Mixture-based Method Research Articles

Disentangling effect size heterogeneity in meta-analysis: A latent mixture approach.

An important task of meta-analysis is to observe, quantify, and explain the heterogeneity across the reported effect sizes of primary studies. A primary issue that challenges this task is the myriad of subtle factors that could have contributed to the observed heterogeneity. We leveraged the recent advances in theoretical machine learning to develop a novel latent mixture-based method for disentangling effect-size heterogeneity in meta-analysis. Mathematical analysis and simulation studies were carried out to demonstrate that, when the observed heterogeneity stems from more than 1 factor, our method can attain a substantially higher statistical power than the traditional methods for moderator analysis without requiring researchers to make judgment calls on which factors to consider or correct for in analyzing the observed heterogeneity. We also conducted a case study with real-world data to show how our method may be used to address long-standing inconsistencies in the literature. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Performance Analysis of MRC Under Spatially Correlated Interference Using Mixture-Based Method

Effect of interference correlation on wireless systems is often studied by modeling the locations of interferers as a Poisson Point Process (PPP). However, in many cases, the complicated nature of this correlation limits the analytical tractability of the PPP-based approach. For example, for an interference-aware $N$-antenna Maximum-Ratio Combining (MRC) receiver, the analytical expression for outage probability is available only for $N=2$. For $N>2$, the exact analysis using standard PPP-based approach becomes intractable because of which one has to either resort to bounds or to simulations. In this letter, we overcome this issue and derive the MRC outage probability for an arbitrary $N$ by employing the mixture-based method of modeling the correlation in the interference powers. This method offers a much simpler analytical structure to the correlated interference, thereby lending analytical tractability to such analyses. The mixture parameter ($q$) is tuned based on the matching of joint Signal-to-Interference Ratio (SIR) statistics, which results in a very accurate mixture-based result. The tightness of these approximations is verified using Monte Carlo simulations.

Spatial–temporal modelling of fMRI data through spatially regularized mixture of hidden process models

Previous work investigated a range of spatio-temporal constraints for fMRI data analysis to provide robust detection of neural activation. We present a mixture-based method for the spatio-temporal modelling of fMRI data. This approach assumes that fMRI time series are generated by a probabilistic superposition of a small set of spatio-temporal prototypes (mixture components). Each prototype comprises a temporal model that explains fMRI signals on a single voxel and the model's “region of influence” through a spatial prior over the voxel space. As the key ingredient of our temporal model, the Hidden Process Model (HPM) framework proposed in Hutchinson et al. (2009) is adopted to infer the overlapping cognitive processes triggered by stimuli. Unlike the original HPM framework, we use a parametric model of Haemodynamic Response Function (HRF) so that biological constraints are naturally incorporated in the HRF estimation. The spatial priors are defined in terms of a parameterised distribution. Thus, the total number of parameters in the model does not depend on the number of voxels. The resulting model provides a conceptually principled and computationally efficient approach to identify spatio-temporal patterns of neural activation from fMRI data, in contrast to most conventional approaches in the literature focusing on the detection of spatial patterns. We first verify the proposed model in a controlled experimental setting using synthetic data. The model is further validated on real fMRI data obtained from a rapid event-related visual recognition experiment (Mayhew et al., 2012). Our model enables us to evaluate in a principled manner the variability of neural activations within individual regions of interest (ROIs). The results strongly suggest that, compared with occipitotemporal regions, the frontal ones are less homogeneous, requiring two HPM prototypes per region. Despite the rapid event-related experimental design, the model is capable of disentangling the perceptual judgement and motor response processes that are both activated in the frontal ROIs. Spatio-temporal heterogeneity in the frontal regions seems to be associated with diverse dynamic localizations of the two hidden processes in different subregions of frontal ROIs.

A general procedure for learning mixtures of independent component analyzers

This paper presents a new procedure for learning mixtures of independent component analyzers. The procedure includes non-parametric estimation of the source densities, supervised–unsupervised learning of the model parameters, incorporation of any independent component analysis (ICA) algorithm into the learning of the ICA mixtures, and estimation of residual dependencies after training for correction of the posterior probability of every class to the testing observation vector. We demonstrate the performance of the procedure in the classification of ICA mixtures of two, three, and four classes of synthetic data, and in the classification of defective materials, consisting of 3D finite element models and lab specimens, in non-destructive testing using the impact-echo technique. The application of the proposed posterior probability correction demonstrates an improvement in the classification accuracy. Semi-supervised learning shows that unlabeled data can degrade the performance of the classifier when they do not fit the generative model. Comparative results of the proposed method and standard ICA algorithms for blind source separation in one and multiple ICA data mixtures show the suitability of the non-parametric ICA mixture-based method for data modeling.

The Spatial Representation of Market Information

To be used effectively, market knowledge and information must be structured and represented in ways that are parsimonious and conducive to efficient managerial decision making. This manuscript proposes a new latent structure spatial model for the representation of market information that meets this requirement. When applied to a priori defined (e.g., socioeconomic) segments, our proposed methodology provides a new way to display marketing data parsimoniously via dimension reduction through a factor-analytic specification. In post hoc studies, we simultaneously derive market segments from the data and represent the structure of market information within each of the unobserved, derived groups/segments. We summarize all relevant information concerning derived market segments via a series of maps that prove conducive to the quick and accurate dissemination of customer and competitor market information. The associations between the variables are captured in a reduced space, where each variable is represented by a vector that emanates from the origin and terminates on a hypersphere of unit (the vector length is arbitrary) radius (e.g., a unit circle in a two-dimensional space). The angles between the variable vectors capture the correlation structure in the reduced space. The method is very general and can be utilized to identify latent structures in a wide range of marketing applications. We present an actual commercial marketing application involving the (normalized) prescription shares (of specialists) of ethical drugs to demonstrate the effectiveness of representing market information in this manner and to reveal the advantage of the proposed methodology over a more general finite mixture-based method. The proposed methodology derives three segments that tend to group specialists with respect to the stage of adoption of innovation in this therapeutic category. The specialists in the first group appear to be laggards because they prescribe more of the older class of brands. However, they also have a higher-than-average preference for a newer and somewhat cheaper brand. This suggests that some of the specialists belonging to this segment may be price sensitive, while others may exhibit a slower adoption cycle, replacing the older class with the newer brands, and thus, skip one stage in the cycle of innovation. The specialists in the second segment are heavy users of the newer class of brands but are not particularly fast to adopt the latest brands. Finally, the last segment clearly consists of innovators. Traditionally, pharmaceutical marketers have viewed specialists in one of two extremes—all specialists are the same (i.e., the market has only one segment) or all specialists are very different (i.e., the market consists of 10,000+ segments of one physician each). Not surprisingly, this analysis suggests a more moderate perspective: specialists adopt new products at different rates.