Using mixture models to detect differentially expressed genes

An important and common problem in microarray experiments is the detection of genes that are differentially expressed in a given number of classes. As this problem concerns the selection of significant genes from a large pool of candidate genes, it needs to be carried out within the framework of multiple hypothesis testing. In this paper, we focus on the use of mixture models to handle the multiplicity issue. With this approach, a measure of the local false discovery rate is provided for each gene, and it can be implemented so that the implied global false discovery rate is bounded as with the Benjamini-Hochberg methodology based on tail areas. The latter procedure is too conservative, unless it is modified according to the prior probability that a gene is not differentially expressed. An attractive feature of the mixture model approach is that it provides a framework for the estimation of this probability and its subsequent use in forming a decision rule. The rule can also be formed to take the false negative rate into account.

Mixture models for detecting differentially expressed genes in microarrays

An important and common problem in microarray experiments is the detection of genes that are differentially expressed in a given number of classes. As this problem concerns the selection of significant genes from a large pool of candidate genes, it needs to be carried out within the framework of multiple hypothesis testing. In this paper, we focus on the use of mixture models to handle the multiplicity issue. With this approach, a measure of the local FDR (false discovery rate) is provided for each gene. An attractive feature of the mixture model approach is that it provides a framework for the estimation of the prior probability that a gene is not differentially expressed, and this probability can subsequently be used in forming a decision rule. The rule can also be formed to take the false negative rate into account. We apply this approach to a well-known publicly available data set on breast cancer, and discuss our findings with reference to other approaches.

Regularisation of mixture density networks

Mixture Density Networks are a principled method to model conditional probability density functions which are non-Gaussian. This is achieved by modelling the conditional distribution for each pattern with a Gaussian Mixture Model for which the parameters are generated by a neural network. This thesis presents a novel method to introduce regularisation in this context for the special case where the mean and variance of the spherical Gaussian Kernels in the mixtures are fixed to predetermined values. Guidelines for how these parameters can be initialised are given, and it is shown how to apply the evidence framework to mixture density networks to achieve regularisation. This also provides an objective stopping criteria that can replace the `early stopping' methods that have previously been used. If the neural network used is an RBF network with fixed centres this opens up new opportunities for improved initialisation of the network weights, which are exploited to start training relatively close to the optimum. The new method is demonstrated on two data sets. The first is a simple synthetic data set while the second is a real life data set, namely satellite scatterometer data used to infer the wind speed and wind direction near the ocean surface. For both data sets the regularisation method performs well in comparison with earlier published results. Ideas on how the constraint on the kernels may be relaxed to allow fully adaptable kernels are presented.

Regularisation of mixture density networks

Mixture Density Networks are a principled method to model conditional probability density functions which are non-Gaussian. This is achieved by modelling the conditional distribution for each pattern with a Gaussian Mixture Model for which the parameters are generated by a neural network. This thesis presents a novel method to introduce regularisation in this context for the special case where the mean and variance of the spherical Gaussian Kernels in the mixtures are fixed to predetermined values. Guidelines for how these parameters can be initialised are given, and it is shown how to apply the evidence framework to mixture density networks to achieve regularisation. This also provides an objective stopping criteria that can replace the `early stopping' methods that have previously been used. If the neural network used is an RBF network with fixed centres this opens up new opportunities for improved initialisation of the network weights, which are exploited to start training relatively close to the optimum. The new method is demonstrated on two data sets. The first is a simple synthetic data set while the second is a real life data set, namely satellite scatterometer data used to infer the wind speed and wind direction near the ocean surface. For both data sets the regularisation method performs well in comparison with earlier published results. Ideas on how the constraint on the kernels may be relaxed to allow fully adaptable kernels are presented.

Improved Hybrid Model of HMM/GMM for Speech Recognition

In this paper, we propose a speech recognition engine using hybrid model of Hidden Markov Model (HMM) and Gaussian Mixture Model (GMM). Both the models have been trained independently and the respective likelihood values have been considered jointly and input to a decision logic which provides net likelihood as the output. This hybrid model has been compared with the HMM model. Training and testing has been done by using a database of 20 Hindi words spoken by 80 different speakers. Recognition rates achieved by normal HMM are 83.5% and it gets increased to 85% by using the hybrid approach of HMM and GMM.

A Note on Bayesian Estimation for the Negative-Binomial Model

2000 Mathematics Subject Classification: 62F15.

Gaussian Process Kernels for Cross-Spectrum Analysis in Electrophysiological Time Series

Multi-output Gaussian processes provide a convenient framework for multi-task problems. An illustrative and motivating example of a multi-task problem is multi-region electrophysiological time-series data, where experimentalists are interested in both power and phase coherence between channels. Recently, the spectral mixture (SM) kernel was proposed to model the spectral density of a single task in a Gaussian process framework. This work develops a novel covariance kernel for multiple outputs, called the cross-spectral mixture (CSM) kernel. This new, flexible kernel represents both the power and phase relationship between multiple observation channels. The expressive capabilities of the CSM kernel are demonstrated through implementation of 1) a Bayesian hidden Markov model, where the emission distribution is a multi-output Gaussian process with a CSM covariance kernel, and 2) a Gaussian process factor analysis model, where factor scores represent the utilization of cross-spectral neural circuits. Results are presented for measured multi-region electrophysiological data.

Exploring Habitability Markers, Biosignatures, and Their False Positives Using Spectral Models of Terrestrial Exoplanets

Thesis (Ph.D.)--University of Washington, 2016-08

Estimating Bat and Bird Mortality Occurring at Wind Energy Turbines from Covariates and Carcass Searches Using Mixture Models

Environmental impacts of wind energy facilities increasingly cause concern, a central issue being bats and birds killed by rotor blades. Two approaches have been employed to assess collision rates: carcass searches and surveys of animals prone to collisions. Carcass searches can provide an estimate for the actual number of animals being killed but they offer little information on the relation between collision rates and, for example, weather parameters due to the time of death not being precisely known. In contrast, a density index of animals exposed to collision is sufficient to analyse the parameters influencing the collision rate. However, quantification of the collision rate from animal density indices (e.g. acoustic bat activity or bird migration traffic rates) remains difficult. We combine carcass search data with animal density indices in a mixture model to investigate collision rates. In a simulation study we show that the collision rates estimated by our model were at least as precise as conventional estimates based solely on carcass search data. Furthermore, if certain conditions are met, the model can be used to predict the collision rate from density indices alone, without data from carcass searches. This can reduce the time and effort required to estimate collision rates. We applied the model to bat carcass search data obtained at 30 wind turbines in 15 wind facilities in Germany. We used acoustic bat activity and wind speed as predictors for the collision rate. The model estimates correlated well with conventional estimators. Our model can be used to predict the average collision rate. It enables an analysis of the effect of parameters such as rotor diameter or turbine type on the collision rate. The model can also be used in turbine-specific curtailment algorithms that predict the collision rate and reduce this rate with a minimal loss of energy production.

Modeling spectral changes in singing voice for pitch modification

We present an advanced method to achieve natural modifications when applying a pitch shifting process to singing voice by modifying the spectral envelope of the audio ex- cerpt. To this end, an all-pole spectral envelope model has been selected to describe the global variations of the spectral envelope with the changes of the pitch. We performed a pitch shifting process of some sustained vowels with the envelope processing and without it, and compared both by means of a survey open to volunteers in our website.

Application of Mixture Models to Survival Data

Survival models are being widely applied to the engineering field to model time-to-event data once censored data is here a common issue. Using parametric models or not, for the case of heterogeneous data, they may not always represent a good fit. The present study relays on critical pumps survival data where traditional parametric regression might be improved in order to obtain better approaches. Considering censored data and using an empiric method to split the data into two subgroups to give the possibility to fit separated models to our censored data, we’ve mixture two distinct distributions according a mixture-models approach. We have concluded that it is a good method to fit data that does not fit to a usual parametric distribution and achieve reliable parameters. A constant cumulative hazard rate policy was used as well to check optimum inspection times using the obtained model from the mixture-model, which could be a plus when comparing with the actual maintenance policies to check whether changes should be introduced or not.

A low carbohydrate diet affects autonomic modulation during heavy but not moderate exercise

The aim of this study was to examine the effects of low carbohydrate (CHO) availability on heart rate variability (HRV) responses during moderate and severe exercise intensities until exhaustion. Six healthy males (age, 26.5 +/- 6.7 years; body mass, 78.4 +/- 7.7 kg; body fat %, 11.3 +/- 4.5%; (V) over dotO(2max), 39.5 +/- 6.6 mL kg(-1) min(-1)) volunteered for this study. All tests were performed in the morning, after 8-12 h overnight fasting, at a moderate intensity corresponding to 50% of the difference between the first (LT(1)) and second (LT(2)) lactate breakpoints and at a severe intensity corresponding to 25% of the difference between the maximal power output and LT(2). Forty-eight hours before each experimental session, the subjects performed a 90-min cycling exercise followed by 5-min rest periods and subsequent 1-min cycling bouts at 125% (V) over dotO(2max) (with 1-min rest periods) until exhaustion, in order to deplete muscle glycogen. A diet providing 10% (CHO(low)) or 65% (CHO(control)) of energy as carbohydrates was consumed for the following 2 days until the experimental test. The Poicare plots (standard deviations 1 and 2: SD1 and SD2, respectively) and spectral autoregressive model (low frequency LF, and high frequency HF) were applied to obtain HRV parameters. The CHO availability had no effect on the HRV parameters or ventilation during moderate-intensity exercise. However, the SD1 and SD2 parameters were significantly higher in CHO(low) than in CHO(control), as taken at exhaustion during the severe-intensity exercise (P < 0.05). The HF and LF frequencies (ms(2)) were also significantly higher in CHO(low) than in CHO(control) (P < 0.05). In addition, ventilation measured at the 5 and 10-min was higher in CHO(low) (62.5 +/- 4.4 and 74.8 +/- 6.5 L min(-1), respectively, P < 0.05) than in CHO(control) (70.0 +/- 3.6 and 79.6 +/- 5.1 L min(-1), respectively; P < 0.05) during the severe-intensity exercise. These results suggest that the CHO availability alters the HRV parameters during severe-, but not moderate-, intensity exercise, and this was associated with an increase in ventilation volume.

Human gait recognition using extraction and fusion of global motion features

This paper proposes a novel computer vision approach that processes video sequences of people walking and then recognises those people by their gait. Human motion carries different information that can be analysed in various ways. The skeleton carries motion information about human joints, and the silhouette carries information about boundary motion of the human body. Moreover, binary and gray-level images contain different information about human movements. This work proposes to recover these different kinds of information to interpret the global motion of the human body based on four different segmented image models, using a fusion model to improve classification. Our proposed method considers the set of the segmented frames of each individual as a distinct class and each frame as an object of this class. The methodology applies background extraction using the Gaussian Mixture Model (GMM), a scale reduction based on the Wavelet Transform (WT) and feature extraction by Principal Component Analysis (PCA). We propose four new schemas for motion information capture: the Silhouette-Gray-Wavelet model (SGW) captures motion based on grey level variations; the Silhouette-Binary-Wavelet model (SBW) captures motion based on binary information; the Silhouette-Edge-Binary model (SEW) captures motion based on edge information and the Silhouette Skeleton Wavelet model (SSW) captures motion based on skeleton movement. The classification rates obtained separately from these four different models are then merged using a new proposed fusion technique. The results suggest excellent performance in terms of recognising people by their gait.

The generalized inverse Weibull distribution

The inverse Weibull distribution has the ability to model failure rates which are quite common in reliability and biological studies. A three-parameter generalized inverse Weibull distribution with decreasing and unimodal failure rate is introduced and studied. We provide a comprehensive treatment of the mathematical properties of the new distribution including expressions for the moment generating function and the rth generalized moment. The mixture model of two generalized inverse Weibull distributions is investigated. The identifiability property of the mixture model is demonstrated. For the first time, we propose a location-scale regression model based on the log-generalized inverse Weibull distribution for modeling lifetime data. In addition, we develop some diagnostic tools for sensitivity analysis. Two applications of real data are given to illustrate the potentiality of the proposed regression model.

Influence of patient age and implantation technique on the probability of re-replacement of the homograft aortic valve

Background and aim of the study: Results of valve re-replacement (reoperation) in 898 patients undergoing aortic valve replacement with cryopreserved homograft valves between 1975 and 1998 are reported. The study aim was to provide estimates of unconditional probability of valve reoperation and cumulative incidence function (actual risk) of reoperation. Methods: Valves were implanted by subcoronary insertion (n = 500), inclusion cylinder (n = 46), and aortic root replacement (n = 352). Probability of reoperation was estimated by adopting a mixture model framework within which estimates were adjusted for two risk factors: patient age at initial replacement, and implantation technique. Results: For a patient aged 50 years, the probability of reoperation in his/her lifetime was estimated as 44% and 56% for non-root and root replacement techniques, respectively. For a patient aged 70 years, estimated probability of reoperation was 16% and 25%, respectively. Given that a reoperation is required, patients with non-root replacement have a higher hazard rate than those with root replacement (hazards ratio = 1.4), indicating that non-root replacement patients tend to undergo reoperation earlier before death than root replacement patients. Conclusion: Younger patient age and root versus non-root replacement are risk factors for reoperation. Valve durability is much less in younger patients, while root replacement patients appear more likely to live longer and hence are more likely to require reoperation.