A Biologically Interpretable Graph Convolutional Network to Link Genetic Risk Pathways and Imaging Phenotypes of Disease 

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 . 1 INTRODUCTION . Neuropsychiatric disorders such as 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 et 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 of a disorder ( Gur et al. , 2010 ) and pinpointing genetic variations ( Ripke et al. , 2014 ) . While these studies have shed new light on psychiatric disorders , the separation between the data modalities provides an incomplete picture of the underlying pathology ( Karlsgodt et 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/fMRI ) , and the genetic variants are typically captured by Single Nucleotide Polymorphisms ( SNPs ) . Data-driven imaging-genetics 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 et al. , 2012 ; Liu et 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 . 2 RELATED WORK : DEEP LEARNING FOR BIOLOGICAL DATA ANALYSIS . The fourth category for imaging-genetics uses deep learning to link the multiple viewpoints ( Srinivasagopalan 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 networks to integrate neuroimaging , SNPs , and diagnosis . While important , this work ( and almost all imaging-genetics analyses ) requires a drastically reduced set of genetic features to ensure model stability ( Bhattacharjee et al. , 2012 ) . 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. , 2015 ) . Within the genetics realm , there is a vast literature that associates SNPs and genes to different biological pathways ( Mi et al. , 2013 ; Ashburner et al. , 2000 ; Carbon et al. , 2021 ) . The works of ( van Hilten et al. , 2020 ; Gaudelet et al. , 2020 ) have used this information to design a sparse ANN that aggregates genetic risk according to these pathways in order to predict a phenotypic variable . While an important first step , their ANN contains just a single hidden layer , which does not account for the hierarchical and interconnected nature of the biological processes . Kulmanov et al . ( 2018 ) ; Ma et al . ( 2018 ) ; Bourgeais et al . ( 2021 ) go a step further and build a sparse multilayer perceptron to capture the hierarchy of gene ontology . While seminal contributions to computational genomics , the perceptron architecture leads to a large number of tunable parameters . In fact , these works require 60K , 3M , and 24K data samples , respectively , to train the model . These numbers are 1-3 orders of magnitude larger than most imaging-genetics datasets . Graph convolutional networks ( GCNs ) ( Kipf & Welling , 2016 ) provide a natural way to leverage the high-dimensional and interconnected genetic relationships . Similar to image convolutions , GCNs allow for parameter sharing , which greatly reduces model complexity . 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 allow us to track the information flow through the graph ( Velicković et al. , 2017 ) . Graph attention has been successful in biological applications , like predicting diseaseRNA association ( Zhang et al. , 2019 ) and essential gene prediction ( Schapke et al. , 2021 ) . Finally , 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 a smaller subgraph . While beneficial for information compression , the clustering operation obscures the interpretation of each node . Our framework bypasses this issue by constructing a 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 . Recently , Lundberg et al . ( 2017 ) has provided a 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 kernel-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 a primary interest in biological datasets . In this paper , we introduce an interpretable Genetics and mUltimodal Imaging based DEep neural network ( GUIDE ) , for whole-brain and whole-genome analysis . We use hierarchical graph convolutions that mimic an ontology based network of biological processes ( Mi et al. , 2013 ) . We use pooling to capture the information flow through the graph and graph attention to 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-genetics fusion in GUIDE achieve better classification accuracy than state-of-the-art baselines . More importantly , GUIDE can identify robust and clinically relevant biomarkers in both data domains . 3 A DEEP MULTIMODAL IMAGING-GENETICS FRAMEWORK . Fig . 1 illustrates our GUIDE framework . Inputs are the gene scores gn ∈ RG×1 for each subject n and the corresponding imaging features i1n ∈ RM1×1 and i2n ∈ RM2×1 obtained from two different acquisitions . The gene scores gn are obtained by grouping the original SNPs according to the nearest gene and aggregating the associated genetic risk weighted by GWAS effect size ( Ripke et al. , 2014 ) . The subject diagnosis ( phenotype ) yn ∈ { 0 , 1 } is known during training but is absent during testing . 3.1 GENETIC GRAPH EMBEDDING The top portion of Fig . 1 illustrates our attention-based graph convolution model for genetic embedding . The underlying graph is based on the gene ontological hierarchy ( Ashburner et al. , 2000 ) that effectively maps each gene to different biological processes . Mathematically , this ontology gives rise to a sparse matrix Ag ∈ { 0 , 1 } G×T , where G is the total number of genes , and T is the number of biological processes ( i.e. , nodes ) . Given this substrate , GUIDE first learns a projection of the gene scores gn onto T graph nodes . Each node signal is a d-dimensional feature vector , pn ( t ) ∈ R1×d . pn ( t ) = PReLU ( g T n ( Wt ⊗Ag [ : , t ] ) ) , ( 1 ) where each of the columns of the learned weight matrix Wt ∈ RG×d 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 a subset of input nodes connected to each hidden node . 3.2 GRAPH ATTENTION AND HIERARCHICAL POOLING In addition to grouping genes into biological processes , a standard ontology also specifies a hierarchical relationship between the biological processes themselves ( Alcocer-Cuarón et al. , 2014 ) . An example of this hierarchy is : generation of neurons→ neurogenesis→ nervous system development . We use a 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 a set of graph convolutional filters that act on each embedded node signal , and the second is a set of subject-specific attention weights that select the discriminative edges . Formally , let the binary matrix Ap ∈ RT×T capture the directed edges in the ontology . Our graph convolution at stage l is : pl+1n ( t ) = σ ∑ j∈Child ( t ) Eln ( t , j ) p l n ( j ) W l + βtp l n ( t ) Ws , ( 2 ) where pln ( t ) ∈ R1×dl is signal for node t at stage l , Wl ∈ Rdl×dl+1 is the convolutional filter between stages l and l + 1 , βt is the self-influence for node t , Ws ∈ Rdl×dl+1 is the convolution filter for self loop , and σ ( · ) 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 Eln ( t , j ) quantify the influence of the child node j over the parent node t at convolutional stage l. Unlike a standard graph convolutional network , in which the edge weights are fixed , we learn Eln ( t , j ) using a graph attention mechanism . Mathematically , we have Eln ( t , j ) = exp ( tanh ( [ pln ( t ) W l pln ( j ) W l ] · cl ) ) ∑ j∈Child ( t ) exp ( tanh ( [ p l n ( t ) W l pln ( j ) W l ] · cl ) ) ( 3 ) where cl is a fixed weight vector learned during training . We estimate the self influence variable as βt = σ ( pln ( t ) Ws · cls ) , where cls 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 ( e.g. , neurogenesis ) to a higher-level biological process ( e.g. , nervous system development ) . Thus , we remove the lowest ( leaf ) layer from the graph at each stage l and continue this process until we reach the root nodes . The genetic embedding ` gn ∈ RD×1 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 in this work contains two fMRI paradigms , leading to inputs i1n and i 2 n of each subject n. However , our framework naturally extends to an arbitrary number of modalities . From a Bayesian viewpoint , the problem of feature selection can be handled by introducing an unobserved binary random vector zmn of the same dimensionality as i m n and inferring its posterior probability distribution given the paired training dataset : D = { imn , yn } , where yn denotes the class label . By defining Im = [ im1 , . . . , i m n ] , Y = [ y1 , . . . , yn ] , and Z m = [ zm1 , . . . , z m n ] , we note that the desired posterior distribution p ( Zm|Im , Y ) is intractable . One strategy is to minimize the KL divergence between an approximate distribution q ( · ) and the true posterior distribution KL ( q ( Zm ) ||p ( Zm|Im , Y ) ) . Mathematically , this optimization can be written as argmin q ( · ) − Eq [ log ( p ( Y|Im , Zm ) ) ] +KL ( q ( Zm ) ||p ( Zm ) ) , ( 4 ) where p ( Zm ) is a prior over the latent masks . While Eq . ( 4 ) does not have a closed-form solution , it can be optimized via Monte Carlo integration by sampling the vectors zmn ∼ Bernoulli ( bm ) , where bm parameterizes the approximate distribution q ( · ) , 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 imn are masked according to z m n . In order to learn the probability maps b m during training , we replace the binary zmn with a continuous relaxation of the Bernoulli distribution : zmn = σ ( log ( bm ) − log ( 1− bm ) + log ( umn ) − log ( 1− umn ) r ) , ( 5 ) where umni is sampled from Uniform ( 0 , 1 ) , the parameter r controls the relaxation from the { 0 , 1 } Bernoulli , and the feature selection probabilities bm are learned during training ( see Section 3.4 ) . 3.4 MULTIMODAL FUSION AND MODEL REGULARIZATION As shown in Fig . 1 , the Bayesian feature selection step is followed by a cascade of fully connected layers , denoted Em ( · ) , to project each imaging modality m onto a low-dimensional latent embedding . Likewise , the genetic embedding ` gn is passed through a separate fully connected cascade Eg ( · ) and onto the same low-dimensional space . To leverage synergies between the imaging and genetics data , we fuse the latent embeddings across modalities to obtain a common representation : ` n = 1 Mn ( E1 ( i1n ⊗ z1n ) + E2 ( i2n ⊗ z2n ) + Eg ( ` gn ) ) , ( 6 ) where ⊗ is the Hadamard product used in the Bayesian feature selection step , ` gn = G-EMBED ( gn ) , where G-EMBED ( · ) represents the genetics network based on the ontological hierarchy , and Mn is the number of modalities present for subject n. Finally , the latent embedding ` n is input to a classification network to tie the learned biomarkers to patient/control phenotype . Notice that our fusion strategy encourages the latent embedding ` n for an 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-DECODE ) on ` gn . This operation unwraps the gene encoding via the same ontology Ashburner et al . ( 2000 ) . Likewise , the imaging regularizer decodes the original feature vectors from ` n via the artificial neural networks Dm ( · ) . Finally , the prior over zmn appears as the KL divergence between the learned distribution Ber ( b m ) and a binary random vector Ber ( s ) with small entries to enforce sparsity . Our loss function during training is : L ( i1 , i2 , g ) = − N∑ n=1 ( yn log ( ŷn ) + ( 1− yn ) log ( 1− ŷn ) ) + 2∑ m=1 KLM ( Ber ( b m ) ||Ber ( s ) ) + λI N1∑ n=1 ||i1n −D1 ( ` n ) ||22 + λI N2∑ n=1 ||i2n −D2 ( ` n ) ||22 + λG Ng∑ n=1 ||gn − G-DECODE ( ` gn ) ||22 ( 7 ) where ŷ is the class prediction , N is the total number of subjects , Nm is the number of subjects with modality m present , and the hyper-parameters { λI , λG } control the contributions of the data reconstruction errors . The function KLM ( ·||· ) in Eq . ( 7 ) averages the element-wise KL divergences across the input feature dimension , thus maintaining the scale of the prior term regardless of dimensionality . The first two terms of Eq . ( 7 ) 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 act as regularizers to ensure that the latent embedding is capturing the original data distribution . Training Strategy : As described in Section 4 , our dataset consists of 1848 subjects with only genetics data and an additional 208 subjects with both imaging and genetics 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 a 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 . We learn the Bayesian feature selection probabilities during training by sampling the random vectors z1n , z 2 n during each forward pass using Eq . ( 5 ) and using them to mask the inputs i 1 n , i 2 n for patient n. 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 ) to construct G-ENCODE . In total , this network encompasses 13595 biological processes organized from 2836 leaf nodes to 3276 root nodes . We perform a grid search over three order of magnitude and fix the hyperparameters λI = 3×10−3 , λG = 10−5 . We fix the signal dimensionality at d = 2 for the gene embedding and dl = 5 for the subsequent graph convolution and deconvolution operations based on the genetics-only subjects . Likewise , the non-linearity in Eq . ( 2 ) selected to be a LayerNorm , followed by PReLU and Dropout , once again using the genetics-only subjects . The Bernoulli prior over zm is set at s = 0.001 , which is consistent with Ghosal et al . ( 2021 ) . 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 PyTorch 3.7 . Training the full model takes roughly 17hrs on a 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 are optimized using a grid search . Parallel ICA + RF : We concatenate the imaging modalities to single vector in = [ i1 T n i 2T n ] T and perform parallel ICA ( p-ICA ) ( Pearlson et al. , 2015 ) with the gene scores gn . Since p-ICA can not handle missing modalities , we fit a multivariate regression model to impute a missing imaging modality from the available ones . Specifically , if in1 is absent , we impute it as : i n 1 = β i n 2 , where β is 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 = Sen and gn = Wfn where S , W are independent source matrices and the en , fn are loading vectors . We concatenate the loading matrices [ eTn , f T n ] and use it as the input feature vector for a random forest classifier . During training , we apply p-ICA to just the training data to estimate the sources { Strain , Wtrain } . We use these estimated sources to obtain the loading matrices for the test data as follows : itest = Straine and gtest = Wtrainf G-MIND : The G-MIND architecture by Ghosal et al . ( 2021 ) is designed for a 1242 genetics input . Thus , we introduce a fully-connected layer to project the high-dimensional gene scores gn onto a 1242 dimensional vector for input to G-MIND ( Ghosal et al. , 2021 ) . We evaluate both random weight initialization and pretraining the genetics branch of G-MIND with the 1848 genetics-only subjects . 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 . We optimize these networks architectures using repeated 10-fold cross validation outlined in Section 3.4 . 3.6 EVALUATION STRATEGY We conduct a comprehensive evaluation of our framework that includes influence of embedding a priori biological information , biomarker reproducibility , and classification performance . Influence of the Ontology-Based Hierarchy : In GUIDE we assume that processing the data according to an established gene ontology will extract more robust and discriminative biomarkers . To test this assumption , we compare our gene ontology network to random networks and to an unstructured model . The random networks contain the same number of nodes in each layer as the ontology-based 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 a fully-connected ANN with the same number of parameters , but no inherent structure between layers . As a 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 a weighted combination of the risk alleles for schizophrenia , as determined by a 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 ) on the 208 imaginggenetics subjects to quantify the performance . The models are trained using 8 folds , and the remaining two folds are reserved for validation and testing . We report accuracy , sensitivity , specificity , Area Under the ROC Curve ( AUROC ) , and Area Under the precision-recall 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 bm 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-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 the entry ‘ 1 ’ indicates that the feature is among the top-K. We compare the BFS features with Kernel SHAP ( Lundberg et al. , 2017 ) . The background values for K-SHAP are 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 an binary indicator vector . 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 the reproducibility of the top-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 . Discovering of Biological Pathways : The attention layer of G-ENCODE provides a subjectspecific 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 a 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 Data and Preprocessing : We evaluate GUIDE on a study of schizophrenia provided by Anonymous Institution that contains SNP data and two fMRI paradigms . Illumina Bead Chipset including 510K/ 610K/660K/2.5M is used for genotyping . Quality control and imputation were performed using PLINK and IMPUTE2 . The resulting 102K linkage disequilibrium independent ( r2 < 0.1 ) indexed SNPs are grouped to the nearest gene ( within 50kb basepairs ) ( Wong et al. , 2017 ) . The 13,908 dimensional input genes cores are computed as weighted average 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 . Imaging data include two task-fMRI paradigms commonly 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 ; res = 3.75 × 3.75 × 6/5 for N-back and SDMT , respectively ) . FMRI preprocessing includes slice timing correction , realignment , spatial normalization to MNI template , smoothing and motion regression . We use SPM 12 to generate contrast maps and the Brainnetome atlas ( Fan et al. , 2016 ) to define 246 cortical and subcortical regions . The inputs i1n , i 2 n correspond to the average contrast over voxels in the respective region . Additional details are reported in Appendix A.2 In total , our dataset contains 1848 subjects ( 792 schizophrenia , 1056 control ) with just SNP data and 208 subjects with imaging and SNP data , divided as 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 hierarchy 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 a 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-inspired architecture can extract robust and predictive genetic biomarkers of a disorder . Classification Performance : Table 1 reports the 10-fold CV testing performance of all the methods on the multimodal imaging-genetics dataset ; we 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 gn and low sample size . Pretraining on a separate genetics dataset improves the AUC of G-MIND , highlighting the benefits of increased data . The multimodal fusion of GUIDE achieves the best performance over the baselines and singlemodality evaluations . This can be attributed to the hierarchical information flow through the ontology graph and the synergy between the imaging and genetics information . Thus , our biologically inspired neural network can extract predictive features from whole-brain and whole-genome data . Reproducibility of BFS Features : Fig . 3 illustrates 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 illustrates 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 illustrates the consistent imaging features that are selected by our method across the folds for K = 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 a reverse-inference procedure to select a set of “ cognitive terms ” associated with a set of input coordinates based on how frequently similar patterns have been observed across the fMRI literature . Fig . 5 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 to the fMRI tasks . 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. , 2008 ) and apply a k-means clustering algorithm . Fig . 6 shows 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 to extract discriminative biological information about neuropsychiatric disorders .

Summary: 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.