Mixture Factor Analysis for Approximating a Nonnormally Distributed Continuous Latent Factor With Continuous and Dichotomous Observed Variables

Mixtures of factor analyzers (MFA) provide a powerful tool for modelling high-dimensional datasets. In recent years, several generalizations of MFA have been developed where the normality assumption of the factors and/or of the errors were relaxed to allow for skewness in the data. However, due to the form of the adopted component densities, the distribution of the factors/errors in most of these models is typically limited to modelling skewness concentrated in a single direction. Here, we introduce a more flexible finite mixture of factor analyzers based on the class of scale mixtures of canonical fundamental skew normal (SMCFUSN) distributions. This very general class of skew distributions can capture various types of skewness and asymmetry in the data. In particular, the proposed mixtures of SMCFUSN factor analyzers (SMCFUSNFA) can simultaneously accommodate multiple directions of skewness. As such, it encapsulates many commonly used models as special and/or limiting cases, such as models of some versions of skew normal and skew t-factor analyzers, and skew hyperbolic factor analyzers. For illustration, we focus on the t-distribution member of the class of SMCFUSN distributions, leading to mixtures of canonical fundamental skew t-factor analyzers (CFUSTFA). Parameter estimation can be carried out by maximum likelihood via an EM-type algorithm. The usefulness and potential of the proposed model are demonstrated using four real datasets.

The Maximum Likelihood (ML) and Best Linear Unbiased (BLU) estimators of the location and scale parameters of an extreme value distribution (Lawless [1982]) are compared under conditions of small sample sizes and Type I censorship. The comparisons were made in terms of the mean square error criterion. According to this criterion, the ML estimator of σ in the case of very small sample sizes (n < 10) and heavy censorship (low censoring time) proved to be more efficient than the corresponding BLU estimator. However, the BLU estimator for σ attains parity with the corresponding ML estimator when the censoring time increases even for sample sizes as low as 10. The BLU estimator of σ attains equivalence with the ML estimator when the sample size increases above 10, particularly when the censoring time is also increased. The situation is reversed when it came to estimating the location parameter μ, as the BLU estimator was found to be consistently more efficient than the ML estimator despite the improved performance of the ML estimator when the sample size increases. However, computational ease and convenience favor the ML estimators. Keywords: maximum likelihood estimatorsbest linear unbiased estimatorslife-testingreliability

Latent factor (LF) models are highly effective in extracting useful knowledge from High-Dimensional and Sparse (HiDS) matrices which are commonly seen in various industrial applications. An LF model usually adopts iterative optimizers, which may consume many iterations to achieve a local optima, resulting in considerable time cost. Hence, how to accelerate the training process of an LF model becomes a highly significant issue. To address it, this work innovatively proposes a randomized latent factor (RLF) model. It incorporates the principle of randomized learning techniques for neural networks into the LF analysis on HiDS matrices to alleviate the computational burden greatly. It also extends the standard learning process for randomized neural networks in context of LF analysis to make the resulting model represent an HiDS matrix correctly. Experimental results on three HiDS matrices from industrial applications demonstrate that compared with state-of-the-art LF models, RLF is able to achieve significantly higher computational efficiency and comparable prediction accuracy for missing data. More importantly, it provides a novel, effective, and efficient approach to LF analysis on HiDS matrices.

Joint latent factors and attributes to discover interpretable preferences in recommendation

How to extract useful knowledge from a high-dimensional and sparse (HiDS) matrix efficiently is critical for many big data-related applications. A latent factor (LF) model has been widely adopted to address this problem. It commonly relies on an iterative learning algorithm like stochastic gradient descent. However, an algorithm of this kind commonly consumes many iterations to converge, resulting in considerable time cost on large-scale datasets. How to accelerate an LF model's training process without accuracy loss becomes a vital issue. To address it, this study innovatively proposes a <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</u> ultilayered-and-randomized <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</u> atent <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</u> actor (MLF) model. Its main idea is two-fold: a) adopting randomized-learning to train LFs for implementing a ‘one-iteration’ training process for saving time; and 2) adopting the principle of a generally multilayered structure as in a deep forest or multilayered extreme learning machine to structure its LFs, thereby enhancing its representative learning ability. Empirical studies on six HiDS matrices from real applications demonstrate that compared with state-of-the-art LF models, an MLF model achieves significantly higher computational efficiency with satisfactory prediction accuracy. It has the potential to handle LF analysis on a large scale HiDS matrix with real-time requirements.

Understanding the reliability of outcomes in randomized controlled trials (RCTs) is crucial, as standard metrics, such as P- value do not fully capture result fragility. This led to the adoption of specific indices: the fragility index (FI), which measures the strength of trial through significant results by calculating the minimum number of patient status changes from nonevent to event required to make the results statistically insignificant; reverse fragility index (RFI), used for insignificant results; and continuous fragility index (CFI), which acts similar to FI for significant continuous outcomes. The objective is to assess the robustness of orthopaedics RCTs using these indices across leading orthopaedic journals. A systematic review of RCTs published between 2019 and 2023 in the top five general orthopaedic journals, identified through Scientific Journal Rankings, was done. Data extraction focused on FI, RFI, and CFI and related measures for 160 RCTs. The indices were calculated using established methodologies, with sample size adjustments. 22 RCTs had statistically significant dichotomous primary outcomes and 17 studies had notable dichotomous secondary outcomes. Twenty-nine had negligible (insignificant) dichotomous primary outcomes, and 92 reported notable continuous outcomes. Only one RCT reported a FI in the article. The median FI was 5 with a median sample size of 142 for dichotomous outcomes. The median RFI was 3 with a median sample size of 100 for negligible outcomes, and the median CFI was 13 with a median sample size of 86.5 for continuous outcomes, showing dichotomous outcomes to be more fragile than continuous ones. Continuous outcomes are less fragile than dichotomous outcomes, with negligible dichotomous outcomes being particularly more fragile. This fragility stems from small sample sizes and limited outcome events. Using these indices, especially when considering patient loss to follow-up, can improve the reliability of findings. I.

Contributions to the Estimation of Mixed-State Conditionally Heteroscedastic Latent Factor Models: A Comparative Study

BackgroundIn investigating differentially expressed genes or other selected features, researchers conduct hypothesis tests to determine which biological categories, such as those of the Gene Ontology (GO), are enriched for the selected features. Multiple comparison procedures (MCPs) are commonly used to prevent excessive false positive rates. Traditional MCPs, e.g., the Bonferroni method, go to the opposite extreme: strictly controlling a family-wise error rate, resulting in excessive false negative rates. Researchers generally prefer the more balanced approach of instead controlling the false discovery rate (FDR). However, the q-values that methods of FDR control assign to biological categories tend to be too low to reliably estimate the probability that a biological category is not enriched for the preselected features. Thus, we study an application of the other estimators of that probability, which is called the local FDR (LFDR).ResultsWe considered five LFDR estimators for detecting enriched GO terms: a binomial-based estimator (BBE), a maximum likelihood estimator (MLE), a normalized MLE (NMLE), a histogram-based estimator assuming a theoretical null hypothesis (HBE), and a histogram-based estimator assuming an empirical null hypothesis (HBE-EN). Since NMLE depends not only on the data but also on the specified value of Π0, the proportion of non-enriched GO terms, it is only advantageous when either Π0 is already known with sufficient accuracy or there are data for only 1 GO term. By contrast, the other estimators work without specifying Π0 but require data for at least 2 GO terms. Our simulation studies yielded the following summaries of the relative performance of each of those four estimators. HBE and HBE-EN produced larger biases for 2, 4, 8, 32, and 100 GO terms than BBE and MLE. BBE has the lowest bias if Π0 is 1 and if the number of GO terms is between 2 and 32. The bias of MLE is no worse than that of BBE for 100 GO terms even when the ideal number of components in its underlying mixture model is unknown, but has high bias when the number of GO terms is small compared to the number of estimated parameters. For unknown values of Π0, BBE has the lowest bias for a small number of GO terms (2-32 GO terms), and MLE has the lowest bias for a medium number of GO terms (100 GO terms).ConclusionsFor enrichment detection, we recommend estimating the LFDR by MLE given at least a medium number of GO terms, by BBE given a small number of GO terms, and by NMLE given either only 1 GO term or precise knowledge of Π0.

Rating prediction using review texts with underlying sentiments

Latent factor models have been widely used for recommendation. Most existing latent factor models mainly utilize the rating information between users and items, although some recently extended models add some auxiliary information to learn a unified latent factor between users and items. The unified latent factor only represents the latent features of users and items from the aspect of purchase history. However, the latent features of users and items may stem from different aspects, e.g., the brand-aspect and category-aspect of items. In this paper, we propose a Neural network based Aspect-level Collaborative Filtering model (NeuACF) to exploit different aspect latent factors. Through modelling rich objects and relations in recommender system as a heterogeneous information network, NeuACF first extracts different aspect-level similarity matrices of users and items through different meta-paths and then feeds an elaborately designed deep neural network with these matrices to learn aspect-level latent factors. Finally, the aspect-level latent factors are effectively fused with an attention mechanism for the top-N recommendation. Extensive experiments on three real datasets show that NeuACF significantly outperforms both existing latent factor models and recent neural network models.

A Flexible State-Space Model with Application to Stochastic Volatility

Likelihood-based methods are developed for analyzing a random sample on two continuous variables when values of one of the variables are missing. Normal maximum likelihood estimates when values are missing completely at random were derived by Anderson (1957). They are also maximum likelihood providing the missing-data mechanism is ignorable, in Rubin's (1976) sense that the mechanism depends only on observed data. A new class of pattern-mixture models (Little, 1993) is described for the situation where missingness is assumed to depend on an arbitrary unspecified function of a linear combination of the two variables. Maximum likelihood for models in this class is straightforward, and yields the estimates of Anderson (1957) when missingness depends solely on the completely observed variable, and the estimates of Brown (1990) when missingness depends solely on the incompletely observed variable. Another choice of linear combination yields estimates from complete-case analysis. Large-sample and Bayesian methods are described for this model. The data do not supply information about the ratio of the coefficients of the linear combination that controls missingness. If this ratio is not well-determined based on prior knowledge, a prior distribution can be specified, and Bayesian inference is then readily accomplished. Alternatively, sensitivity of inferences can be displayed for a variety of choices of the ratio.

The Multiple Comparison Procedures with Modeling Techniques (MCP-Mod) framework has been recently approved by the U.S. Food, Administration, and European Medicines Agency as fit-for-purpose for phase II studies. Nonetheless, this approach relies on the asymptotic properties of Maximum Likelihood (ML) estimators, which might not be reasonable for small sample sizes. In this paper, we derived improved ML estimators and correction for their covariance matrices in the censored Weibull regression model based on the corrective and preventive approaches. We performed two simulation studies to evaluate ML and improved ML estimators with their covariance matrices in (i) a regression framework (ii) the Multiple Comparison Procedures with Modeling Techniques framework. We have shown that improved ML estimators are less biased than ML estimators yielding Wald-type statistics that controls type I error without loss of power in both frameworks. Therefore, we recommend the use of improved ML estimators in the MCP-Mod approach to control type I error at nominal value for sample sizes ranging from 5 to 25 subjects per dose.

For a balanced two‐way mixed model, the maximum likelihood (ML) and restricted ML (REML) estimators of the variance components were obtained and compared under the non‐negativity requirements of the variance components by Lee and Kapadia (1984). In this note, for a mixed (random blocks) incomplete block model, explicit forms for the REML estimators of variance components are obtained. They are always non‐negative and have smaller mean squared error (MSE) than the analysis of variance (AOV) estimators. The asymptotic sampling variances of the maximum likelihood (ML) estimators and the REML estimators are compared and the balanced incomplete block design (BIBD) is considered as a special case. The ML estimators are shown to have smaller asymptotic variances than the REML estimators, but a numerical result in the randomized complete block design (RCBD) demonstrated that the performances of the REML and ML estimators are not much different in the MSE sense.

Over-the-air computation (OAC) is a promising technique to realize fast model aggregation in the uplink of federated edge learning (FEEL). OAC, however, hinges on accurate channel-gain precoding and strict synchronization among edge devices, which are challenging in practice. As such, how to design the maximum likelihood (ML) estimator in the presence of residual channel-gain mismatch and asynchronies is an open problem. To fill this gap, this paper formulates the problem of misaligned OAC for FEEL and puts forth a whitened matched filtering and sampling scheme to obtain oversampled, but independent samples from the misaligned and overlapped signals. Given the whitened samples, a sum-product ML (SP-ML) estimator and an aligned-sample estimator are devised to estimate the arithmetic sum of the transmitted symbols. In particular, the computational complexity of our SP-ML estimator is linear in the packet length, and hence is significantly lower than the conventional ML estimator. Extensive simulations on the test accuracy versus the average received energy per symbol to noise power spectral density ratio (EsN0) yield two main results: 1) In the low EsN0 regime, the aligned-sample estimator can achieve superior test accuracy provided that the phase misalignment is not severe. In contrast, the ML estimator does not work well due to the error propagation and noise enhancement in the estimation process. 2) In the high EsN0 regime, the ML estimator attains the optimal learning performance regardless of the severity of phase misalignment. On the other hand, the aligned-sample estimator suffers from a test-accuracy loss caused by phase misalignment.