We present a novel unsupervised deep learning approach called BindVAE, based on Dirichlet variational autoencoders, for jointly decoding multiple TF binding signals from open chromatin regions. BindVAE can disentangle an input DNA sequence into distinct latent factors that encode cell-type specific in vivo binding signals for individual TFs, composite patterns for TFs involved in cooperative binding, and genomic context surrounding the binding sites. On the task of retrieving the motifs of expressed TFs in a given cell type, BindVAE is competitive with existing motif discovery approaches.

The aim of this work is to solve the case study singular model involving the Neumann-Robin, Dirichlet, and Neumann boundary conditions using a novel computing framework that is based on the artificial neural network (ANN), global search genetic algorithm (GA), and local search sequential quadratic programming method (SQPM), i.e., ANN-GA-SQPM. The inspiration to present this numerical framework comes through the objective of introducing a reliable structure that associates the operative ANNs features using the optimization procedures of soft computing to deal with such stimulating systems. Four different problems that are based on the singular equations involving Neumann-Robin, Dirichlet, and Neumann boundary conditions have been occupied to scrutinize the robustness, stability, and proficiency of the designed ANN-GA-SQPM. The proposed results through ANN-GA-SQPM have been compared with the exact results to check the efficiency of the scheme through the statistical performances for taking fifty independent trials. Moreover, the study of the neuron analysis based on three and 15 neurons is also performed to check the authenticity of the proposed ANN-GA-SQPM.

Precise estimation of uncertainty in predictions for AI systems is a critical factor in ensuring trust and safety. Deep neural networks trained with a conventional method are prone to over-confident predictions. In contrast to Bayesian neural networks that learn approximate distributions on weights to infer prediction confidence, we propose a novel method, Information Aware Dirichlet networks, that learn an explicit Dirichlet prior distribution on predictive distributions by minimizing a bound on the expected max norm of the prediction error and penalizing information associated with incorrect outcomes. Properties of the new cost function are derived to indicate how improved uncertainty estimation is achieved. Experiments using real datasets show that our technique outperforms, by a large margin, state-of-the-art neural networks for estimating within-distribution and out-of-distribution uncertainty, and detecting adversarial examples.

In a multinomial set-up with k possible outcomes, we develop estimation under a \"middle censoring\" paradigm, which is as defined in Jammalamadaka and Mangalam (2003). This problem has many special features because of the inter-dependent probabilities, which we explore here.

Molecular ecology regularly requires the analysis of count data that reflect the relative abundance of features of a composition (e.g., taxa in a community, gene transcripts in a tissue). The sampling process that generates these data can be modelled using the multinomial distribution. Replicate multinomial samples inform the relative abundances of features in an underlying Dirichlet distribution. These distributions together form a hierarchical model for relative abundances among replicates and sampling groups. This type of Dirichlet-multinomial modelling (DMM) has been described previously, but its benefits and limitations are largely untested. With simulated data, we quantified the ability of DMM to detect differences in proportions between treatment and control groups, and compared the efficacy of three computational methods to implement DMM-Hamiltonian Monte Carlo (HMC), variational inference (VI), and Gibbs Markov chain Monte Carlo. We report that DMM was better able to detect shifts in relative abundances than analogous analytical tools, while identifying an acceptably low number of false positives. Among methods for implementing DMM, HMC provided the most accurate estimates of relative abundances, and VI was the most computationally efficient. The sensitivity of DMM was exemplified through analysis of previously published data describing lung microbiomes. We report that DMM identified several potentially pathogenic, bacterial taxa as more abundant in the lungs of children who aspirated foreign material during swallowing; these differences went undetected with different statistical approaches. Our results suggest that DMM has strong potential as a statistical method to guide inference in molecular ecology.

Preventing and controlling zoonoses through the design and implementation of public health policies requires a thorough understanding of transmission pathways. Modelling jointly the epidemiological data and genetic information of microbial isolates derived from cases provides a methodology for tracing back the source of infection. In this paper, the attribution probability for human cases of campylobacteriosis for each source, conditional on the extent to which each case resides in a rural compared to urban environment, is estimated. A model that incorporates genetic data and evolutionary processes is applied alongside a newly developed genetic-free model. We show that inference from each model is comparable except for rare microbial genotypes. Further, the effect of \'rurality\' may be modelled linearly on the logit scale, with increasing rurality leading to the increasing likelihood of ruminant-sourced campylobacteriosis.

In population genetics, the Dirichlet (also called the Balding-Nichols) model has for 20 years been considered the key model to approximate the distribution of allele fractions within populations in a multi-allelic setting. It has often been noted that the Dirichlet assumption is approximate because positive correlations among alleles cannot be accommodated under the Dirichlet model. However, the validity of the Dirichlet distribution has never been systematically investigated in a general framework. This paper attempts to address this problem by providing a general overview of how allele fraction data under the most common multi-allelic mutational structures should be modeled. The Dirichlet and alternative models are investigated by simulating allele fractions from a diffusion approximation of the multi-allelic Wright-Fisher process with mutation, and applying a moment-based analysis method. The study shows that the optimal modeling strategy for the distribution of allele fractions depends on the specific mutation process. The Dirichlet model is only an exceptionally good approximation for the pure drift, Jukes-Cantor and parent-independent mutation processes with small mutation rates. Alternative models are required and proposed for the other mutation processes, such as a Beta-Dirichlet model for the infinite alleles mutation process, and a Hierarchical Beta model for the Kimura, Hasegawa-Kishino-Yano and Tamura-Nei processes. Finally, a novel Hierarchical Beta approximation is developed, a Pyramidal Hierarchical Beta model, for the generalized time-reversible and single-step mutation processes.

Planned interventions and/or natural conditions often effect change on an ordinal categorical outcome (e.g., symptom severity). In such scenarios, it is sometimes desirable to assign a priori scores to observed changes in status, typically giving higher weight to changes of greater magnitude. We define change indices for such data based upon a multinomial model for each row of a c × c table, where the rows represent the baseline status categories. We distinguish an index designed to assess conditional changes within each baseline category from two others designed to capture overall change. One of these overall indices measures expected change across a target population. The other is scaled to capture the proportion of total possible change in the direction indicated by the data, so that it ranges from -1 (when all subjects finish in the least favorable category) to +1 (when all finish in the most favorable category). The conditional assessment of change can be informative regardless of how subjects are sampled into the baseline categories. In contrast, the overall indices become relevant when subjects are randomly sampled at baseline from the target population of interest, or when the investigator is able to make certain assumptions about the baseline status distribution in that population. We use a Dirichlet-multinomial model to obtain Bayesian credible intervals for the conditional change index that exhibit favorable small-sample frequentist properties. Simulation studies illustrate the methods, and we apply them to examples involving changes in ordinal responses for studies of sleep deprivation and activities of daily living.