A Neural Network Model to Translate Brain Developmental Events across Mammalian Species

Translating the timing of brain developmental events across mammalian species using suitable models has provided unprecedented insights into neural development and evolution. More importantly, these models can prove to be useful abstractions and predict unknown events across species from known empirical event timing data retrieved from published literature. Such predictions can be especially useful since the distribution of the event timing data is skewed with a majority of events documented only across a few selected species. The present study investigates the choice of single hidden layer feed-forward neural networks (FFNN) for predicting the unknown events from the empirical data. A leave-one-out cross-validation approach is used to determine the optimal number of units in the hidden layer and the decay parameter for the FFNN. It is shown that unlike the present Finlay-Darlington (FD) model, FFNN does not impose any constraints on the functional form of the model and falls under the class of semiparametric regression models that can approximate any continuous function. The results from FFNN as well as FD model also indicate that a majority of events with large absolute prediction errors correspond to those of primates and late events comprising the tail of event timing data distribution with minimal representation in the empirical data. These results also indicate that accurate prediction of primate events may be challenging

Absolute prediction error across primates and non-primates.

<p>Number of events whose absolute prediction error was greater than a given threshold days determined independently using FD and FFNN from their LOO predictions are shown in (a) and (b) respectively. Number of overlapping events (FFNN+FD) across FD (a) as well as FFNN (b) is shown in (c) for comparison. Contributions from primates (dotted lines), non-primates (dashed lines) and all species (solid lines) for each of the cases is also included in (a–c).</p

Optimal parameters of the feed-forward neural network.

<p>Variation of the prediction error as a function of the decay parameter and units for a single realization of the single layer feed-forward neural network. The shaded area represents the region where the prediction error exhibits a prominent decrease.</p

Comparison of the results from FFNN and FD models.

<p>The prediction error as a function of the number of units and optimal decay parameter = 0.05 for the FFNN in the presence (S = T) and absence (S = F) of the skip-layer is shown in (a). The prediction error for the FD regression model obtained using the LOO approach is also shown for comparison in (a). The residuals as a function of the predicted values obtained using the LOO approach in the log-scale for the FD model and FFNN are shown in (b) and (d) respectively. The corresponding scatter plots are shown in (c) and (e) respectively.</p

Estimating probabilities under the three-parameter gamma distribution using composite sampling

Composite sampling may be used in industrial or environmental settings for the purpose of quality monitoring and regulation, particularly if the cost of testing samples is high relative to the cost of collecting samples. In such settings, it is often of interest to estimate the proportion of individual sampling units in the population that are above or below a given threshold value, C. We consider estimation of a proportion of the form p=P(X>C) from composite sample data, assuming that X follows a three-parameter gamma distribution. The gamma distribution is useful for modeling skewed data, which arise in many applications, and adding a shift parameter to the usual two-parameter gamma distribution also allows the analyst to model a minimum or baseline level of the response. We propose an estimator of p that is based on maximum likelihood estimates of the parameters [alpha], [beta], and [gamma], and an associated variance estimator based on the observed information matrix. Theoretical properties of the estimator are briefly discussed, and simulation results are given to assess the performance of the estimator. We illustrate the proposed estimator using an example of composite sample data from the meat products industry.