text:
\section{Introduction}
Graph Neural Networks (GNNs)~\cite{gori2005new,kipf2016semi-GCN} have emerged as a heated field in machine learning in recent years. Among the widely known GNN models~\cite{kipf2016semi-GCN,Hamilton2017InductiveRL,Velickovic2018GraphAN,Grand,chen2020simple}, which one is the best? Most GNN papers demonstrate their performance on the task of semi-supervised learning on graphs following GCN, where a widely-used benchmark includes Cora, CiteSeer, and PubMed~\cite{Sen2008CollectiveCI}.

This benchmark is competitive but unstable. For example, the accuracy of GCNII~\cite{chen2020simple} (SOTA method) on Cora is $85.5\%$ with a dropout rate of  $0.6$, but it will drop to $79.0\%$ if we slightly increase the dropout rate to $0.75$. In contrast, the reported accuracy of GCN is about 81.5\%.\footnote{The experiments can be  reproduced using the CogDL package~\cite{Cen2021CogDLAE}.}
Previous researchers attributed this kind of instability to the \emph{small size} of the graphs and put forward larger benchmarks, e.g., OGB~\cite{Hu2020OpenGB} and HGB~\cite{hgb}. However, to the best of our knowledge, few works challenge the \emph{setting} of semi-supervised learning on graphs.

A similar predicament of the unstable performance also exists in few-shot natural language understanding, where~\citeauthor{zheng2021fewnlu}~\shortcite{zheng2021fewnlu} recently found that models were over-fitting the validation set via hyper-parameters. Since the labels in the validation set are even more than those in the training set, the searched value of hyper-parameters becomes vitally important.
Inspired by this finding, we hypothesize that the same reason could also, to some extent, account for the instability of semi-supervised learning on graphs, since the size of the validation set is also usually much larger than that of the training set (e.g., 140 training samples vs. 500 validation samples in Cora)~\cite{NELL}.
Meanwhile, recent GNNs show a trend of owning more hyper-parameters. While GCN has very few hyper-parameters,
GAT needs the accuracy on the validation set to determine its structures (e.g., the number of attention heads and the existence of a residual connection). PPNP~\cite{klicpera2019predict} further requires a global diffusion radius and a teleport probability $\alpha$. GDC~\cite{klicpera2019diffusion} searches a diffusion radius and a threshold for sparsification as hyper-parameters on the validation set, which is improved in ADC~\cite{zhao2021adaptive} by replacing the grid-search with gradient-based optimization for layerwise and channel-wise diffusion radii. This evolving path of GNNs suggests that GNN models utilize the validation set to a greater and greater extent and that the more explicit utilization improves and stabilizes the training. This benchmark leads to an unfair comparison favoring models with larger sizes of hyper-parameters.

The same phenomenon still exists in OGB~\cite{Hu2020OpenGB}, even though its percentage of validation set is much smaller than that of Cora. The participants~\cite{wang2021pairwise} find that directly merging validation set into the training set can significantly increase the performance, which is then only allowed on the collab dataset according to the updated OGB rules. Moreover, C\&S~\cite{huang2020combining} incorporates the labels in the validation set during label propagation and obtains a great improvement. All of them indicate that
simply reducing the validation set ratio or to increase the graphs' size is not a satisfying solution to the problem.

The findings urge us to rethink the setting of the semi-supervised learning on graphs and the meaning of validation set.
On the one hand, the original motivation of introducing  validation set is to optimize the hyper-parameters, which cannot be directly optimized by usual methods, e.g., stochastic gradient descent (SGD).
On the other hand, we have only two kinds of samples in real-world applications, labeled and unlabeled.
We have to split out a part of the labeled data as the validation set to search for the best hyper-parameters.
This means it is a disadvantage instead of a merit to own a large set of hyper-parameters because they use a great quantity of labeled data as a validation set and result in a smaller training set providing real-world information. However, under the current setting, the extra and informative validation set encourages the model to equip itself with more hyper-parameters to fully utilize the labels in the validation set, which deviates from the real-world scenarios. In this work, we name the problem of ``using hyper-parameters to fit validation labels'' as \textbf{over-tuning}.

\textbf{Present work.} In this paper, we analyze the influence of the size of validation set and propose \textbf{ValidUtil}, a method to make any GNN fully utilize the label information in the validation set. \textbf{ValidUtil} explores the limit of over-tuning hyper-parameters. To avoid meaningless optimization towards the utilization of validation set and increase the stability of GNN benchmarks, we construct the i.i.d. graph benchmark (\textbf{IGB}) with the following two improvements:
\begin{itemize}
    \item \emph{Unify the training and validation set.} In IGB, the graphs have no pre-defined ratio of training and validation set but only labeled data and unlabeled data. Different models can freely split the labeled data into training and validation set based on the number of hyper-parameters. In this way, the over-tuning of hyper-parameters is discouraged.
    \item \emph{Multiple i.i.d. graphs and diverse domains.} We have 4 datasets consisting of a co-authorship network, a social network, a knowledge graph, and a photo sharing network. In each dataset, we sample 100 subgraphs using a modified Random-Walk method. The sampled graphs are approximately i.i.d, while each gives a reliable evaluation of GNN performance. Therefore, we can obtain more stable metrics by averaging performances over them.
\end{itemize}

\section{The Risk of Over-tuning of Semi-supervised Learning on Graphs}
\subsection{Semi-Supervised Learning on Graphs}
\textbf{Definition. } Given an undirected graph $G=(V,E)$, where the node set $V$ contains $n$ nodes $\{v_1,...,v_n\}$ and $E$ is the edge set.
Each node $v_i$ is associated with a feature vector $\2x_i$ and a class label $y_i$. We denote the set of node labels as $\2Y$.
In the task of semi-supervised node classification on graphs (transductive), only a small part of node labels $\mathbf { Y } ^ { L } \subset \mathbf { Y }$ are given, and the rest label set $\mathbf { Y } ^ { U } = \mathbf { Y } - \mathbf { Y } ^ { L }$ needs to be predicted. Usually $ \abs{{ \mathbf{ Y } } ^ { L }} \ll \abs{\mathbf { Y } ^ { U }}$.

Here, we briefly introduce three widely used citation networks (i.e., Cora, CiteSeer, PubMed) for the analysis in this section. In these datasets, node features are bag-of-words representations of documents. Each dataset is a connected graph constructed based on the citation links between documents. Each dataset uses 20 training samples per class as labeled data in the semi-supervised setting. Table~\ref{tab:planetoid} shows the statistics of the three datasets.

\begin{table}[h]
\centering
\caption{Statistics of Cora / CiteSeer / PubMed datasets.}
\small
\label{tab:planetoid}
\setlength{\tabcolsep}{1.0mm}\begin{tabular}{l|rrccr}
	\toprule
	Dataset &  Nodes &  Edges & Split & Classes & Features \\
	\midrule

	Cora & 2,708 & 5,429 & 140 / 500 / 1,000 & 7&1,433  \\
	CiteSeer & 3,327 & 4,732 & 120 / 500 / 1,000 & 6 & 3,703 \\
	PubMed & 19,717 & 44,338 & 60 / 500 / 1,000 & 3 & 500 \\
	\bottomrule
\end{tabular}
\end{table}

\subsection{An Analysis of Over-tuning in Current GNNs}
In this section, we will investigate the over-tuning phenomenon in current GNNs. As discussed above, the hyper-parameters act as a tool to utilize the labels in the validation set. Therefore, the models' performance should improve as we increase the size of the validation set. We select five representative GNNs, GCN, GAT, APPNP, GDC-GCN, and ADC, and exhibit their accuracy on Cora with different sizes of validation set. The search scope of the hyper-parameters includes learning rate, hidden size, early stopping iteration, number of layers, the dropout rate, the diffusion radius of APPNP and GDC, the sparsification threshold of GDC, etc. We use grid search to find the best hyper-parameters for each model. Details about the search scopes are shown in the released codes.

We run the experiments on the public split~\cite{NELL} of Cora, ranging the size of validation set from 10 to 500 by hiding a part of the labels. For each validation size, we report the accuarcy on the test set after training the model with the best searched hyper-parameters. The results are demonstrated in Figure~\ref{fig:varying_valid}.
\begin{figure}[h]
    \centering
    \includegraphics[width=0.9\linewidth]{acc.pdf}
    \caption{The accuracy of models with different size of the validation set on Cora. The test accuracy is the average of 20 runs with different random seeds.}
    \label{fig:varying_valid}
\end{figure}

\begin{figure*}[t]
    \centering
    \includegraphics[width=\textwidth]{validutil.pdf}
    \caption{The test accuracy of ValidUtil plus GCN, GAT, MixHop and PPNP on Cora, Citeseer, and PubMed. The horizontal axis means the number of new hyper-parameters from ValidUtil, where 0 is equivalent to the original GNN without ValidUtil.}
    \label{fig:validutil}
\end{figure*}
Figure~\ref{fig:varying_valid} shows that the GNN models have a clear trend that the performance is usually better with a larger validation set. Since the validation set can only affect the model via the hyper-parameters, we can conclude that the model benefits from the validation labels with the help of hyper-parameters. The accuracy improvement is up to $1\%\sim3\%$ if we increase the size of validation set from 100 to 500, which is significant enough to suggest that the over-tuning already exists.

\subsection{ValidUtil: Exploring the Limits of Over-tuning}\label{sec:validutil}

Although the analysis above shows that over-tuning influences GNN models' performance, we wonder to what extent the influence could achieve. If the importance of validation labels is much smaller than that of model structures, the previous benchmarks will still be a proper choice for GNN benchmarks. If not, we should rethink and re-design the evaluation pipeline and datasets for semi-supervised learning on graphs.

The most intuitive method to fully utilize the validation labels is to merge the validation set into the training set. However, this operation is universally acknowledged as invalid and is forbidden since it is a kind of data leakage. In this section, we put forward ValidUtil, a technique to mimic this operation via searching hyper-parameters. ValidUtil is \emph{not} really a method to improve GNNs, but more like a ``reduction to absurdity''. The full pipeline of ValidUtil is defined as follows and in Algorithm \ref{alg:valid_util}:

\begin{algorithm}[h]
    \caption{ValidUtil}
    \label{alg:valid_util}
    \textbf{Input} Graph $G$ with nodes in training/validation/test set. We denote their labels as $Y^{L}/Y_{valid}/Y_{test}$. There are $k$ classes. \\
    \textbf{Output} Accuracy of the GNN model on test set.
    \begin{algorithmic}[1]
    \State Train a GNN model $M$ with $Y^{L}$.
    \State Predict the labels of validation set with $M$ as $Y^P=\{y'_1, ..., y'_t\}$.
    \State Add $t$ extra hyper-parameters $Y^T=\{\hat{y}_1, ..., \hat{y}_t\}$.
    \State Initialize $Y^T = Y^P$.

    \For{$i$ from $1$ to $t$}
        \For{$l$ from $1$ to $k$}
            \State $\hat{y}_i = l$.
            \State Train a GNN $M$ with $Y^{L} \cup Y^T$.
            \State $Acc_l$ = the accuracy of $M$ on validation set.
        \EndFor
        \State $l_{max}$  = $\underset{l \in \{1,...,k\}}{\arg\max} {Acc_l}$.
        \If{$Acc_{l_{max}} > Acc_{l_{y_i'}}$}
        \State $\hat{y}_i$ = $l_{max}$
        \Else
            \State $\hat{y}_i$ = $y'_i$
        \EndIf
    \EndFor

    \State Train a new GNN $M$ with $Y^{L} \cup Y^T$.
    \State \Return the accuracy of $M$ on test set.

    \end{algorithmic}

\end{algorithm}

\begin{enumerate}
    \item \textbf{Add hyper-parameters.} For any given model, we add $t$ extra hyper-parameters $\2Y^T=\{\hat{y}_1, ..., \hat{y}_t\}$, which refers to ``pseudo-labels of the $t$ nodes in the validation set''. These hyper-parameters affect the model training in a way that they act as a known label for the corresponding validation node; that is to say, the model will be trained on an augmented training set $\2Y^L \cup \2Y^T$. And since the labels of the validation set given to the model are not ground-truth labels, this is not a data leakage process.
    \item \textbf{Alternately optimize hyper-parameters.} The most common search method for hyper-parameters is grid search, but it is time-consuming when there are many hyper-parameters. Thus, we alternately search the best value of each $\hat{y}_i$ individually. In the beginning, each $\hat{y}_i$ is initialized as the predicted label $y'_i$ of the GNN without ValidUtil. We will search and fix the best $\hat{y}_i$ one by one, following the method described in the next paragraph. We set the dropout rate as 0 when searching for the best pseudo-labels.
    \item \textbf{Search the best pseudo-label for each validation node.} To search for the best value of $\hat{y}_i$, we enumerate all possible values of $\hat{y}_i$ while keeping the other hyper-parameters unchanged. For each possible value, we train a GNN model using labels $\2Y^L \cup \2Y^T$ and select the best value according to the accuracy of the validation set. This is the standard process of searching a hyper-parameter.
    \item \textbf{Train the final model based on the best pseudo-labels.} After the pseudo-labels are determined, we can train on $\2Y^L \cup \2Y^T$, and use ordinary grid search to determine other hyper-parameters, including the dropout rate, and report the results on the test set.
\end{enumerate}

\textbf{Analysis of Effectiveness.} The key reason for the effectiveness of ValidUtil is that in most cases, we can obtain the true label $y_i$ for validation node $v_i$ in step 3, which makes the final training equivalent to the training on the union of training and validation set. If the model is over-parameterized, it is powerful enough to overfit the predicted label of $v_i$ as the true label $y_i$ after sufficient training
\footnote{Some weak GNNs, e.g. vanilla GCN and GAT on CiteSeer, cannot well distinguish nodes in a strongly connected graph, and therefore cannot overfit the given labels. We add an additional self-loop for each node for GCN to solve the problem. This trick is already implemented in PyG~\cite{Fey/Lenssen/2019} by passing \texttt{improved=True} for GCNs.
}.
Then in most cases, the highest accuracy is reached if and only if $\hat{y}_i = y_i$. We find that most GNNs models are powerful enough to overfit the pseudo-labels on Cora, Citeseer, and PubMed in practice.
\begin{table}[h]
\small
\centering
\caption{Comparison between ValidUtil and the sota methods on Cora, Citeseer, and PubMed.}\label{tab:validutil_performance}
\begin{tabular}{lccc}
\toprule
     & Cora & Citeseer & PubMed \\
    \midrule
GCNII (sota Cora) & \textbf{85.5} & 73.4& 80.3\\
GRAND (sota Citeseer)& 85.4 & \textbf{75.4}& 82.7\\
SAIL (sota PubMed) & 84.6& 74.2 &\textbf{83.8}\\
\midrule
GCN + ValidUtil   &\textbf{85.8}& 76.0 & 83.8 \\
MixHop + ValidUtil  & 84.9 & 75.5 & 84.2\\
PPNP + ValidUtil  &\textbf{85.8}& \textbf{77.3}& \textbf{84.7}\\
\bottomrule
\end{tabular}
\end{table}

We demonstrate the performance of ValidUtil plus three GNN models, GCN, PPNP, and MixHop, in Figure~\ref{fig:validutil}. We find that even only $20\sim60$ hyper-parameters from ValidUtil can bring about a leap in performance for some models. When we add hyper-parameters for all the 500 nodes in the validation set, PPNP can achieve an accuracy much better than that of the sota methods in Table~\ref{tab:validutil_performance}.

\textbf{Remark.} Although ValidUtil works purely by utilizing the validation labels, it is totally valid under the current setting. If we treat the GNN+ValidUtil as a black-box model, the training process is quite normal.
ValidUtil actually utilizes the labels with low efficiency, because each hyper-parameter can only learn the information of one node -- but this is enough to verify our hypothesis. \textbf{The current setting cannot prevent the validation labels from ``leaking'' during hyper-parameters tuning.}
We believe that there exist some more efficient ways to define \emph{influential} hyper-parameters. These hyper-parameters could be entangled with the features or model structures, and they can acquire information from multiple validation labels. According to Figure~\ref{fig:varying_valid}, such influential hyper-parameters might already exist in some models and cannot be easily detected. Therefore, it is urgent to construct a new benchmark for semi-supervised learning on graphs to avoid over-tuning and fairly and robustly compare GNN models.

\section{IGB: An Independent and Identically Distributed Graph Benchmark}

\subsection{Overview}
Our new benchmark has two aims: avoiding over-tuning and being more robust.

To avoid over-tuning, we propose a new setting where there are only two sets of nodes, labeled and unlabeled. The model can use the labeled set in any way to train the best model and evaluate its performance on the unlabeled (test) set. If we need to search hyper-parameters, we can split out a part of the labeled nodes as the validation set. The over-tuning problem is eliminated because the validation labels are already exposed. This setting is closer to real-world scenarios and enables fair comparison between models with different sizes of hyper-parameters. To easily migrate the GNNs to this new setting, we will introduce a simple and powerful method to create validation set in section~\ref{sec:pipe}.

To construct a more robust benchmark, we expect models' performances to be stable for different random seeds. One of the most common methods in machine learning to reduce the variance of evaluation results is to test repeatedly and report the average performance. To achieve that, we expect to test a model's performance on multiple i.i.d graphs.
However, how can we get multiple i.i.d. Cora-like graphs to evaluate the results?

If we think about the construction of the citation networks such as Cora and Citeseer, we will find that the papers are crawled down by spiders from the Internet, which means these networks can be seen as sampled from the large real-world citation network. A similar assumption is already used in previous works~\cite{yang2020understanding} that the real-world graph data are sampled from a large underlying graph. To acquire i.i.d. graphs, we could sample ``again'' from an established graph. With appropriate sampling strategies, we can construct a group of i.i.d. graphs. The details about sampling are introduced in section~\ref{sec:sampling}.

\subsection{The Pipeline of Evaluation}\label{sec:pipe}
To solve the over-tuning problem, we have to update the pipeline of the task of semi-supervised learning on graphs. Following the real-world scenarios, we only split the nodes in a graph into two sets, labeled and unlabeled (with a ratio of 1:4 by default in IGB). The model can use the labeled set in any way to train the best model, and evaluate its performance on the unlabeled (test) set. A recommended method is as follows:
\begin{enumerate}
    \item Divide the labeled set into training and validation sets.\footnote{The best ratio may differ from model to model. In practice, we find that 1:1 is an appropriate ratio for most models.}
    \item Find the best hyper-parameters using grid search on the training and validation sets from the first step.
    \item Train the model with the best hyper-parameters on the full labeled nodes.
    \item Test the performance of the model from the third step on the unlabeled (test) sets.
    \item Repeat the above steps on each graph in a dataset and report the average accuracy.
\end{enumerate}
The first two steps aims to find the best hyper-parameters for the GNN model. We believe that this approach is suitable for many GNN models to get satisfying hyper-parameters. If there are other reasonable methods to decide the best hyper-parameters with the labeled set, they will also be encouraged to replace the first two steps in this pipeline. In this way, we can avoid over-tuning by directly exposing all the label information in the validation set later in the third step.

\subsection{Datasets}

IGB consists of four datasets: AMiner~\cite{AMiner}, Facebook~\cite{Facebook}, NELL~\cite{NELL}, and Flickr~\cite{Amazon}. Each dataset contains 100 undirected connected graphs, sampled from the original large graph according to the random walk method in section~\ref{sec:sampling}.
We also report the average node \emph{overlap rate}, the ratio of common nodes to the total size of nodes for a pair of sampled graphs.
The coverage rate is defined as the ratio of the union of the 100 sampled graph to the original large graph.
Lower overlap rate and higher coverage rate are preferred.
The statistics of the datasets are reported in Table \ref{tab:dataset_statistics}.

\begin{table}[h]
    \centering
    \caption{Statistics of the datasets in IGB. }
    \label{tab:dataset_statistics}
    \scalebox{0.8}{
    \begin{tabular}{lcccc}
    \toprule
        & AMiner& Facebook & NELL & Flickr \\
    \midrule
     Average Nodes & 4,485 $\pm$ 26 & 3,475 $\pm$ 71 & 3,540$\pm$ 68 & 4,452 $\pm$ 31\\
     Edges & 5,000 & 5,000 & 5,000 & 5,000 \\
     Features & 3,883 & 128 & 10,000 & 500\\
     Classes & 8 & 4 & 164 & 7\\
     Original Size & 236,017 & 22,470 & 63,910 & 89,250 \\
     Overlap Rate & 0.083 & 0.339 & 0.146 & 0.119 \\
     Coverage Rate & 0.550 & 0.958 & 0.956 & 0.969 \\
    \bottomrule
    \end{tabular}
    }
\end{table}

\vpara{AMiner.}
The AMiner dataset is a co-authorship graph extracted from the AMiner system~\cite{AMiner}. Nodes represent authors, while edges mean co-authorship in at least one paper. Node features indicate the venues in which the author has publications. Specifically, each feature has 3,883 dimensions, and each dimension is 0 or 1, representing whether or not an author has had publications in the corresponding venue. Node labels represent the authors' main research fields.

\vpara{Facebook.}
The Facebook dataset is the Facebook Page-Page dataset from the paper~\cite{Facebook}. It is a graph of official Facebook pages. Nodes are official Facebook pages, while edges are mutual likes between the pages. Node features are extracted from the page descriptions. Node labels are one of the following 4 categories defined by Facebook: politician, governmental organization, television show, and company.

\vpara{NELL.}
The NELL dataset is a knowledge graph dataset generated from the NELL knowledge graph~\cite{NELL_raw}. Nodes represent entities, and edges represent relationships between two entities. Each node initially has a 61,278-dimension feature, a binary bag-of-words representation of entity descriptions. We only reserve the features of the most frequent 10,000 words for efficiency.

\vpara{Flickr.}
The Flickr dataset is a graph of photos uploaded to the Flickr website. Each node represents a photo, and an edge means two photos share some properties in common, such as from the same location or the same gallery. 500-dimension node features are bag-of-words representations of photos. The labels are one of 7 classes developed by \citeauthor{Amazon} from 81 original tags.

\subsection{Sampling Algorithm}\label{sec:sampling}
The simplest way to make the subgraph's node label distribution similar to that of the original graph is vertex sampling. However, it does not meet our expectations because it generates unconnected subgraphs. To obtain nearly i.i.d. subgraphs for our benchmark, we must carefully design the sampling strategy and principles. Specifically, we expect the sampling strategy to have the following properties:

\begin{enumerate}
    \item The sampled subgraph is a connected graph.
    \item The distribution of the subgraph's node labels is close to that of the original graph.
    \item The distribution of the subgraph's edge categories (edge category is defined by the combination of its two endpoints' labels) is close to that of the original graph.
\end{enumerate}

The first property can be well satisfied by the Random-Walk (RW) algorithm. When performing RW on an undirected graph $G = (V,E)$, we start sampling from node $u = n_0$, and the following nodes can be selected by the transition possibility:
$$
P _ { u , v } = \left\{ \begin{array} { l l } \frac{1}{d_u} , & if  \  (u, v )\in E, \\ 0,& otherwise, \end{array} \right.
$$
where $P _ { u , v }$ is the transition possibility from node $u$ to $v$, and $d_u$ is the degree of node $u$.

We retreat to \emph{reject sampling}-like methods to guarantee the second and third properties.
Here we introduce the Kullback–Leibler divergence (KL divergence) as a metric to measure the difference between two different distributions. Aiming to get 100 subgraphs with relatively low KL divergence of node labels' distribution (``Node KL'') and edge categories' distribution (``Edge KL''), we set a pre-defined threshold to decide whether to accept a sampled subgraph or not.
The comparison of the results before and after adding the threshold is shown in Table \ref{tab:RW+ statistics}.

\begin{table}[h]
    \centering
    \caption{KL divergence of the sampling results.}
    \label{tab:RW+ statistics}
    \scalebox{0.65}{
    \begin{tabular}{lcccc}
    \toprule
        & AMiner& Facebook & NELL & Flickr \\
    \midrule

     Node KL & 0.0186 $\pm$ 0.0107 & 0.1306 $\pm$ 0.0427 & 0.4393 $\pm$ 0.1008 & 0.0060 $\pm$ 0.0025\\
     Edge KL & 0.0189 $\pm$ 0.0149 & 0.0284 $\pm$ 0.0121 & 0.2796 $\pm$ 0.0678 & 0.0046 $\pm$ 0.0015\\
    \midrule
    \emph{+Thresholds}\\
    \midrule
     Node KL  & 0.0123 $\pm$ 0.0024 & 0.0326 $\pm$ 0.0064 & 0.3184 $\pm$ 0.0243 & 0.0041 $\pm$ 0.0006\\
     Edge KL & 0.0062 $\pm$ 0.0008 & 0.0243 $\pm$ 0.0120 & 0.2068 $\pm$ 0.0179 & 0.0021 $\pm$ 0.0003\\

    \bottomrule
    \end{tabular}
    }
\end{table}

\begin{table}[t]

\centering
 \caption{Evaluation Results of GNNs on IGB.}
 \label{tab:result}
 \small
\scalebox{0.9}{
\begin{tabular}{lccccc}
    \toprule & AMiner & Facebook & NELL & Flickr & Avg\\
    \midrule
    Grand  & 82.5$\pm$0.8 & 88.9$\pm$1.0 & 84.4$\pm$1.1 & 44.3$\pm$0.8  & 75.0 \\
    GCN & 76.5$\pm$1.1 & 87.9$\pm$1.0 & 93.9$\pm$0.7 & 41.9$\pm$1.3 & 75.1 \\
    GAT & 78.8$\pm$1.0 & 88.3$\pm$1.2 & 91.1$\pm$1.2 & 43.1$\pm$1.3 & 75.3 \\
    GraphSAGE & 81.6$\pm$0.8 & 87.2$\pm$1.1 & \textbf{94.9}$\pm$\textbf{0.6} & 43.4$\pm$0.9 & 76.8 \\
    APPNP & 87.0$\pm$1.0 & 88.0$\pm$1.3 & 93.0$\pm$0.8 & 44.6$\pm$0.9 & 78.2 \\
    MixHop & 86.1$\pm$1.1 & 89.1$\pm$0.9 & 94.7$\pm$0.7 & 43.5$\pm$1.2 & 78.4 \\
    GCNII & \textbf{88.4}$\pm$\textbf{0.6} & \textbf{89.5}$\pm$\textbf{0.9} & 91.5$\pm$1.0 & \textbf{44.7}$\pm$\textbf{0.8} & \textbf{78.5} \\

    \bottomrule
  \end{tabular}
   }
\vspace{-2mm}%
\end{table}

\subsection{Benchmarking Results}
We evaluate 7 representative GNNs on IGB: Grand~\cite{Grand}, GCNII~\cite{chen2020simple}, APPNP~\cite{klicpera2019predict}, GAT~\cite{Velickovic2018GraphAN}, GCN~\cite{kipf2016semi-GCN}, GraphSAGE~\cite{Hamilton2017InductiveRL} and MixHop~\cite{MixHop}. The results are shown in Table~\ref{tab:result}.

To evaluate the GNN model, we first define a search scope for each hyper-parameter. The scope is carefully chosen in order to include the best values on all the datasets. For each model, the best hyper-parameters in its original paper and the best hyper-parameters reported by CogDL~\cite{Cen2021CogDLAE} are usually included in the search scopes. After that, we use our IGB benchmark to evaluate each model under the setting introduced in the section~\ref{sec:pipe}.

\subsection{The Stability of IGB}
We verify the stability of IGB in two ways. Firstly, we verify its stability when evaluating models on different graphs, as each IGB dataset contains 100 nearly i.i.d. graphs. Specifically, we compare the variances of the accuracies on 100 AMiner's subgraphs (IGB style) and on 100 Cora's random data splits (Cora style). The result shown in Figure~\ref{fig:gnns_on_aminer} strongly suggests that the evaluation on IGB is more stable than Cora style, even though each AMiner graph uses random data split.
\begin{figure}[h]
    \centering
    \includegraphics[width=\linewidth]{GNNS_Comparison.pdf}
    \caption{Accuracy of GNNs on AMiner and Cora. The blue area is the fluctuation range of the test accuracy. The results are based on 100 runs on AMiner's subgraphs or Cora's random splits. }
    \label{fig:gnns_on_aminer}
\end{figure}

Secondly, we focus on IGB's stability when evaluating models with different random seeds. In a stable benchmark, the ranks of different models should not easily change when changing the random seed. To verify this, we use the ``inversion number'' \footnote{The definition of ``Inversion'' can be seen in \href{https://en.wikipedia.org/wiki/Inversion_(discrete_mathematics)}{Wikipedia}.} of the ranking as a metric. Specifically, we evaluate the seven models using ten different random seeds, providing ten ranking sequences $S_i (i\in{[1,10]})$. On each ranking sequence, we sort models according to their accuracy. The ranking sequence of the first seed is used as a \emph{reference} sequence $S_1 = \{m_1, m_2...m_7\}$, where $m_i$ is a GNN model. We call $m_j>m_k$ if and only if $m_j$ ranks higher than $m_j$ on $S_1$. For another sequence $S_i, i\neq 1$, if $m_j>m_k$, but $m_j$ ranks lower than $m_k$ on $S_i$, we call $(j,k)$ an inversion pair in $S_i$. ``Inversion number'' is the number of inversion pairs in all sequences $S_i, i\neq 1$. Therefore, a high ``inversion number'' indicates a high instability of evaluation with different seeds.
The result is reported in Table \ref{reverse_order_pair}. IGB has a significantly smaller inversion number than Cora, CiteSeer, and PubMed, demonstrating its strong stability.

\begin{table}[h]
\centering
\caption{The inversion numbers of the ranking sequences using 10 different random seeds. Smaller inversion number indicates better stability.}
\label{reverse_order_pair}
\scalebox{0.8}{
\begin{tabular}{ccccccc}
    \toprule
     Cora & CiteSeer & PubMed & AMiner & Facebook & NELL & Flickr \\
     \midrule
     67 & 45 & 107 & 0 & 9 & 0 & 5 \\
    \bottomrule
\end{tabular}
}
\vspace{-3mm}%
\end{table}

\section{Discussion}
\textbf{Is limiting the number of hyper-parameters a good way to solve the over-tuning problems? } In section 2, we illustrate the power of over-tuning, where the improvements basically correlate with the number of hyper-parameters. However, if we set a hard limit for the number of hyper-parameters, complicated optimizers with many hyper-parameters, e.g. Adam~\cite{kingma2014adam}, will not be encouraged due to this limit. The models will also be encouraged to investigate more influential hyper-parameters to utilize the labels in the validation set under the limited budget of hyper-parameters. Therefore, the most fundamental solution is to change the evaluation setting as IGB.\vspace{2mm}\\

\noindent\textbf{What is the best GNN? }In the results of IGB, GCNII performs the best. However, the performance differs in different datasets. For example, the sota method on Citeseer, GRAND, performs badly on NELL and thus gets a low average score, because NELL is a knowledge graph, whose distribution is quite different from that of citation networks. Will a GNN be good at all kinds of graphs, or do we need to design different GNNs for different categories of graphs?

\section{Conclusion}
In this paper, we revisit the setting of semi-supervised learning on graphs, identify the over-tuning problem, and prove its significance via the experiments of ValidUtil. To solve it, we propose a new benchmark, IGB, with a more reasonable evaluation pipeline. To further increase evaluation stability, we propose a sampling algorithm based on RW. GNNs are evaluated on the new benchmark, and the results demonstrate a stable performance rank. We expect that IGB can benefit the graph learning community by stabilizing the evolving path of GNNs in the future.

\clearpage

\bibliographystyle{named}

\section{RELATED WORK}

\subsection{GRAPH SAMPLING}
For the graph sampling algorithm, many algorithms have been proposed to make the sampled graphs more valuable and suitable for practical application scenarios. A more detailed survey of the theoretical algorithm is given by Hu and Lau \cite{Hu2013ASA}. Snowball Sampling\cite{biernacki1981snowball} has long been used in sociology studies, where an investigation is performed on a hidden population \cite{biernacki1981snowball}, it can extract some features of the vertices.

There are also a number of random walk-based graph sampling methods called the simple random walk \cite{rasti2009respondent,gjoka2011practical} and Metropolis-Hastings random walk \cite{metropolis1953equation,hastings1970monte,MHRW2009}. The former initiates a simple walk on a graph, moving from a node to one of its randomly chosen neighbors to collect the random sample of nodes; the latter obtains a uniform sample of nodes in a random walk by introducing acceptance probabilities.

\subsection{GRAPH BENCHMARK}
The real performance assessment of GNNs is not easy because the results reported in the paper may be closely related to the way the models are
implemented and trained and their hyper-parameters. Open Graph Benchmark(OGB)\cite{Hu2020OpenGB} is a diverse set of challenging and realistic benchmark datasets to facilitate scalable, robust, and reproducible graph machine learning (ML) research. It gives a representation of graph networks in various domains, such as biological networks, molecular graphs, source code ASTs, and knowledge graphs.

In addition to using PyTorch Geometric to implement models and evaluate them on OGB, Cogdl\cite{Cen2021CogDLAE} also gives a set of easy methods to implement graph neural networks, in which common datasets and GNN models are given. This work gives evaluation results for some of the popular GNN models, and users can easily reproduce the results in the leaderboard.

Graph Convolution Network (GCN)~\cite{kipf2016semi-GCN} propagates information from each node to its neighbors with a localized first-order approximation of spectral graph convolutions. Graph Attention Network (GAT)~\cite{Velickovic2018GraphAN} replaces the graph convolution layers with masked self-attentional layers, aiming to overcome the shortcomings of methods based on graph convolutions. PPNP and its fast approximation APPNP ~\cite{klicpera2019predict} also replace the power of graph convolution matrix with the PageRank matrix to solve the over-smoothing problem in GCN model. There are also extensions of GCN like GCNII~\cite{chen2020simple} which is a deeper graph neural network. GraphSAGE~\cite{Hamilton2017InductiveRL} is a general inductive framework that leverages node features information to generate node embeddings for previously unseen data.

redpajama_set_name: RedPajamaArXiv


text:
UAMC South offers emergency rooms for psychiatric patients
Dedicados a excavar la tierra del desierto
Mental Health Week
Sheryl Kornman
The University of Arizona Medical Center South Behavioral Health Pavilion on Tucson's South Side has new emergency department with a separate area built just for psychiatric patients. It also has more inpatient beds for psychiatric patients.
"We're the largest inpatient psychiatric services in Pima County," said Patricia Harrison-Monroe, Ph.D., chief of behavioral health services at UAMC South. "We have 48 general psychiatric beds and 14 for geriatric psychiatric patients 55 and older. It's the only place specifically for them, though we're looking forward to St. Mary's opening up some (geriatric) beds."
The emergency department at the facility, 2800 E. Ajo Way, was expanded a year ago to 42 treatment rooms – nine of them designated specifically for psychiatric patients. Those rooms are separate from rest of emergency department. The idea is to minimize the trauma for patients brought to the emergency room, keep the mentally ill from being exposed to people screaming in pain, or an agitated psychiatric patient.
"We make an effort to make sure people are safe," Harrison-Monroe said. "The psychiatric area of the emergency room is built with safety glass, hardened ceilings, no protruding medical equipment. All the equipment is brought into the room, to protect the patient who may be homicidal. There are no gases, nothing they can use to harm themselves. And the rooms are separately staffed with personnel trained to interact with patients who are having a psychiatric emergency."
Harrison-Monroe said the Crisis Response Center is located across the pathway. Patients who come there in a mental health crisis may be transferred to the ED if they have medical as well. Some may need admission to inpatient services.
"The UA Department of Psychiatry staffs the CRC 24 hours, covering its adult and juvenile sections." she said.
A crisis stay there has a 24-hour limit. If appropriate community referrals can't be made in 24 hours, there is a short-stay unit for 3- to 5-day says, only for adults. "That unit is unfortunately often full. If an adult requires more than 24 hours, we'll make a transfer into a psychiatric hospital, Sonora Behavioral Health for children and Palo Verde Hospital for adults," she said.
The CRC primarily takes walk-ins and individuals brought to the facility by law enforcement, she said.
"We work very collaboratively together."
Before the new facilities were built, law enforcement brought mentally ill individuals in crisis to area hospital emergency rooms where they would wait for hours for the person to be evaluated.
"Now, law enforcement doesn't have to wait. The minimal paperwork is completed (at the new facilities) and law enforcement is on their way. It's a benefit to the other emergency rooms as well," said Harrison-Monroe. She is also clinical assistant professor in the Department of Psychiatry at the College of Medicine at the University of Arizona.
"We get patients brought in by Immigration and Customs Enforcement, police, sheriff's deputies and emergency medical services providers.
"Before we opened, we had open houses for law enforcement so they would be aware of access issues and have a chance to tour the ED and CRC."
Geriatric patients are very difficult to place, she said. "They have so many medical and psychiatric issues. "They may have multiple psychotic symptoms, may be suicidal and have depression."
"At some point they need to come back into the community and there are limited community resources for geriatric psychiatric patients. They end up staying in our unit for longer periods of time than they would if there were beds for them. We always have geriatric patients waiting in our emergency room, waiting for a room."
Inpatient services at the South Campus Behavioral Health Pavilion provide care for individuals with acute psychiatric disorders, anxiety, depression, psychoses, those who are a danger to themselves or others, and those with withdrawn behavior.
There are more crisis services available in the system because of the CRC but ongoing services are limited for people who have dropped off AHCCS.
It is very challenging, she said, to serve those who have lost their benefits and will need psychiatric services once they leave the facility.
When AHCCC (Arizona's version of Medicaid) cuts came through last July, she said," it significantly impacted the level of psychiatric services available in the community for people who are underinsured and uninsured."
"And when these individuals do have access to psychiatric medication and are eligible for public benefits, the formulary is limited and they can't take the latest and maybe the most effective drugs. They are very costly," Harrison-Monroe said.
It's a challenge for the mentally ill to get benefits so they can take the medication that can control their symptoms, she said.
"It's not easy to apply for any kind of benefits. If you have all your faculties, it's difficult but if you have difficulty concentrating or are hearing voices, it's difficult to be persistent enough to get services.
"Most of the seriously mentally ill can't do this. They can't remember when their next appointment is. They can't just get on a bus to get over here. They're brought here because of their bizarre behavior by friends, family members, emergency medical workers and police."
It's important to get the word out, she said, so people in trouble who need psychiatric services know where they can go.
Harrison-Monroe said UAMC South's ED is now a trauma level 3 facility, complementing UAMC-University Campus's trauma level 1 ED, at 1501 North Campbell Avenue. There is a helipad at UAMC South than can accommodate two helicopters and provide easy access to the facility's emergency room.
For those not in an immediate crisis, outpatient psychiatric services are offered through UAMC's Department of Psychiatry clinic by its faculty and advanced trainees. Consultation, evaluation, medication and couples and individual therapy are available.
Anyone may call 874-7500 to make an appointment.
There is also an outpatient treatment program called Epicenter for individuals with psychotic illness, including schizophrenia and bipolar disorder with psychotic features.
UA telemedicine program to expand rural services
Myths of the healthy uninsured
Pima County's new crisis center: 11,000 calls for help each month
Clergy look to help with mental illness
news, crime & safety, health, local, arizona, breaking,
crisis response center, mental health, mental health week, ua,
More by Sheryl Kornman
Foreclosure-forced moves no bar to voting
'Dreamer' info promoted at Grijalva event
"we shine a light on this town because we love it"

redpajama_set_name: RedPajamaCommonCrawl


text:
Saint of the Day – 16 August – Saint Ugolina of Vercelli (c 1239-c 1300)
Posted on August 16, 2021 August 15, 2021 by AnaStpaul
Saint of the Day – 16 August – Saint Ugolina of Vercelli (c 1239-c 1300) Virgin, Anchorite Recluse, Penitent, Spiritual advisor. The very strange story that of this Blessed Vercellese who lived in the late 1200s – early 1300s. She went to shut herself up in a hermitage, passing herself off as a man and remained there for forty-seven years to escape the aims of her father. In order not to reveal her secret, she called himself Ugo without revealing her identity to anyone. In the hermitage she grew in faith and prayer. When she died then it became known that she was a woman and it was possible to reconstruct her story in the midst of everyone's surprise and admiration.
The first biographer of St.Ugolina, who wrote immediately after her death, was the Dominican Confessor Father Valentino. These important memories, already unavailable in the 18th century, are cited by the Franciscan, Ludovico della Croce who, consulting them, wrote in the mid-17th century what is today the oldest biography. Unfortunately, the work has the main purpose of handing down the virtues and not the historical information on this Saint, whose life is similar to other figures that arose in the Middle Ages, in imitation of the eastern anchorites.
Ugolina was born in Vercelli in 1239, in the noble and wealthy De Cassami family (or De Cassinis, according to recent studies). Her coming into the world was a grace for the pious parents who saw in her, an only child, a precious gift and surrounded her with thoughtful care.
At the age of ten, she admirably exercised charity towards his neighbour, the constant practice of personal and community prayer and perfect adherence to the teachings of her parents. She had a great love for pilgrims, who were numerous in those times. When she learned that the destination was the Holy Land, her interest became intense, giving them food and money for the journey.
The first great test for the young woman came when she was only fourteen years old – the one who had physically generated her and who had formed her spirit according to the noblest Christian sentiments ,died. So she stayed with her father who, unfortunately, only briefly curbed the urge to seduce her. The most horrendous of family crimes was thus about to be consummated, in that once happy home. The Lord did not abandon Ugolina who, with good manners and, above all with prayer, managed to lead her father back to the right path. The family balance, however, was compromised and Ugolina matured the vocation that she already felt in her heart. The only confidant was a woman named Libera, to whom she manifested the desire to serve Christ with prayer, living withdrawn from the world. Libera told her to ponder the decision thoroughly, waiting for a heavenly sign. Ugolina decided that she would carry out the escape when her father was absent for business and this happened the very next day, when the parent went to Turin. Wearing men's clothes and a hood, the maiden left the palace.
The extraordinary and dangerous inspiration led her to a wood, a mile away from the City, where the Chapel of St Mary of Bethlehem stood. Next to it was the cell, now empty, of a hermit named Favorino who, on his return from the Holy Land, had built that hermitage to live in holiness. Ugolina decided that it would be her new home.
For forty-seven years, pretending to be a man named Ugone, she lived with the bare necessities, in prayer, between intense talks with God and penances to fight the temptations that certainly were not lacking.
The distance from the City was ,however, short and, therefore ,the Chapel became a point of reference for the whole surrounding area, a place of prayer, comfort, advice, for people of different social classes. Ugolina communicated, without showing her face, through a small window. Only the Confessor and confidant ,Libera, knew who that anchorite really was.
The ancient biographer gives us a singular fact. A poor widow from Vercelli, heavily harassed by the City's evil Procurator, asked Ugolina for help, who exceptionally let her into her cell. At midnight the following day, in the Chapel next door, an Angel comforted them by telling them that the persecutor would pay for his misdeeds. Shortly thereafter he was in fact condemned. The woman kept the secret, then went every day to see her. So many years passed, until Ugolina's health declined – stomach upsets and fevers forced her to bed. A few days before her death she called Father Valentino for general Confession and Holy Communion. She died on 16 August c 1300.
The news quickly spread around the City. The Priest went to the Bishop, Aimone di Challant, who was already informed of the facts. In solemn procession, with the clergy and the people, he wanted to pay homage to her. Ugolina, on a poor bed, rested in the peace of the Lord, with the side of the Crucifix, which she held in her hands, resting on her mouth. The Bishop, moved, knelt down and kissed her hands. All the people paraded in front of the body, finally discovering that she was the daughter of the rich De Cassami.
According to her will, she was buried in the cell, then, subsequently, in the Church. The tomb became a destination for pilgrims, often miraculous. She was a Saint by popular acclaim, with a feast on 8 August. In 1453 the Franciscans erected an important Convent next to the Church, called St Maria di Billiemme (from Bethlehem), continuing their devotion to the Saint.
The Chapel, with its ribbed vaults, was exquisitely frescoed in the 16th century, while the cell was destroyed in the siege of 1704. In 1996 the centuries-old presence of the Franciscans ceased, taken over by the Marianist Fathers.
Tagged: stugolinaofvercelli
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Super Model Kate Moss will be releasing a book titled KATE: The Kate Moss Book, which will be published by Rizzoli. This book will document Kate's 20 year modeling career in the industry. KATE will release with 8 different covers with photos shot by Juergen Teller, Mert & Marcus, Craig McDean, Mario Testino and others.
This entry was posted on August 9, 2012 by He Who Wins. It was filed under Models/ Celebs and was tagged with books, kate moss, rizzoli.


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text:
The Horrors: "2017 was turbulent, inspiring and full of change"
The Horrors reached a new milestone this year - their fifth album.
Published: 2:54 pm, December 05, 2017
2017 has been rubbo for a lot of things, but not bands. We've had a bumper crop of returning superstars, dazzling debut albums and live shows that'll knock your socks off.
Any year that features a new album from The Horrors is obviously a good 'un.
Hey Tom, how was your 2017?
2017 was turbulent, inspiring and full of change.
Congrats on your new album 'V', were you pleased with the response?
Yes, of course, we're conditioned from a young age to respond well to praise and it no doubt fills your brain with all kinds of lovely chemicals.
Album release aside, what have been your defining moments of 2017?
Realising London didn't need to be my home anymore after it being my home all my life.
What do you think has been the biggest music-related news story of 2017?
Oh god I have no idea, it's probably the subject I read the least about. I'm quite excited for Ableton Live 10. Anything else is just noise.
"pull" text="My plans for next year? Move to the seaside, never come back.
What's your album of the year?
It's still Frank Ocean's 'Blonde'. Nothing's beaten that yet, not that I've heard anyway.
Where will The Horrors be this Christmas?
Having a leather party.
Do you have any favourite Christmas party games?
Hide the sausage.
Which big or buzzy bands do you think will make a comeback in 2018?
Do you have any exciting plans for next year yet?
Move to the seaside, never come back.
Do you have any resolutions for 2018?
Be a good human.


text:
Una O'Connor was born Agnes Teresa McGlade in Belfast, Ireland, in 1880. She took her stage name when she joined Dublin's prestigious Abbey Players. By the 1930s, she was appearing in West End stage productions and had small roles in films like Alfred Hitchcock's Murder (1930).
She didn't attract much attention until she appeared in the Academy Award-winning adaptation of Noel Coward's play Cavalcade (1933). She and Herbert Mundin played the Bridges, servants to the upper-class Marryot family—a concept not dissimilar to the later acclaimed television drama Upstairs, Downstairs. That performance provided O'Connor with a ticket to Hollywood, where her patented hysterics kept her in demand for almost three decades.
She was a favorite of both James Whale and John Ford. For Whale, she made memorable supporting appearances in The Invisible Man (1933) and The Bride of Frankenstein (1935). She played more serious characters for Ford in 1935's The Informer (as Wallace Ford's mother) and The Plough and the Stars (1936).
O'Connor seems to have made a movie with almost every big Hollywood star at one time or other. She was in three Errol Flynn films: The Adventures of Robin Hood (a delightful turn as Marian's maid-in-waiting), The Sea Hawk, and The Adventures of Don Juan. She also appeared in films with Ronald Colman (Random Harvest), Barbara Stanwyck (Christmas in Connecticut), Bob Hope (My Favorite Spy), Bing Crosby (The Bells of St. Mary's), Norma Shearer and Fredric March (The Barretts of Wimpole Street), and Jennifer Jones (Cluny Brown).
Her most frequent co-star was Charles Laughton. They worked together in The Barretts of Wimpole Street, This Land is Mine, The Canterville Ghost, Forever and a Day, and Witness for the Prosecution. Indeed, Witness for the Prosecution provided O'Connor with her most famous role, as the hard-of-hearing housekeeper Janet McKenzie. She played the part for two years on Broadway and reprised it for Billy Wilder's film version. It was her final performance.
Una O'Connor died of heart disease in 1959. She never married.
Labels: rick29 (author), una o'connor, underrated performer of the week
toto2 January 3, 2010 at 3:33 PM
What an outstanding choice for Underrated Performer of the Week! Una O'Connor is a wonderful scene stealer. She is magical in "The Adventures of Robin Hood," while protecting her sweet lamb, Maid Marian, yet falling for the undeniable charm of Sir Robin of Locksley. I loved her work in "Witness for the Prosecution," too, opposite the irascible Sir Wilfrid Robarts.
Excellent post about an unforgettable character actress!
Paul 2 January 3, 2010 at 6:11 PM
Rick and Toto2 ,saying Una was a scene stealer is a under statement. Great choice Rick.
Aki January 3, 2010 at 7:37 PM
Great choice Rick. She was one of those actresses you saw in many movies and never knew her name. I always remember her the best in Flynn's The Adventures of Robin Hood. She had an unforgettable giggle.....so charming I can remember it today.
Dawn January 4, 2010 at 12:51 PM
Rick, wonderful review. I remember Una O'Connor in:
Christmas in Connecticut (1945)
The Bells of St. Mary's (1945)
love the picture you picked for your post.
wallace ford was the son to una o'conner not wallace beery
Rick29 February 28, 2010 at 6:43 PM
Thanks, Anonynmous, for catching an embarrassing typo that no one else saw! It's been fixed.