## 2 Materials and Methods
### The Classification Algorithm  
The Machine Learning application presented here is a classification task, with the ultimate target of finding a model capable of attributing sex based on a limited number of metric cranial features. The steps followed in the procedure described below are summarised in Figure 2. The implementation of the classification task was performed using the open-source Machine Learning platform \"H2O\" through the R interface package \"h2o\" [49]. The sex-classification model was implemented using a feedforward neural network [50], consisting of an input layer (that introduces the features into the network), one or more hidden layers (that transform the input features), and an output layer (the last layer that receives the data processed within the network and produces a result). Each layer is made of nodes (also called neurons or perceptrons), which are the network's computational units. Every time an input travels to a node of the hidden layers, it is multiplied by some weight, which modifies the influence of that input on the output. At each node of the hidden layers, multiple weighted input features arrive and are combined by an activation function, whose output is a new input to another hidden layer or to the output layer. In this work, we use a \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Dataset** & **Source** & **Population** & **Sex (F:M)** \\ \hline Training and & [PERSON]’s & & \\ Validation & craniometric dataset & & \\  & & & Anaman & 31:33 \\  & & Arikara & 27:36 \\  & & Atayal & 17:26 \\  & & Australia (aboriginals) & 49:50 \\  & & Berg & 53:53 \\  & & Buriat & 54:45 \\  & & Bushman & 46:39 \\  & & Dogon & 51:45 \\  & & Easter Island & 37:42 \\  & & Egypt (600–200 B.C.) & 53:53 \\  & & Eskimo & 55:43 \\  & & Guam & 27:28 \\  & & Hainan & 38:43 \\  & & Mokapu & 49:45 \\  & & Moriori & 51:54 \\  & & Japan (North) & 32:52 \\  & & Japan (South) & 41:45 \\  & & Norse (medieval) & 54:52 \\  & & Peru & 55:49 \\  & & Santa Cruz & 51:47 \\  & & Tasmania (aboriginals) & 42:40 \\  & & Teita & 50:32 \\  & & Tolai & 54:49 \\  & & Zalavar (medieval) & 45:49 \\  & & Zulu & 46:50 \\  & & University of Tennessee & \\  & & Database for Forensic & \\  & & Anthropology in the & Ancestry unknown & 303:303 \\  & & United States & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Details of the sample used. Source, population (if known), and sex attribution are reported. Sample sizes refer to the datasets after the transformations operated for the scores of the current study. non-linear activation function (see Table 3) to allow the output model to identify non-linear patterns in the differences between females and males. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value*** \\ \hline Epochs & 1000 \\ Stopping metric & Log loss \\ Loss function & Cross entropy \\ Distribution & Bernoulli \\ Learning rate & \(5\times 10^{-4}\) \\ Momentum start & 0.5 \\ Momentum ramp & \(1\times 10^{-6}\) \\ Momentum stable & 0.99 \\ Stopping rounds & 20 \\ Stopping tolerance & \(1\times 10^{-4}\) \\ Input dropout ratio & 0 \\ Number of folds & 10 \\ Fold assignment & Stratified \\ Activation function & Rectifier with dropout \\ L1 regularisation & 0 \\ L2 regularisation & \(0,1\times 10^{-4},5\times 10^{-4},1\times 10^{-3},5\times 10^{-3},1\times 10^{-2},\) and \(5\times 10^{-2}\) \\ Hidden layers & 1 and 2 \\ Nodes per layer & 3, 7, 11, 15, 19, 23, and 27 \\ \hline \hline \end{tabular}  
* The values used for the parameters refer to the options set in the h2o.deeplearning function in the “h2o” R package [51]. Parameters not shown are left as default as per version 3.36.0.3 of the ”h2o” package. When multiple values are shown, the parameter underwent tuning via the brute force approach.  
\end{table} 
Table 3: Crucial parameters of the neural network algorithm, definitions, and values adopted. Figure 2: Schematic representation of the machine learning workflow adopted.