cluster distance is computed based on the GMM parameters, and the distance threshold serves as the stopping criterion. ASR entails the conversion of an unknown speech waveform into a corresponding written transcription. The speech signal is analyzed using synchronized algorithms, taking into account the pitch frequency. Our primary objective typically revolves around developing a model that minimizes the Word Error Rate (WER) metric during speech transcription.

A 2D analytical turbulent diffusion model for particle dispersion and deposition at different heights across the pipe flow and circumferential deposition has been developed. This liquid-solid turbulent diffusion model presented in this paper has emanated from an existing gas-liquid turbulent diffusion model. Simultaneously a comprehensive 3D numerical investigation has been carried out to study the above making of multiphase mixture model available in Fluent 6.1. In both studies different particles sizes and densities were used. The deposition was studied as a function of particle diameter, density and fluid velocity. The deposition of particles, along the periphery of the wall and at different depths, was also investigated. Both studies showed that the deposition of heavier particles at the bottom of the pipe wall was found to be higher at lower velocities and lower at higher velocities. The lighter particles were found mostly suspended with homogeneous distribution. Smaller partic...

A comprehensive 3D numerical investigation of hydrodynamics of particles flowing through a horizontal pipe loop consisting of four bends has been modeled. The multiphase mixture model available in Fluent 6. 1 [6] is used in this study. In this numerical simulation five different particles have been used as secondary phases to calculate real multiphase effect in which inter-particle interaction has been accounted. The deposition of particles, along the periphery of the wall around bends has been investigated. The effect of bend and fluid velocity on particle deposition has also been investigated. The maximum particle deposition is at the bottom wall in the pipe before entering the bends conversely, downstream of bends the maximum deposition is not at the bottom -as seen upstream of the bends -rather it occurs at an angle of 60 0 toward the inner side from the bottom. The larger particles clearly showed deposition near the bottom of the wall except downstream of the bends. As expected, the smaller particles showed less tendency of deposition and this is more pronounced at higher velocity. This numerical investigation showed good agreement with the experimental results conducted by CSIRO team [9].

Video analysis often begins with background subtraction. This problem is often approached in two steps -a background model followed by a regularisation scheme. A model of the background allows it to be distinguished on a per-pixel basis from the foreground, whilst the regularisation combines information from adjacent pixels. We present a new method based on Dirichlet process Gaussian mixture models, which are used to estimate per-pixel background distributions. It is followed by probabilistic regularisation. Using a non-parametric Bayesian method allows per-pixel mode counts to be automatically inferred, avoiding over-/under-fitting. We also develop novel model learning algorithms for continuous update of the model in a principled fashion as the scene changes. These key advantages enable us to outperform the state-of-the-art alternatives on four benchmarks.

An unsupervised classification algorithm is derived by modeling observed data as a mixture of several mutually exclusive classes that are each described by linear combinations of independent non-Gaussian densities. The algorithm estimates the data density in each class by using parametric nonlinear functions that fit to the non-Gaussian structure of the data. This improves classification accuracy compared with standard Gaussian mixture models. When applied to textures, the algorithm can learn basis functions for images that capture the statistically significant structure intrinsic in the images. We apply this technique to the problem of unsupervised texture classification and segmentation.

Gene families are frequently gained and lost from prokaryotic genomes. It is widely believed that the rate of loss was accelerated for some but not all gene families in lineages that became parasites or endosymbionts. This leads to a form of heterotachy that may be responsible for the poor performance of phylogeny estimation based on gene content. We describe a mixture model that accounts for this heterotachy. We show that this model fits data on the distribution of gene families across bacteria from the COG database much better than previous models. However, it still favors an artifactual tree topology in which parasites form a clade over the more plausible 16S topology. In contrast to a previous model of genome dynamics, our model suggests that the ancestral bacterium had a small genome. We suggest that models of gene family gain and loss are likely to be more useful for understanding genome dynamics than for estimating phylogenetic trees.

Background Phylogenetic reconstruction methods based on gene content often place all the parasitic and endosymbiotic eubacteria (parasites for short) together in a clan. Many other lines of evidence point to this parasites clan being an artefact. This artefact could be a consequence of the methods used to construct ortholog databases (due to some unknown bias), the methods used to estimate the phylogeny, or both. We test the idea that the parasites clan is an ortholog identification artefact by analyzing three different ortholog databases (COG, TRIBES, and OFAM), which were constructed using different methods, and are thus unlikely to share the same biases. In each case, we estimate a phylogeny using an improved version of the conditioned logdet distance method. If the parasites clan appears in trees from all three databases, it is unlikely to be an ortholog identification artefact. Accelerated loss of a subset of gene families in parasites (a form of heterotachy) may contribute to ...

The purpose of this paper is to present a novel approach to the Gaussian mixture background modeling model (GMM) that we call the median mixture model (MMM). The proposed method is based on the same principles as the GMM, but all of the background model parameters are estimated in a much more efficient way resulting in accelerating the algorithm by about 25% without deteriorating the modeling results. The second part of this paper describes a method of uniting three MMMs where three different sets of input data undergo modeling in order to achieve even better results. This approach called the united median mixtures is more robust to random noise as well as unwanted shadows and reflections. Both algorithms are thoroughly tested and compared against the Gaussian mixture model, taking into consideration robustness to noise, shadows and reflections.

Although aggressive medical treatment protocols have led to 80% five-year survival rates for most childhood cancer patients, many long-term survivors experience multiple troubling symptoms. Using data from 100 adult survivors of childhood cancers (ACC-survivors), we used latent variable mixture modeling to generate unique subgroups of survivors based on their experiences with a cluster of eight symptoms: lack of energy, worry, pain, difficulty sleeping, feeling irritable, feeling nervous, difficulty concentrating, and feeling sad (as measured by the Memorial Symptom Assessment Scale). We also examined factors that were likely to predict subgroup membership (chronic health conditions [CHCs], health-promoting lifestyle, and demographic variables) and determined the extent to which satisfaction with quality of life (QoL) varied across the subgroups. The final mixture model included three subgroups of ACC-survivors: high symptoms (HS; n ¼ 21), moderate symptoms (MS; n ¼ 45), and low symptoms (LS; n ¼ 34). ACC-survivors who reported at least one CHC were six times as likely to be classified in the HS subgroup as compared with the LS subgroup. Mean health-promoting lifestyle scores were lowest in the HS subgroup and highest in the LS subgroup. Differences in QoL among the subgroups were statistically significant, thus validating that the subgroups were characterized uniquely for identifying those symptoms with highest life impact. To our knowledge, we are the first to identify distinct subgroups of ACCsurvivors differentiated by symptom cluster experience profiles. The findings warrant additional research to confirm the subgroup-specific symptom cluster experience profiles in larger studies of ACC-survivors.

Data on contestants' choices in Italian Game Show Affari Tuoi are analysed in a way that separates the effect of risk attitude from that of beliefs concerning the amount of money that will be offered to contestants in future rounds. The importance of belief-formation is confirmed by the estimation of a mixture model which establishes that the vast majority of contestants are forward-looking as opposed to myopic. The most important issue addressed in the paper is what belief function is actually being used by contestants. This function is estimated in an unconstrained way as a component of the choice model, which is estimated using maximum simulated likelihood. Separate identification of the belief function and preferences is possible by virtue of the fact that at a certain stage of the game, beliefs are not relevant, and risk attitude is the sole determinant of choice. The rational expectations hypothesis is tested by comparing the estimated belief function with the "true" offer function which is estimated using data on offers actually made to contestants. We find that there is a significant difference between these two functions, and hence we reject the rational expectations hypothesis. However, when a simpler "rule-of-thumb" structure is assumed for the belief function, we find a correspondence to the function obtained from data on actual offers. Our overall conclusion is that contestants are rational to the extent that they make use of all available relevant information, but are not fully rational because they are not processing the information in an optimal way. The importance of allowing the choice data to convey the belief function without prejudice is emphasised.

Preference elicitation is a key problem facing the deployment of intelligent systems that make or recommend decisions on the behalf of users. Since not all aspects of a utility function have the same impact on object-level decision quality, determining which information to extract from a user is itself a sequential decision problem, balancing the amount of elicitation effort and time with decision quality. We formulate this problem as a partially-observable Markov decision process (POMDP). Because of the continuous nature of the state and action spaces of this POMDP, standard techniques cannot be used to solve it. We describe methods that exploit the special structure of preference elicitation to deal with parameterized belief states over the continuous state space, and gradient techniques for optimizing parameterized actions. These methods can be used with a number of different belief state representations, including mixture models.

Progress in immunotherapy revolutionized the treatment landscape for advanced lung cancer, raising survival expectations beyond those that were historically anticipated with this disease. In the present study, we describe the methods for the adjustment of mixture parametric models of two populations for survival analysis in the presence of long survivors. A methodology is proposed in several five steps: first, it is proposed to use the multimodality test to decide the number of subpopulations to be considered in the model, second to adjust simple parametric survival models and mixture distribution models, to estimate the parameters and to select the best model fitted the data, finally, to test the hypotheses to compare the effectiveness of immunotherapies in the context of randomized clinical trials. The methodology is illustrated with data from a clinical trial that evaluates the effectiveness of the therapeutic vaccine CIMAvaxEGF vs the best supportive care for the treatment of advanced lung cancer. The mixture survival model allows estimating the presence of a subpopulation of long survivors that is 44% for vaccinated patients. The differences between the treated and control group were significant in both subpopulations (population of shortterm survival: p = 0.001, the population of long-term survival: p = 0.0002). For cancer therapies, where a proportion of patients achieves long-term control of the disease, the heterogeneity of the population must be taken into account. Mixture parametric models may be more suitable to detect the effectiveness of immunotherapies compared to standard models.

Genomic comparisons provide evidence for ancient genome-wide duplications in a diverse array of animals and plants. We developed a birth-death model to identify evidence for genome duplication in EST data, and applied a mixture model to estimate the age distribution of paralogous pairs identified in EST sets for species representing the basal-most extant flowering plant lineages. We found evidence for episodes of ancient genome-wide duplications in the basal angiosperm lineages including Nuphar advena (yellow water lily: Nymphaeaceae) and the magnoliids Persea americana (avocado: Lauraceae), Liriodendron tulipifera (tulip poplar: Magnoliaceae), and Saruma henryi (Aristolochiaceae). In addition, we detected independent genome duplications in the basal eudicot Eschscholzia californica (California poppy: Papaveraceae) and the basal monocot Acorus americanus (Acoraceae), both of which were distinct from duplications documented for ancestral grass (Poaceae) and core eudicot lineages. Among gymnosperms, we found equivocal evidence for ancient polyploidy in Welwitschia mirabilis (Gnetales) and no evidence for polyploidy in pine, although gymnosperms generally have much larger genomes than the angiosperms investigated. Cross-species sequence divergence estimates suggest that synonymous substitution rates in the basal angiosperms are less than half those previously reported for core eudicots and members of Poaceae. These lower substitution rates permit inference of older duplication events. We hypothesize that evidence of an ancient duplication observed in the Nuphar data may represent a genome duplication in the common ancestor of all or most extant angiosperms, except Amborella.

In economic applications it is often the case that the variate of interest is nonnegative and its distribution has a mass-point at zero. Many regression strategies have been proposed to deal with data of this type but, although there has been a long debate in the literature on the appropriateness of di¤erent models, formal statistical tests to choose between the competing speci…cations are not often used in practice. We use the non-nested hypothesis testing framework of Several tests for model speci…cation in the presence of alternative hypotheses," Econometrica, 49, 781-793) to develop a novel and simple regression-based speci…cation test that can be used to discriminate between these models.

This is a comparative study on mixture distribution; where the study seeks to ascertain whether higher number of k-component mixtures could result to development of models that show better fits. In the performance comparison, special consideration was given to univariate one parameter distributions derived using mixture models, and the results show that distributions of higher k-mixture components  relatively have greater propensity to exhibit better fit than the lesser mixture component distributions (k < 3).

In the field of classification, the main task of most algorithms is to find a perfect decision boundary. However, most decision boundaries are too complex to be discovered directly. Therefore, in this paper, we proposed an Incremental Maximum Gaussian Mixture Partition (IMGMP) algorithm for classification, aiming to solve those problems with complex decision boundaries. As a self-adaptive algorithm, it uses a divide and conquer strategy to calculate out a reasonable decision boundary by step. An Improved K-means clustering and a Maximum Gaussian Mixture model are used in the classifier. This algorithm also has been tested on artificial and real-life datasets in order to evaluate its remarkable flexibility and robustness.

Size, weight, and power constrained platforms impose constraints on computational resources that introduce unique challenges in implementing localization algorithms. We present a framework to perform fast localization on such platforms enabled by the compressive capabilities of Gaussian Mixture Model representations of point cloud data. Given raw structural data from a depth sensor and pitch and roll estimates from an on-board attitude reference system, a multi-hypothesis particle filter localizes the vehicle by exploiting the likelihood of the data originating from the mixture model. We demonstrate analysis of this likelihood in the vicinity of the ground truth pose and detail its utilization in a particle filter-based vehicle localization strategy, and later present results of real-time implementations on a desktop system and an off-the-shelf embedded platform that outperform localization results from running a state-of-theart algorithm on the same environment.

3D data sensors provide an enormous amount of information. It is necessary to develop efficient methods to manage this information under certain time, bandwidth or storage space requirements. In this work, we propose a 3D compression and decompression method. This method also allows the use of the compressed data for a registration process. First, points are selected and grouped, using a 3D-model based on planar surfaces. Next, we use a fast variant of Gaussian Mixture Models and an Expectation-Maximization algorithm to replace the points grouped in the previous step with a set of Gaussian distributions. These learned models can be used as features to find matches between two consecutive poses and apply 3D pose registration using RANSAC. Finally, the 3D map can be obtained by decompressing the models.

The planthopper family Cixiidae (Hemiptera: Fulgoromorpha) comprises approximately 160 genera and 2000 species divided in three subfamilies: Borystheninae, Bothriocerinae and Cixiinae, the later with 16 tribes. The current paper represents the first attempt to estimate phylogenetic relationships within Cixiidae based on molecular data. We use a total of 3652 bp sequence alignment of four genes: the mitochondrial coding genes Cytochrome c Oxidase subunit 1 (Cox1) and Cytochrome b (Cytb), a portion of the nuclear 18S rDNA and two non-contiguous portions of the nuclear 28S rDNA. The phylogenetic relationships of 72 terminal specimens were reconstructed using both maximum parsimony and Bayesian inference methods. Through the analysis of this empirical dataset, we also provide comparisons among different a priori partitioning strategies and the use of mixture models in a Bayesian framework. Our comparisons suggest that mixture models overcome the benefits obtained by partitioning the data according to codon position and gene identity, as they provide better accuracy in phylogenetic reconstructions. The recovered maximum parsimony and Bayesian inference phylogenies suggest that the family Cixiidae is paraphyletic in respect with Delphacidae. The paraphyly of the subfamily Cixiinae is also recovered by both approaches. In contrast to a morphological phylogeny recently proposed for cixiids, subfamilies Borystheninae and Bothriocerinae form a monophyletic group.

Traces collected at monitored points around the Internet contain representative performance information about the paths their probes traverse. Basic measurement attributes, such as delay and loss, are easy to collect and provide a means to both build and validate empirical performance models. However, the task of analysis and extracting performance conclusions from measurements remains challenging. Ideally, performance modelling aims to find a set of self-contained parameters to describe, summarise, profile and easy display network performance status at a time. This can result in the provision of meaningful information to address applications in fault and performance management, hence providing input to network provisioning, traffic engineering and performance prediction. In this work we present the Weibull Mixture Model, a method to characterise endto-end network delay measurements within a few simple, accurate, representative and handleable parameters using a finite combination of Weibull distributions, with all the aforementioned benefits. The model parameters are related to meaningful delay characteristics, such as average peak and tail behaviour in a daily profile, and can be optimally found using an iterative algorithm known as Expectation Maximisation. Studies on such parameter evolution can reflect current workload status and all possible network events impacting packet dynamics, with further applications in network management. In addition, a self-sufficient procedure to implement the Weibull Mixture Model is presented, along with a set of matching examples to real GPS synchronised measurements taken across the Internet, donated by RIPE NCC.

This paper investigates kernel-based probabilistic neural networks for speaker verification in clean and noisy environments. In particular, it compares the performance and characteristics of speaker verification systems that use probabilistic decision-based neural networks (PDBNNs), Gaussian mixture models (GMMs) and elliptical basis function networks (EBFNs) as speaker models. Experimental evaluations based on 138 speakers of the YOHO corpus and its noisy variants were conducted. The original PDBNN training algorithm was also modified to make PDBNNs appropriate for speaker verification. Experimental evaluations, based on 138 speakers and the visualization of decision boundaries, indicate that GMM-and PDBNN-based speaker models are superior to the EBFN ones in terms of performance and generalization capability. This work also finds that PDBNNs and GMMs are more robust than EBFNs in verifying speakers in noise environments.

Gaussian Mixture Models are one of the most studied and mature models in unsupervised learning. However, outliers are often present in the data and could influence the cluster estimation. In this paper, we study a new model that assumes that data comes from a mixture of a number of Gaussians as well as a uniform "background" component assumed to contain outliers and other non-interesting observations. We develop a novel method based on robust loss minimization that performs well in clustering such GMM with a uniform background. We give theoretical guarantees for our clustering algorithm to obtain best clustering results with high probability. Besides, we show that the result of our algorithm does not depend on initialization or local optima, and the parameter tuning is an easy task. By numeric simulations, we demonstrate that our algorithm enjoys high accuracy and achieves the best clustering results given a large enough sample size. Finally, experimental comparisons with typical clustering methods on real datasets witness the potential of our algorithm in real applications.

Gaussian Mixture Models are one of the most studied and mature models in unsupervised learning. However, outliers are often present in the data and could influence the cluster estimation. In this paper, we study a new model that assumes that data comes from a mixture of a number of Gaussians as well as a uniform "background" component assumed to contain outliers and other non-interesting observations. We develop a novel method based on robust loss minimization that performs well in clustering such GMM with a uniform background. We give theoretical guarantees for our clustering algorithm to obtain best clustering results with high probability. Besides, we show that the result of our algorithm does not depend on initialization or local optima, and the parameter tuning is an easy task. By numeric simulations, we demonstrate that our algorithm enjoys high accuracy and achieves the best clustering results given a large enough sample size. Finally, experimental comparisons with typical clustering methods on real datasets witness the potential of our algorithm in real applications.