A Biologically Interpretable Graph Convolutional Network to Link Genetic Risk Pathways and Imaging Phenotypes of Disease 
Authors: Sayan Ghosal
Qiang Chen
Giulio Pergola
Aaron L Goldman
William Ulrich
Daniel R Weinberger
Archana Venkataraman
Venue: ICLR 2022 Poster (2022)
Keywords: Imaging-genetics
Hierarchical Graph Convolution
Gene Ontology
Bayesian Feature Selection
Schizophrenia

Abstract: We propose a novel end-to-end framework for whole-brain and whole-genome imaging-genetics. Our genetics network uses hierarchical graph convolution and pooling operations to embed subject-level data onto a low-dimensional latent space. The hierarchical network implicitly tracks the convergence of genetic risk across well-established biological pathways, while an attention mechanism automatically identifies the salient edges of this network at the subject level. In parallel, our imaging network projects multimodal data onto a set of latent embeddings. For interpretability, we implement a Bayesian feature selection strategy to extract the discriminative imaging biomarkers; these feature weights are optimized alongside the other model parameters. We couple the imaging and genetic embeddings with a predictor network, to ensure that the learned representations are linked to phenotype. We evaluate our framework on a schizophrenia dataset that includes two functional MRI paradigms and gene scores derived from Single Nucleotide Polymorphism data. Using repeated 10-fold cross-validation, we show that our imaging-genetics fusion achieves the better classification performance than state-of-the-art baselines. In an exploratory analysis, we further show that the biomarkers identified by our model are reproducible and closely associated with deficits in schizophrenia. 

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A BIOLOGICALLY INTERPRETABLE GRAPH CONVOLU- TIONAL NETWORK TO LINK GENETIC RISK PATHWAYS AND NEUROIMAGING MARKERS OF DISEASE
Sayan Ghosal', Qiang Chen?, Giulio Pergola?3, Aaron L. Goldman?, William UIrich?, Daniel R. Weinberger", and Archana Venkataraman
Department of Electrical and Computer Engineering, Johns Hopkins University, USA
Lieber Institute for Brain Development, USA Department of Basic Medical Sciences, University of Bari Aldo Moro, Italy
ABSTRACT
We propose novel end-to-end framework for whole-bbain and whole-gene -eooee imaging-geneen genetics. Our genetics network uses hierarchical graph convolution and pooling operations to embed subject-level data onto low-dimensional latent space. The hierarchical network implicitly tracks the convergence of genetic risk across well-established biological pathways, while an attention mechanism automatically identifies the salient edges of this network at the subject level. In parallel, our imaging network projects multimodal data onto a set of latent embeddings. For interpretability, implement Bayesian feature selection strategy to extract the discriminative imaging biomarkers; these feature weights are optimized alongside the other model parameters. We couple the imaging and genetic embeddings with a predictor network, to ensure that the learned representations are linked to phenotype. We evaluate our framework on a schizophrenia dataset that includes two functional MRI paradigms and gene scores derived from Single Nucleotide Polymorphism data. Using repeated 10-fold cross- validaaali,,,on,, we show that our imaging-gent genetics fusion achieves the better classification performance than state-of-the-an baselines. In an exploratory analysis, we further show that the biomarkers identified by our model are reproducible and closely associated with deficits in schizophrenia.
INTRODUCTION
Neuropsychiatric disorders such autism and schizophrenia have two complementary viewpoints. On the one hand, they are associated with behavioral and cognitive dysfunction (Kay et al.) 1987]
Bowie et al.) 2006), which results in altered brain activity (Karlsgodt al. 2010). On the other hand, they are highly heritable, which suggests a strong genetic underpinning (Gejman et al. 2010
Ripke et al. 2014). Most studies decouple the problems of disentangling the neural mechanisms (Gur ct al. 2010) and pinpointing genetic variations (Ripke et 2014), which ultimately provides an incomplete picture of the underlying disorder (Karlsgodt al. 2010 Karam et al. 2010)).
Imaging-genetics is an emerging field that tries to merge these complementary viewpoints (Hariri & Weinberger 2003). The imaging features are often derived from structural and functional MRI (s/MMRI), and the genetic variants are typically captured by Single Nucleotide Polymorphisms (SNPs). Data-driven mmaging-genetie methods can be grouped into four categories. The first category uses sparse multivariate regression to predict one or more imaging features based on a linear combination of SNPs (Wang al. 2012; Liu al., 2014). The second category uses representation learning (Pearlson et al. 2015 Hu et al. 2018) to maximally align the data distributions of the two modalities.
These prior works focus on finding associations between imaging and genetics, whereas recent works are starting to incorporate additional phenotypes like disease status. The third category relies on generative models (Batmanghelich et al. 2016 Ghosal et al. 2019) to fuse imaging and genetics data with subject diagnosis. While this fusion extracts discriminative biomarkers, the generative nature makes it hard to compensate for missing data or to add data modalities. In fact, clinical neuroscience is moving towards multimodal imaging acquisitions where different modalities contain potentially orthogonal information about the disease. However, with multimodal data come the problem of missing data acquisitions, thus underscoring the need for flexible and adaptable methods.

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2 RELATED WORK: DEEP LEARNING FOR BIOLOGICAL DATA ANALYSIS
The fourth category for imaging-gennties uses deep learning to link the multiple viewpoints (Srini vasagopalan et al., 2019; Zeng et al. 2018 Eraslan et al. 2019 Shen & Thompson 2020). For example, the seminal work of (Ghosal et al. 2021) uses coupled autoencoder and predictor net- works to integrate neuroimaging, SNPs, and diagnosis. While important, this work (and almost all imaging-geneties analyses) requires drastically reduced set of genetic features to ensure model stability (Bhattacharjee et al. 2012). In terms of scale, raw dataset of 100K SNPs is reduced to 1K SNPs, often based on a Genome- Wide Association Study (GWAS) (Ripke et al.) 2014). In contrast, neuropsychiatric disorders are polygenetic, meaning that they are influenced by numerous genetic variants interacting across many biological pathways. The GWAS sub-selection step effectively removes the downstream information about these interactions (Horváth et al., 2013). Within the genetics realm, there is a vast literature that associates SNPs and genes to different biological path- ways (Mi et al.] 2013 Ashburner al. 2000; Carbon et al. 202T). The works of (van Hilten et al.) 2020; Gaudelet et al. 2020) have used this information to design sparse artificial neural network that aggregates genetic risk according to these pathways in order to predict phenotypic variable. While an important first step, their ANN contains just single hidden layer, which does not account for the hierarchical and interconnected nature of the biological processes.
Graph convolutional networks (GCNs) (Kipf & Welling 2016) provide natural way to leverage the high-dimensional and interconnected genetic relationships. GCNs have gained immense popularity in protein structure prediction (Fout et al. 2017), drug discovery (Stokes et al. 2020), and gene-gene interactions (Yuan & Bar-Joseph] 2020). Beyond the architectural design, graph attention layers learn edge weightings that allows to track the information flow through the graph /Velicković et al., 2017). The attention focuses on the most discriminative set of interactions between the nodes, often leading to better generalization on unseen data. Graph attention has been successful in biological applications, like predicting disease-RNe -NAAA association (Zhang et al. (019) and essential gene prediction (Schapke) et al.. 2021). Finally, similar the standard max-pooling operation, graph pooling allows us to aggregate information at each level of the hierarchy (Bruna et al., 2013 Lee et al. 2019 Ying et al.) 2018). During standard graph pooling. the nodes at each level are clustered to form smaller subgraph. These clusters can be obtained via deterministic algorithms (Bruna et al.) 2013) or be learned during training (Ying et al.) 2018 Lee et al. 2019). While beneficial for information compression, the clustering operation obscures the interpretation of each node. Our framework bypasses this issue by constructing sparse hierarchical graph for convolution and pooling based on a well-known ontology.
One drawback of deep learning is the black- box nature of the models. Recemtly,Lundbeg et al. (2017) has provided framework, SHAP (SHapley Additive exPlanations), to compute feature importance for interpretability. SHAP assigns a score to each feature equal to the marginal contribution of that feature to the output, as averaged over all possible feature subsets. Variants like Semel-SHAP provide for increased flexibility of the feature importance computation (Ribeiro et al.) 2016). While SHAP provides a model-agnostic tool to quantify input-output relationships, it says little about how groups of input features affect the output, which is primary interest in biological datasets.
In this paper, we introduce an interpretable Genetics and m mltimodal Imaging based DEep neural network (GUIDE), for whole-brain and whole-genome analysis. We use hierarchical graph con- volutions that mimic an ontology based network of biological processes (Mi et al. 2013). We use pooling capture the information flow through the graph and graph attention learn the salient edges, thus identifying key pathways associated with the disorder. On the imaging front, we use an encoder coupled with Bayesian feature selection to learn multivariate importance scores. The latent embeddings learned by our genetics graph convolutions and imaging encoder are combined for disease prediction. We demonstrate that both the ontology network and the imaging imaging-genetics fusion in GUIDE achieve better classification accuracy than state-of-the- baselines. More importantly, GUIDE can identify robust and clinically relevant biomarkers in both data domains.
A DEEP MULTIMODAL AMAGING-GENETIO FRAMEWORK
Fig. iillustrates GUIDE framework. Inputs are the gene scores g. E R for each subject and the corresponding imaging features i, E R xl and f E R Maxi obtained from two different acquisitions. The gene scores ga are obtained by grouping the original SNPs according to the nearest
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Graph Convolution
Gruph Conrolation
Readont
Bological Process
Geres Scorss
Interaction between processes
Genetic Graph Embedding (G-EMBED)
Bayes Feature Selection
g
G-EMBED
Model Regularization
246
E((),E())=
())
Phenotype Prediction
H
80
Calegoriall
Gene embedding using attention based hierar- chical graph convolution, Bottom: Imaging and genetics integration; both modalities are coupled for phenotype prediction-in our case, disease classification. The variables {iz, i correspond the imaging data, and ga is the genetic data. E(-) is set of fully connected layers that encodes the input data modalities. We further provide the architectural details of model in Appendix A.I
Figure 1: Overview of the GUIDE framework. Top:
gene and aggregating the associated genetic risk weighted by GWAS effect size (Ripke et al. 2014). The subject diagnosis (phenotype) yn. {0, 13 is known during training but absent during testing.
3.1 GENETIC GRAPH EMBEDDING
The top portion of Fig. iillustrates our attention-baset graph convolution model for genetic embed- ding. The underlying graph is based on the gene ontological hicrarchy (Ashburner et al., 2000) that effectively maps each gene to different biological processes. Mathematically, this ontology gives rise to sparse matrix Ag E (0, 1) 1)GT where G the total number of genes, and T is the number of biological processes (i.e., nodes). Given this substrate, GUIDE first learns projection of the gene scores gn onto 7 graph nodes. Each node signal is d-dimensional feature vector, p., (f) E R Ixd
(1) = PReLU & (We @ Ag (:))))
where each of the columns of the learned weight matrix W, R are masked by the nonzero entries in the tth column of Ag. We note that this projection step is similar to a single-layer perceptron with only subset of input nodes connected each hidden node.
3.2 GRAPH ATTENTION AND HIERARCHICAL POOLING
In addition to grouping genes into biological processes, a standard ontology also specifies a hierar- chical relationship between the biological processes themselves (Alcocer-Cuard) et al. 2014). example of this hierarchy is: generation of neurons - neurogenesis -> nervous system development.
We use graph convolution to mimic the flow of information through the hierarchy of biological processes. Here, GUIDE learns two complementary pieces of information. The first is set of graph convolutional filters that act on each embedded node signal, and the second is set of subject-specific attention weights that select the discriminative edges. Formally, let the binary matrix Ap R T'x capture the directed edges in the ontology. Our graph convolution at stage is:
P 1 =
Σ (t B.P.
jEChald()
where (t) E R
lxd: 4 is signal for node at stage I, W E Rdxde is the convolutional filter between stages 1 and 1, 3, is the self-influence for node W, dd is the convolution

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filter for self loop, and or-)) is the nonlinearity. The summation in Eq. (2) aggregates the influence over all child nodes defined by the graph Ap. thus respecting the high-level ontology.
The variables E (t,j) quantify the influence of the child node j over the parent node t at convolutional stage I. Unlike standard graph convolutional network, in which the edge weights are fixed, we learn E,, (t using graph attention mechanism. Mathematically, we have
(4,5) = exp (tanh ([p%, (
()) ct))
(3)
LjEChadgy) exp (Lanh (L)W D .c)
where et a fixed weight vector learned during training. We estimate the self influence variable as 3i (t), c)), where ef is another weight vector learned during training.
Finally, we use hierarchical pooling to coarsen the graph. As formulated in Eq. (2). the graph convolution passes information "upwards" from child nodes to parent nodes. From the ontology standpoint, each stage of the hierarchy goes from a lower-level biological process (c.g. neurogenesis) to higher-level biological process (e.g., nervous system development). Thus, remove the lowest (leaf) layer from the graph at each stage and continue this process until we reach the root nodes. The genetic embedding 2% Px1 is obtained by concatenating the signals from each root node.
3.3 BAYESIAN FEATURE SELECTION
The bottom branch of Fig. 1 shows our embedding and feature selection procedure for the imaging modalities. Our dataset this work contains two fMRI paradigms, leading to inputs i!, and i, of each subject However, our framework naturally extends to arbitrary number of modalities.
From a Bayesian viewpoint, the problem of feature selection can handled by introducing an unobserved binary random vector 2 of the same dimensionality as i and inferring its posterior probability distribution given the paired training dataset: D {in yn where yn denotes the I.". Y (y...... Bn). and ZTd 2 ...., 2 we note
class label. By defining 1 = [1"" that the desired posterior distribution p(Z" ITT Y) is intractable. One strategy is to minimize the KL divergence between approximate distribution q()) and the true posterior distribution KL (g(ZT)) ([p( Imm Y)). Mathematically, this optimization can be written as
argmin ((-)
E, [log (p (Y|I", ])] + KL (g(Z")))lpt IP)(""))
(4)
where p(Z") is a prior over the latent masks. While Eq. (4) does not have a closed-form solution, can be optimized via Monte Carlo integration by sampling the vectors z, ~ Bernoulli("") where hthh parameterizes the approximate distribution ((), and minimizing the empirical form of Eq. (4)
(Gal & Kendall] Kingma & Welling). In this case, the first term becomes the binary cross entropy loss
where the input features 1sT are masked according to z In order to learn the probability maps tdr during training, we replace the binary z" with a continuous relaxation of the Bernoulli distribution:
log (bm) log(1 1 b") + log(u.)) log(1 u
2 =
(5)
where U is sampled from Uniformd 1). the parameter r controls the relaxation from the {0. 1) Bernoulli, and the feature selection probabilities bdd are learned during training (see Section 3.4).
3.4 MULTIMODAL FUSION AND MODEL REGULARIZATION
As shown in Fig. [ the Bayesian feature selection step is followed by cascade of fully connected layers, denoted 8 (-), to project each imaging modality m onto a low-dimensional latent embedding. Likewise, the genetic embedding f9 is passed through separate fully connected cascade 8 and onto the same cow-dimensional space. To leverage synergies between the imaging and genetics data, we fuse the latent embeddings across modalities to obtain a common representation:
M₁ (8' (i), 2/) + E2 (1, @ 2222 + E ((R))
where @ is the Hadamard product used in the Bayesian feature selection step, E = G-EMBED (g.)) where G-EMBED(.) represents the genetics network based on the ontological hierarchy, and M,
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is the number of modalities present for subject Finally, the latent embedding én is imput to classification network to tie the learned biomarkers to patient/control phenotype.
Notice that fusion strategy encourages the latent embedding ln for individual patient to have a consistent scale, even when constructed using a subset of the modalities. Thus, we can accommodate missing data during training by updating individual branches of the network based on which modalities are present. In this way, GUIDE can maximally use and learn from incomplete data.
We introduce three regularizers to stabilize the model. The genetic regularizer reconstructs the gene scores by performing a hierarchical graph decoding (G-DECOD on 4% This operation unwraps the gene encoding via the same ontology Ashburner et al. 2000). Likewise, the imaging regularizer decodes the original feature vectors from én via the artificial neural networks D (-). Finally, the prior over zn appears as the KL divergence between the learned distribution (er(b")) and a binary random vector Ber(s) with small entries to enforce sparsity. Our loss function during training is:
N
C(1,, 12,8) = Σ
(Un log(ūn) + (1 - y/n) log(1 - (nn))
n=1
2
N2
KLM (Ber(b"")|Ber(s) + Ar Σ I1i D (ee))1
+ A Σ 1 - D²(Gn)112 71
m=1
N, ||g. C-DECODE((!)I)
+ AG
(7)
n=1
where ý is the class prediction. N is the total number of subjects, N' is the number of subjects with modality m present, and the hyper-parameters {A,, À control the contributions of the data recon- struction errors. The function (-Il- in Eq. 7 averages the element-win KL divergences across the input feature dimension, thus maintaining the scale of the prior term regardless of dimensionality.
The first two terms of Eq. correspond to the classification task and the feature sparsity penalty, which are empirical translations of Eq. (4). The final three terms are the reconstruction losses, which regularizers ensure that the latent embedding is capturing the original data distribution.
Training Strategy: As described in Section our dataset consists of 1848 subjects with only genetics data and additional 208 subjects with both imaging and geneties data. Given the high genetics dimensionality, we pretrain the G-EMBED and G-DECODE branches and classifier of GUIDE using the 1848 genetics-only subjects. These 1848 subjects are divided into training and validation set, the latter of which is used for early stopping. We use the pretrained model to warm start GUIDE framework and perform 10-fold nested CV over the 208 imaging genetics cohort.
imaging-genetics
We learn the Bayesian feature selection probabilities during training by sampling the random vectors 2,, zi, during each forward pass using Eq. (5) and using them mask the inputs i,, 12 for patient Finally, if a data modality is missing for subject n. we simply fix the corresponding encoder-decoder branch and update the remaining branches and predictor network using backpropagation.
Implementation Details: We use the first five layers of the gene ontology (Ashburner et al. 2000 construct G-ENCODE. In total, this network encompasses 13595 biological processes organized from 2836 leaf nodes to 3276 root nodes. We perform grid search over three order of magnitude and fix the hyperparameters X = 3 10-3, AG 10-5 We fix the signal dimensionality at d for the gene embedding and d; = 5 for the subsequent graph convolution and deconvolution operations based on the genetics-only subjects. Likewise, the non-linearity Eq. ? selected to be a Layer Norm, followed by PReLU and Dropout, once again using the genetics-only subjects. The Bernoulli prior over zd is set at s = 0.001, which is consistent with Ghosal et al. (202I). Further architectural details are provided in the Appendix. We train GUIDE using ADAM with an initial learning rate of 0.0002 and decay of 0.7 every 50 epochs. Our code is implemented using Matlab 2019b and PyTorh 3.7. Training the full model takes roughly I 7hrs 4.9GB Nvidia K80 GPU.
3.5 BASELINE COMPARISON METHODS
We compare GUIDE with two conventional imaging-genetics methods and with single modality versions of our framework. In each case, the hyperparameters optimized using grid search.
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Parallel ICA RF: We concatenate the imaging modalities single vector i, E 1 1T and perform parallel ICA (p-ICA) (Pearlson et al. 2015) with the gene scores ga- Since p-ICA cannot handle missing modalities, we fit multivariate regression model to impute a missing imaging modality from the available ones. Specifically, if iý is absent, we impute it as: ip = f iz. where B the regression coefficient matrix obtained from training data. After imputation, we use p-ICA to decompose the imaging and genetics data into independent but interrelated networks:
in = S C and En W f
where S, W are independent source matrices and the Cn f, are loading vectors. We concatenate the loading matrices [c% [ and use it as the input feature vector for random forest classifier.
During training, we apply p-ICA to just the training data to estimate the sources (Strain; W Wirain)- We use these estimated sources to obtain the loading matrices for the test data follows:
test
Strain and
glest
W train
The G-MIND architecture by Ghosal al. (2021) designed for 1242 genetics input. Thus, we introduce cully-connected layer to project the high-dimensions gene scores gn onto 1242 dimensional vector for input to G-MIND (Ghosal al. 202T). We evaluate both random weight initialization and pretraining the genetics branch of G-MIND with the 1848 genetics-only subjects.
G-MIND:
Single Modality Prediction: We consider two versions GUIDE. The first consists the genetics branches and classifier, and the second consists of just the imaging branches and classifier. We optimize these networks architectures using repeated 10-fold cross validation outlined in Section 3.4.
3.6 EVALUATION STRATEGY
We conduct comprehensive evaluation of our framework that includes influence of embedding priori biological information, biomarker reproducibility, and classification performance.
Influence of the Ontology-Based Hierarchy: In GUIDE assume that processing the data ac- cording to an established gene ontology will extract more robust and discriminative biomarkers. To test this assumption, we compare our gene ontology network random networks and to an unstructured model. The random networks contain the same number of nodes in each layer as the ontology-basee -ased graph. However, we randomly permute edges between the parents and children nodes, and between the genetic inputs gn and nodes. The corresponding unstructured model is fully-connected ANN with the same number parameters, but no inherent structure between layers. As benchmark, we compare the deep learning models with the gold-standard Polygenetic Risk Score (PRS) for schizophrenia developed by the PGC consortium (Ripke et al., 2014). Broadly, the PRS is weighted combination of the risk alleles for schizophrenia, as determined by large GWAS study. We run a logistic regression on the (scalar) PRS to determine class membership.
Classification Performance; We use repeated 10-fold cross validation (CV) the 208 imaging- genetics subjects to quantify the performance. The models are trained using folds, and the remaining two folds reserved for validation and testing. We report accuracy, sensitivity, specificity, Area Under the ROC Curve (AUROC), and Area Under the precision-recht Curve (AUPRC). The operating point is chosen by minimizing the classification error on the validation set. We further use DeLong tests to compare statistical difference in AUROC between GUIDE and the baselines.
Reproducibility of Feature Importance Maps: The probability maps bn capture the importance of each feature of modality m. We evaluate both the predictive performance and the reproducibility of our Bayesian feature selection (BFS) scheme. We extract the the top- features of b,, learned during each training fold of our repeated 10-fold CV setup and encode this information indicator vector, where the entry '1' indicates that the feature is among the top-K. We compare the BFS features with Kernel SHAP (Lundberg al. 2017). The background values for K-SHAP fixed to the average input data across the training set. We use the validation set to select the top K K-SHAP features and encode them in binary indicator vector.
binary
To quantify predictive performance, we mask our test data from each fold using the BFS and K-SHAP indicator vectors and send it through GUIDE for patient versus control classification. To quantify

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the reproducibility of the top-K K features, calculate the pairwise cosine similarity between all the binary vectors across the folds as identified by either BFS or K-SHAP. The distribution of similarities tells us how often the same imaging features are selected across subsets of the data.
Discovering of Biological Pathways: The attention layer of G-ENCODE provides a subject- specific measure of "information flow" through the network. To identify discriminative pathways, we first trace all possible paths between leaf and root nodes. The importance of edges along these paths are used in a logistic regression framework to predict the subject class label. We then perform likelihood ratio test and obtain a p-value (FDR corrected) for each path in terms of patient/control differentiation. For robustness, we repeat this experiment 10 times using subsets of 90% of our total dataset 1848 + 208 subjects and select pathways that achieve p < 0.05 in at least 7 of the 10 subsets.
4 RESULTS
0.9
Data and Preprocessing: We evaluate GUIDE on a study of schizophrenia provided by Anonymous Insti- tution that contains SNP data and two iMRI paradigms.
0.8
True Positive Rate
0.7
0.6
Illumina Bead Chipset including 510K/ 610K/660K/2.5M used for genotyping. Quality control and imputation were performed using PLINK and IMPUTE2. The result- ing 102K linkage disequilibrium independent (r² < 0.1) indexed SNPs are grouped to the nearest gene (within 50kb basepairs) (Wong et al.) [017)). The 13,908 dimen- sional input genes cores are computed as weighted av- erage of the SNPs using GWAS effect size (Ripke et al.) 2014). We note that the GWAS was performed on a separate dataset that did not include our site.
0.5
0.4
0.3
Random Graphs (0.51)
ANN (0.52)
PRS (0.58)
Ontology (0.67)
0
0.2
0.4
0.6
0.8
Positive Rate
Figure 2: ROCs for the PRS (blue), un- structured ANN (green) and the struc- tured models where G-EMBED and G- DECODE use either random graphs (red) or the gene ontology network (magenta). The AUROC is given in parentheses.
Imaging data include two task-fMRI paradigms com- monly used in the schizophrenia literature. The first paradigm is a working memory task (N-back), and the second is a simple declarative memory task (SDMT). FMRI data was acquired on 3T GE Sigma scanner (EPI, TR/TE 2000/28 msec; preprocessing includes slice timing correction, realigument, spatial normalization to MNI template, smoothing and motion regression. We SPM 12 generate contrast maps and the Brainnetome at- las (Fan et al. 2016) to define 246 cortical and subcortical regions. The inputs i 13 correspond to the voxels in the respective region. Additional details reported in Appendix (A.2
3.75 x 3.75 x 6/5 for N-back and SDMT, respectively). FMRI
average contrast
In total, our dataset contains 1848 subjects (792 schizophrenia, 1056 control) with just SNP data and 208 subjects with imaging and SNP data, divided follows: 98 subjects (42 schizophrenia, 56 control) with SNP and N-back data, 48 subjects (17 schizophrenia, 31 control) with SNP and SDMT data, and 62 subjects (38 schizophrenia, 24 control) who have all the three data modalities.
Benefit of the Gene Ontology Network: To quantify the value of embedding a biological hierar- chy into our model architecture, we first train just the genetics branch and classifier for all three deep networks (unstructured, random graphs, ontology) using the 1848 genetics-only subjects and test them on the SNP data from the other 208 subjects. We sample 10 random graphs in this experiment.
Fig. 2 illustrates the ROC curve over the test data. As seen, the testing performance is near-chance using both random graphs and the ANN. The gold-standard PRS does slightly better; however, this measure was derived on much larger consortium dataset. In contrast, our gene ontology network (magenta line in Fig. 2 achieves the best performance of any method, suggesting that our biologically-inspee architecture can extract robust and predictive genetic biomarkers of disorder.
Table the 10-fold CV testing performance all the methods on the multimodal imaging-genetics genetics dataset; repeat the CV procedure 10 times to obtain standard deviations for each metric. We note that P-ICA and G-MIND with random initialization have relatively poor performance, likely due to the high dimensionality of ga and low sample size. Pretraining on
Classification Performance:
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Table 1: Classification performance (mean + std) across repeated CV runs. P-values obtained from DeLong test indicate significantly greater AUROC for GUIDE than each of the baselines.
Perf
Sensitivity
Specificity
Accuracy
AUPRC
AUROC
P-Value
Method
P-IAA
0.30 0.10
0.07
0.56 +: 0.03
0.54 0.04
0.59 : 0.04
10
G-MIND (random)
0.62 0.08
0.65 + 0.05
0.63 + 0.02
0.62 0.03
0.67 + 0.03
< 10
G-MIND (pretrain)
0.60 0.07
0.66 + 0.07
0.63 + 0.03
0.62 0.03
0.68 + 0.02
< 10
Imaging Only
0.18
0.76 0.14
0.61 + 0.01
0.62 0.02
0.66 +: 0.02
< 10
Genetic Only
0.54 0.15
0.69 0.10
0.62 + 0.02
0.63 0.03
0.68 + 0.02
< 10-1
GUIDE (Random Dropout)
0.51 0.14
0.79 + 0.12
0.66 + 0.02
0.70 0.02
0.75 + 0.01
0.27
GUIDE
0.62 1: 0.04
0.76 + 0.04
0.69 + 0.01 0.70 0.03
0.75 = 0.01
a separate genetics dataset improves the AUC of G-MIND, highlighting the benefits of increased
data. We also evaluate replacing the GUIDE BFS layer with random dropout. While the quantitative performance is similar, the feature reproduciblity is much higher with BFS (see Appendix (A.3). This result underscores the dual value of BFS for predictive performance and biomarker discovery.
Reproducibility of BFS Features: Fig. iillustrates the classification AUC when the input features are masked according to the top-K importance scores learned by the BFS (solid blue) and K-SHAP (dashed red) procedures. The confidence intervals are obtained across the repeated CV folds. As seen, both feature selection schemes achieve similar AUCs as the number of features K is varied across its entire range, thus highlighting the robustness of our (simpler) BFS approach.
Fig. 4 iilustrates the distribution of cosine similarities between the masked feature vectors learned by BFS and K-SHAP for K 50. Once again, the repeated CV procedure is run 10 times, yielding 100 total folds and 4950 pairwise comparisons per method. Notice that our BFS procedure achieves significantly higher cosine similarity values, which suggests that it selects a more robust set of features that is consistent across subsets of our main cohort. In contrast, K-SHAP relies heavily on individual subject data, which varies considerably across random subsets of the cohort.
Imaging Biomarkers: Fig. 5 iillusraaes the consistent imaging features that selected by method across the folds for A 50. We have colored each brain region according to the selection frequency. For clarity, we have displayed only the top 40% regions. We observe that the N-back biomarkers involve the Middle Frontal Gyrus (MFG), Inferior Frontal Gyrus (IFG), and default mode network which are associated with schizophrenia (Callicott et al. 2003 Wang et al., 2015). The SDMT biomarkers implicate the Supramarginal Gyrus (SMG), Superior Frontal Gyrus (SFG), along with Precuneus and Cuneus. We further interpret the higher order brain states implicated by these regions using Neurosynth (Yarkoni et al. 2011). Neurosynth uses reverse-inferent select set of "cognitive terms" associated with a set of input coordinates based on how frequently similar patterns have been observed across the fMRI literature. F shows that the N-back and SDMT biomarkers are associated with memory retrieval and attention (Carter et al. 2010: Guo et al. 2019). thus verifying that GUIDE captures information relevant the fMRI tasks.
procedure to
0.8
Bayes Importance
0.8
Mark
SOMT
0.7
K-SHAP Importance
Covine Similarity
0.7
AUC
0.4
0.6
0.3
0.2
0.5
50
100
150
200
250
0.1
K-HAP
Sagee Importance
K-SHAP
Bayes Importance
Figure 3: Mean AUC and confidence interval when masking the top-K imaging features learned by BFS (solid blue) and K-SHAP (dashed red). K is varied along the x-axis.
Figure 4: Distribution of pairwise cosine sim- ilarities between the feature masks learned by BFS and K-SHAP across the repeated CV folds. Here, we fix K 50 for both.
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N-Blckk
Defsult Mode
SDMI
PGL
SWO
Atsemtional
Theory Mind
Vissuniizz
Visual
Social
MTG
ANYG
Seratum STC
Execution
Autobiographical
Memory Retrieval
Bellefs
Nback
SONT
NeuroSynth
Figure 5: Left: The consistent set of brain regions captured by the dropout probabilities {b', , b²} for = 50. The color bar denotes the selection frequency. Right: Brain states associated with the selected regions for each fMRI task, decoded by Neurosynth.
Genetic Pathways: GUIDE contains 14881 "biological pathways" between the leaf and root nodes, Using the likelihood ratio test outlined in Section 3.6, we are able to identify 152 pathways with p < 0.05 after FDR correction that appear in at least 7 of the 10 random training datasets. We cluster these pathways into 10 categories based on their semantic similarity. Here, we use the tf-idf (Beel et al. 2016) information retrieval scheme to extract keywords in the pathways; we then embed them in a two-dimensional space using t-SNE (Van Der Maaten et al. (008) and apply a k-means clustering algorithm. Fig. shoows the clusters along with the most frequent keywords within each cluster. As seen, the frequent biological processes involve calcium signaling, regulation of macrophage and immunological synapse formation which have been previously linked to schizophrenia (Ormel et al. 2017, [Berridge| (2013) Van Kesteren et al.) 2017). This exploratory experiment shows that GUIDE can be used extract discriminative biological information about neuropsychiatric disorders.
CONCLUSION
We propose novel biologically interpretable graph convolutional network that integrates imaging and genetics data to perform disease prediction. This model is able to leverage prior biological information of different connected biological processes to identify patterns from both imaging and genetic data sets. Additionally, the unique use of Bayesian feature selection is able to find a set of clinically relevant biomarkers. The improved classification performance shows the ability of this model to build comprehensive view about the disorder based the incomplete information obtained from different modalities. We note that, our framework can easily be applied to other imaging modalities, such structural and diffusion MRI, simply by adding encoder-decoder branches. In future, will apply our framework to other application domains, such as autism and Parkinson's 's disease.
Pathway Embedding
Neuronal Action Potential, Extracellular Matrix Secretion
10
Immunological Synapse, Macrophage Derived Foam Cell Differentiation
1-NNE Dimonziion
sev
Epithelial to Mesenchymal Transition, Cardiac Septum/Atrium Morphogenesis
-5
Calcium lon Transport, Calcium lon Into Cytosol
-10
Histone Methylation, Meiotic Cell Cycle
-20
-15
-10
10
Suppression by Virus of Host STAT/Molecular Activity
4-SNE Dimossion
Lipid Storage, Sequestering of Triglyceride
Endoplasmic Reticulum Stress Induces Dephosphorylation
Cholesteral/Sterol Blosynthetic Process
Stimulus Involved Sensory Percoption, Pseudouridine Synthesis
8
Figure 6: Ten different categories of pathways based on their semantic similarity. The key words show the most frequent biological processes within each cluster.

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Acknowledgemmntt:: This work was supported by NSF CRCNS 1822575, NSF CAREER 1845430, and the National Institute of Mental Health extramural research program.
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Biological Process
Gruph Consolution
Graph Convolution
SNPs
Intoraction between proceses
Genetic Graph Embedding (G-EMBED)
Reconstruct Nodes
Grapk Unpooling
Graph Unpooling
Reconstruct
09
Hierarchical Graph Decoding (G-DECODE)
Bayes Feature Selection
gn
G-EMBED
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G-DECODE
gn
Model Regularization
246
D)(() i1
8
n
1
8
-
E)
ly
()) 22
n
m
C(-) Yn
22
.2
(-)
8
71
Categorical
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246
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())))()) +
D* ()()
C(-
PReLU-Dropout
BatchNorm
FCN
Haddamard Product
Figure Overview of the GUIDE framework. Top: Gene embedding using attention based hicrarchical graph convolution. We also depict the unpooling operation used as regularizer. Bottom: Imaging and genetics integration; both modalities are coupled for disease classification. The variables (1), ig) correspond to the imaging data, and gn. is the genetic data. E(.), D(-), C(.) are the feature extraction, model regularization, and classification operations, respectively.
A APPENDIX
A.1 DETAILED GUIDE ARCHITECTURE
GUIDE a biologically interpretable deep neural network that couples imaging and genetics data for simultaneous biomarker discovery and phenotypic prediction. GUIDE consists of a graph-based genetic encoder, parallel imaging encoder, a phenotypic predictor, and model regularizers. The genetic module uses hierarchical graph convolutions and pooling operations to strategically embed the genetic data to latent space. This architecture mimics the organization ontology. The imaging encoder uses fully connected layers to project the data the latent space. Finally, the predictor uses the fused latent representation for disease diagnosis. The regularizers reconstruct the data ensure that the latent embedding capturing the original data distribution.
well-established gene
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K-SHAP
Bayes Importance
K-SHAP
Bayes Importance
0.8
0.8
Cosine Similarity
Cosine Similarity
0.6
0.6
1
0.4
0.2
10
20
100
150
100
150
20
100 1.5
100
150
Nback
SDMT
Figure 8: The reproducibility of imaging biomarkers when the feature selection has been done using K-SHAP vs Bayesian dropout. Left shows the performance on Nback data, Right shows the performance on SDMT data
Fig. iillustrates the detailed architecture GUIDE. The top portion captures the genetic encoding and the decoding process. We use the gene ontology network to build the graph and use hierarchical pooling to control the flow of information according to the relationships between the biological processes. At the same time, graph attention mechanism tracks the salient edges at the subject level. The bottom portion shows the integration of the imaging and genetics modules. G-EMBED, and (-)(-) encodes the genetics and imaging data, respectively, and fuse the latent representation to fn- The latent embedding is passed through decoding operations (G-DECODE, D (-)) to reconstruct the input data. These decoding operations act as regularizers and stabilize the model.
A.1.1 FURTHER VALIDATION THE BAYESIAN FEATURE SELECTION
The Bayesian feature selection layer of GUIDE is used to learn discriminative imaging biomarkers for phenotypic prediction, captured by the probability maps b In this section, evaluate the stability the biomarkers across different subsets of the cohort. To start, we extract the top-K features of bm learned during each training fold of our repeated 10-fold CV setup and encode this information as a binary indicator vector, where '1' indicates that the feature is among the top- We compare the Bayesian Feature Selection (BFSS) with Kernel SHAP (Lundberg et al., 2017). To quantify the reproducibility of the top-K K features, we calculate the pairwise cosine similarity between all the binary vectors across the folds as identified by either BFS or K-SHAP. The distribution of similarities tells us how often the same imaging features are selected across subsets of the data.
Fig. 8 reports the distribution of cosine similarities between the masked feature vectors learned by BFS and K K-SHPP for K 10, 20, 50, 100, 150. The repeated CV procedure is run 10 times, yielding 100 total folds and 4950 pairwise comparisons per method. Notice that our BFS procedure achieves significantly higher cosine similarity values at each setting for K, which suggests that it selects more robust set features that is consistent across subsets of our main cohort.
A.2 DATA DESCRIPTION
We validate our framework on IMRI and genetic data acquired at the Anonymous Institution. Our imaging data include two standard task-fMRI paradigms acquired from 208 subjects. This section provides the details of the experimental paradigms and the subject demographics.
Neuroimaging Data:
As shown in Fig. 9 our data include two standard task-fMRI paradigms that were previously designed to study memory deficits in schizophrenia (Anonymous et al., Anonymous et al.). The first paradigm is block design working memory task (N-Back). During the O-back blocks, participants were instructed to press a button corresponding to number displayed on the screen. During the 2-back working memory blocks, participants were instructed to recall the number they had seen two stimuli previously. We use Generalized Linear Model (GLM) to obtain the activation map for each task block. The final contrast the subtraction 922 back
Go back- We compute the region-
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NO-Back
N2-Back
Time
Time
N-Back
SDMT
Figure Left The experimental paradigm of the N-Back task. The top row shows a sample response for NO-Back and the bottom row shows a sample response for N2-Back. Right The experimental setup for the SDMT task. Subjects are asked to view neutral and aversive stimuli.
Demographic
Anonymous
Data Sets
Sex (MFF)
113/17
70/40
ENP-Only
SDMT
(ycars)
Cases
Controls
Cases
Controls
Cases
Controls
Cases
Controls
Education (yeans)
2
12:22
793
1056
17
38
102
105
104-
10
Table 2: Demographic infor- mation for subjects provided by Anonymous Institution.
Table Breakdown patients and controls for each configuration.
wise inputs the average of these contrast values across all voxels in each particular region. The second paradigm is a simple declarative memory task (SDMT) which involves incidental encoding of complex aversive visual scenes. Similar N-back we estimate the brain activity associated with the encodig task. The SDMT contrast map is the subtraction Saversive Berosshair- Again, our region wise imputs are the average of these contrast values across all voxels in each parcel of brain. Additional details for generating the contrast maps can be found in (Friston et al. 1995).
Our imaging dataset incomplete, as many subjects were only scanned using one of the two fMRI paradigms. Table reports the breakdown of patients and controls for each configuration. Finally, Table reports the demographic information for the cohort. In each case, the patient and control groups were matched age, IQ (WRAT score), and years of education.
Gene Ontology The ontology provides pre-defined hierarchical network of biological processes, which has been curated by experts in biology. From modeling perspective, the biological processes can be thought of as nodes in a graph. The two main parts of the ontology (Ashburner et al.) 2000), Mi et al.) (2033) are the assignment of genes these biological processes (i.e., the input projection layer) and the directed edges between the biological processes (i.e., the hierarchical graph).
A.3 BASELINE HYPERPARAMETER SELECTION
We compare GUIDE with current machine learning models for imaging-genetiin and with single- modality versions our framework. We optimize the hyperparameters using grid search. This section provides the details of the hyperparameters used by the models.
Parallel ICA RF: We use the standard implementation of Parallel ICA (p-ICA) from the Fusion ICA (FIT) toolbox (Rachakonda al. 2012). The loading scores obtained from p-ICA are fed to random forest model for classification. Our hyperparameter tuning optimizes the number and depth of the decision trees. We control the tree depth by setting the minimum number of observations per leaf node. After the grid search, these parameters are set to (No. trees = 10000, M Minleaf Size = 50).
GMIND: Ghosal et al. 1022 selected the hyperparameters powers of 10 such that the rescaled terms in the loss function li within the same order of magnitude [1-10]. This criterion intuitive (i.e., equal importance is given to both the imaging and genetic data), and it not performance
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Table Classification performance (mean + std) across repeated CV runs. P-values obtained from DeLong test indicate significantly greater AUROC for GUIDE than each of the ablated models.
Perf
Sensitivity
Specificity
Accuracy
AUPRC
AUROC
P-Value
Method
Attention
0.49 + 0.09
0.79 0.08
0.65 + 0.03
0.70 0.02
0.73 0.02
0.01
No Feature Selection
0.73 0.10
0.63
0.67 0.03
No Decoder
0.58 + 0.18
0.66 +: 0.17
0.62 + 0.02
0.65 = 0.02
0.70 0.01
10
No Attention, No Feature Selection
0.56 + 0.18
0.72 + 0.13
0.64 + 0.02
0.67 + 0.08
0.73 0.03
0.05
No Attention, Decoder
0.50 + 0.16
0.76 0.12
0.64 +: 0.03
0.66 #: 0.02
0.71 0.02
10
No Feature Selection, Decoder
0.69 0.10
0.63
0.03
0.72 0.03
Attention, No Feature Selection.
+ 0.68 0.17
0.63 +
0.03
0.71 0.02
Decoder
GUIDE
0.62 + 0.04
0.76 0.04
0.69 + 0.01
0.70 0.03
0.75 0.01
driven. We use a similar strategy and fix the hyperparameters genetic reconstruction loss, imaging reconstruction loss, classification loss, and sparsity loss to 0.0001, 0.1, 1, 0.001, respectively.
Single Modality Prediction: We consider two versions of GUIDE. The first consists of the genetics branches and classifier, and the second consists of just the imaging branches and classifier. These baselines probe the advantages of integrating imaging and genetics data modalities in single framework. The hyperparameters for single modality prediction are the same as the full model.
A.4 ABLATION STUDY
In this section, evaluate the gain from three novel components of GUIDE: graph attention, feature selection, and the decoder for regularization. Specifically, the graph attention encourages GUIDE focus on the discriminative interaction patterns in the genetic data, the Bayesian feature selection identifies the most predictive brain regions and the decoders ensure that the low-dimensional embedding faithfully captures the original data distribution.
Table compares the performance of the ablated models with GUIDE. This ablation study allows us to quantify both the improvement of each component when they are incorporated in the model and the degradation in performance when one component is ablated from the full model. For example, removing the decoders causes the classification performance to degrade, regardless of the other components (i.e., GUIDE is better than "No Decoder" and "No Attention, No Feature Selection" is better than "No Attention, No Feature Selection, No Decoder"). We observe similar trends for both graph attention and Bayesian feature selection components. Thus, our ablation study demonstrates that all three components of GUIDE are essential for phenotypic prediction.
A.5 ADDITIONAL BASELINE COMPARISONS
In this section, we compare the performance of GUIDE with additional baseline models.
GUIDE (Random Dropout): The feature selection layer of our original GUIDE framework both regularizes the model and identifies potential imaging biomarkers. this baseline, we replace the Bayesian feature selection layer with random dropout.
The G-MIND architecture proposed by (Ghosal et al. 2021 relies on subselection of SNPs based on the p-values reported in a prior GWAS analysis of schizophrenia (Ripke) et al. 2014). Here, we subselect the same set of SNPs and feed them to the G-MIND model. This baseline captures the performance change when the ontology- based representation is replaced with the GWAS sub-selection. We use the hyperparameters reported in (Ghosal et al. 2021).
G-MIND (Sub-selection):
Hierarchical GCN: GUIDE utilizes an ontology to flow the information through the graph. The gene ontology network is curated based a priori information. In this baseline, we replace the
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Table Classification performance (mean + std) across repeated CV runs. P-values obtained from DeLong test indicate significantly greater AUROC for GUIDE than each of the baselines
Perf
Sensitivity
Specificity
Accuracy
AUPRC
AUROC:
Value
Method
GUIDE (Random Dropout)
0.51 + 0.14
0.79 + 0.12
0.66 0.02
0.70 0.02
0.75 0.01
0.27
G-MIND (Sub-sclcction)
0.63 + 0.08
0.67 + 0.06
0.65 0.01
0.63 0.04
0.70 0.02
< 10"4
Hierarchical GCN
0.48 = 0.17
0.75 + 0.13
0.62 0.02
0.65 0.02
0.71 = 0.02
1.8 x 10-4
GColMaxPooling
0.43 = 0.19
0.76 0.14
0.61 0.03
0.64 0.02
0.69 0.02
< x100
GUIDE
0.62 :: 0.04
0.76 0.04
0.69 0.01
0.70 : 0.03
0.75 0.01
ontology based graph with random graph. The construction of this graph is explained in Section 3.6. This baseline captures the performance gain for embedding biological knowledge into our architecture.
GCN + MaxPooling We compare our model with a standard GCN introduced by Kipf & Welling (016)). In this baseline, generate weighted adjacency matrix (A R 123908X1339 13908) using absolute correlation values between the gene scores from the pretraining data (i.e., 1848 genetic only subjects). This adjacency matrix acts as undirected graph between the nodes. Unlike GUIDE, the nodes represent each gene score instead of a biological process. We also perform hierarchical pooling with max pooling operation (Gao Ji, 2019) to reduce the data dimension between the graph convolution layers. This is in stark contrast to GUIDE where we use biological knowledge to consolidate the information flow through the network. Here, we note that the adjacency matrix A is not sparse, resulting in a significantly higher computational overhead than GUIDE.
In this baseline, we use two graph convolutional layers, each followed by max- max-pooling poooloonn layer. The max-pooling layer reduces the number of nodes by approx 50% such that after the final layer, the reduced data of the same dimension as lg in GUIDE. This architecture balances the computational requirements and the data representation ability of the model. Finally, we fix the readout layers, the imaging modules, and the classification module to the same architecture GUIDE.
Classification Performance Table reports the 10-fold CV testing performance of the baselines. Once again, we repeat the CV 10 times to obtain the standard deviation of cach metric. We note that G-MIND with subselcction of SNPs performs poorly compared to GUIDE. This may be the result of the complex and polygenic nature of schizophrenia. Finally, we compare GUIDE with two graph convolution-bast based models. In the first model, we see that replacing the structured representation of the nodes with a random hierarchical graph reduces performance. Hence, the ontological representation extracting meaningful information from the data. The second model compares GUIDE with standard GCN and max-pooling. This GCN uses dense graph for convolution and relies on data-driven strategy for dimensionality reduction. Again, we observe poor performance, in this case likely due to the large model size. In comparison, GUIDE operates on sparse graph and relies biological knowledge for dimensionality reduction on small datasets.
GUIDE shows similar performance with both random dropout and BFS layer. Thus, both strategies are effective in regularizing the model. However, the difference becomes apparent when we consider robustness of the selected biomarkers. To this end, we evaluated the stability of the input importances of GUIDE with random dropout using K-SHAP. We also apply K-SHAP to a version of GUIDE where we remove the dropout layer altogether (i.e., "No Feature Selection" reported in Appendix A.3). In Fig. I0 we see that the reproducibility is lower in both bascline models than the BFS strategy. Hence, our BFS procedure maintains performance while identifying robust biomarkers.
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Figure 10: The reproducibility of imaging biomarkers when the input layer of GUIDE is trained without dropout, with random dropout, and with Bayesian feature selection.
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Reviews:
[{"review_id": "syD26CYU1n", "reviewer": "Reviewer_WH5x", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "Minor comments:\nEq. (1): A pair of parentheses needs to be put around $\\mathbf{W}_t \\otimes \\mathbf{A}_g[:,t]$.\nSecond line below Eq. (1): There is a redundant ``that\" in ``that that\".\n``an binary indicator vector\" should be ``a binary indicator vector\" (i.e., with article ``a\" instead of ``an\" before ``binary\").\nIn Section 4, it says ``1848 subjects (793 schizophrenia, 1056 control)\". But 793+1056 = 1849 is not equal to 1848.", "summary_of_the_paper": "This paper proposes a novel end-to-end framework for whole-brain and whole-genome imaging-genetics. The genetics network uses hierarchical graph convolution and pooling operations to embed subject-level data onto a low-dimensional latent space. The imaging network projects multimodal data onto a set of latent embeddings. For interpretability, a Bayesian feature selection strategy is implemented to extract the discriminative imaging biomarkers; these feature weights are optimized alongside the other model parameters. The imaging and genetic embeddings are coupled with a predictor network, to ensure that the learned representations are linked to phenotype. Experiments on a schizophrenia dataset show that the proposed method hasthe better classification performance than state-of-the-art baselines, and the biomarkers identified are reproducible and confirmed to be closely associated with deficits in schizophrenia.", "summary_of_the_review": "The paper is generally well written, clearly presented, and a pleasure to read. The technique look sound and contributions look solid.", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "q9B-RXddb3_", "reviewer": "Reviewer_NHuX", "summary": "", "questions": "", "limitations": "", "rating": 8, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "Strengths\n1. The paper is well written overall, with problems of existing methods nicely laid out and provides just the right level of details for intuition.\n2. Most existing methods stop at gene-to-geneset when incorporating prior info. GUIDE additionally encodes a hierarchy of relationships between biological processes.\n3. The experiments carefully test each property of GUIDE, i.e. compared structured vs. random vs. fully connected graph as well as with and without imaging data.\n4. GUIDE achieves better classification performance than some state-of-the-art baselines, and features highlighted by GUIDE match with what are known to be implicated in schizophrenia.\n\nWeaknesses\n1. The motivation for this work is partly flawed. While it is true that many existing methods do not consider phenotypes, this is not the intended application of those methods. Instead, those methods are for finding associations between imaging and genetics, which GUIDE does not do, i.e. GUIDE does directly not tell us which genes are associated with which brain regions. \n2. How was polygenic score computed? Are cis SNPs of each gene aggregated using univariate GWAS beta? Any pruning of SNPs prior to combining? How was LD accounted for?\n3. There are a lot of hyperparameters in the model. Which hyperparameters are important and which do not affect results (as) much? How to set the important ones?\n4. In Fig. 2, while prior info helps, the overall AUROC is not particularly high. What is the best reported AUC with comparable genetics data in the literature? For example, in “Artificial image objects for classification of schizophrenia with GWAS-selected SNVs and convolutional neural network”, seems like their proposed method achieved AUC > 0.7 with just genetics. Also, in “Application of deep canonically correlated sparse autoencoder for the classification of schizophrenia states”, accuracy of 95.65% for SNP data sets and an accuracy of 80.53% for fMRI data sets were attained.\n", "summary_of_the_paper": "This paper proposes GUIDE for integrating imaging and genetics data for predicting phenotypes. GUIDE uses prior info from gene ontology to restrict connections between genes and biological processes under a graph convolution network (GCN) framework. The genetic and imaging representations are combined for phenotype prediction. Graph pooling and graph attention are used for finding key pathways, and Bayesian feature selection is used for finding key imaging features. GUIDE is evaluated on a schizophrenia dataset.", "summary_of_the_review": "The paper proposes a useful tool for integrating imaging and genetics with improved accuracy shown on schizophrenia prediction. The proposed interpretability strategy also seems useful. While many parts are based on existing methods, working out the details for combining various components is nontrivial.\n\nPost-revision Summary\nWhile the authors have addressed all my comments, the results are not quite at the level for a score of 10. So I will be keeping my score as 8.", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "jeVofwj7KwR", "reviewer": "Reviewer_b8wX", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "Overall, the paper is well-written and organized. \nIt is interesting to use the ontological gene hierarchy to define a graph for gene embedding and design imaging features selection in a Bayesian approach. However, the methodological contribution is limited, and several issues need to be justified or supported by experiments.\n\nThere should be more rigorous experiments to validate the proposed method, concerning the target classification task, (1) the existing GCN-based methods, (2) the use of preselected SNPs directly, instead of the hierarchical ontology representation, e.g., replacing G-EMBED with G-MIND in GUIDE, (3) random dropout in imaging feature selection in GUIDE.\n\nIn the full pipeline of preprocessing and network modeling, none of the test samples be involved in any of the steps in the pipeline. \nIn this sense, it should be clarified whether the contrast maps generation, regarded as a hyperparameter, was conducted on the training samples only.\n\nThe reported performance is relatively too low compared to the existing work on schizophrenia identification with task-/rest-fMRI (mostly higher than 80% in accuracy).\n\nIt would be interesting and more informative to illustrate the distribution of cosine similarities for different values of K, instead of a fixed value 50.\n\nIt is required to present the validity of handling missing modalities by using public datasets, possibly missing genetic or imaging data.\n", "summary_of_the_paper": "This work introduces a framework for fusing genetic and imaging data for schizophrenia classification. In particular, the authors propose to exploit the ontological gene hierarchy to define a graph reflecting genetic risk pathways and to use an attention mechanism for subject-level graph edges identification. They also implemented a Bayesian feature selection strategy using a dropout mechanism in discriminative imaging feature extraction.", "summary_of_the_review": "While the paper is well organized and written overall, the methodological innovation is limited and the arguments were not well supported from the experiments.", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "jLzCzkypnDj", "reviewer": "Reviewer_1JN7", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "- Major comments\nThe paper is very poorly structured with no cohesive approach. For example, the imaging and genetics inputs are discussed way before the actual data is introduced.\n\nHow is the ontology network constructed? The explanation is too spare and incomplete.\nGiven that the key insight of the paper was to use the ontological network, it is important to explain this in detail.\n\nWhat are the imaging features that go into the algorithm? Are they the t-values or some other measures? It is important to give the exact information, dimensionality of these features.\n\nAre the tSNE clustering surprising given the ontological structure was used to begin with?\n\n- Minor comments\n 1. Spell check and several instances of grammatical error", "summary_of_the_paper": "This paper is the latest in a quest to combine imaging and genetics information for diagnosis and/or biomarker identification. The key idea here is to use the prior knowledge of biological processes as an inductive bias to set up the graph architecture. \nThe paper also proposes Bayesian approaches to weigh feature importance for biomarker discovery.\n", "summary_of_the_review": "The basic idea and premise of the paper are promising. But the quality is presentation is very poor along with insufficient explanations and experiments to justify publication.\n", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "1: The contributions are neither significant nor novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}]

Author rebuttal:

Meta-review: In this paper, the authors present a method that combines genetic data (using a hierarchical, graph convolution approach) with imaging data to predict schizophrenia. The reviewers raised several concerns that the authors have addressed. Some of the concerns were relevant to writing, the authors have clarified these points. Another important concern was about the baselines. The authors added other baselines. One of the baselines they added was GUIDE with random dropout, this baseline performs as well as GUIDE, but the authors argue that GUIDE leads to robust features. 

I ask the authors to move the other baseline results, specifically the GUIDE with random dropout, and the relevant discussion to the main manuscript, and to consequently temper the discussion of the bayesian feature selection. Currently these additional results are only in the appendix, and not the text. Conditional on this, I recommend acceptance.
Decision: Accept (Poster)