Optimizing differential identifiability improves connectome predictive modeling of cognitive deficits from functional connectivity in Alzheimer's disease

Abstract Functional connectivity, as estimated using resting state functional MRI, has shown potential in bridging the gap between pathophysiology and cognition. However, clinical use of functional connectivity biomarkers is impeded by unreliable estimates of individual functional connectomes and lack of generalizability of models predicting cognitive outcomes from connectivity. To address these issues, we combine the frameworks of connectome predictive modeling and differential identifiability. Using the combined framework, we show that enhancing the individual fingerprint of resting state functional connectomes leads to robust identification of functional networks associated to cognitive outcomes and also improves prediction of cognitive outcomes from functional connectomes. Using a comprehensive spectrum of cognitive outcomes associated to Alzheimer's disease (AD), we identify and characterize functional networks associated to specific cognitive deficits exhibited in AD. This combined framework is an important step in making individual level predictions of cognition from resting state functional connectomes and in understanding the relationship between cognition and connectivity.


| INTRODUCTION
The biological underpinnings of all neurodegenerative disorders remain poorly understood, contributing significantly to the bottleneck in treating these disorders (Montague, Dolan, Friston, & Dayan, 2012).
In recent years, the application of analyses based on complex systems approaches for understanding how neural activity and connectivity facilitate cognition has led to significant strides in characterizing these disorders (Fornito & Bullmore, 2015;Fornito, Zalesky, & Breakspear, 2015). One such approach, functional brain connectomics, models functional brain networks as pairwise statistical dependencies in regional neural activity. This provides a framework to assess critical aspects of the brain, such as integration and segregation (Sporns, 2013), and ultimately communication (Avena-Koenigsberger, Misic, & Sporns, 2017;Bullmore & Sporns, 2009). At the same time, the advent of functional MRI (fMRI) has allowed for in-vivo characterization of whole brain functional connectomes (FC) in humans (Bullmore & Sporns, 2009), leading to the discovery of several critical brain networks implicated in schizophrenia, attention deficit hyperactivity disorder, autism, and Alzheimer's disease (AD) (Fornito & Bullmore, 2015).
Despite their potential to enhance our understanding of neurologic disorders, approaches based on functional connectivity have not yet been used translationally in the treatment of cognitive and behavioral disorders (Yahata, Kasai, & Kawato, 2017;Yamada et al., 2017).
To advance the treatment of such disorders, there is a critical need to develop clinical biomarkers that are (a) robustly modulated by disease mechanisms and (b) specifically associated with disease related outcomes (Yamada et al., 2017). Though functional connectivity has shown potential in bridging the gap between pathophysiology and cognition, its clinical use is impeded by unreliable estimation of subject level FC (Braun et al., 2012), lack of precision in inter-subject differentiability in FC (Noble et al., 2017), and lack of generalizability of models predicting subject-level cognitive outcomes from FC (Yamada et al., 2017). Here we show that improving the subject level fingerprint of resting-state FC also improves prediction of a heterogeneous set of cognitive deficits in AD, both in new data from the training cohort as well as data from a validation cohort. We also identify functional networks associated to specific cognitive deficits exhibited in AD.
1.1 | Toward improving clinical utility of FC While FC shows differential group level associations across cognitive outcomes (Amico, Arenas, & Goni, 2019;Amico & Goñi, 2018) and across disease conditions (Badhwar et al., 2017;Brier, Thomas, & Ances, 2014;Contreras et al., 2017;Fornito & Bullmore, 2015;Svaldi et al., 2018), it falls short of predicting clinically meaningful outcomes at the individual level. The reason for this, is insufficient "fingerprint" or within-subject reliability and betweensubject differentiability to capture individual differences that may be related to cognition or behavior (Amico & Goñi, 2018;Finn et al., 2015;Mars, Passingham, & Jbabdi, 2018;Pallares et al., 2018;Satterthwaite, Xia, & Bassett, 2018;Seitzman et al., 2019). In terms of reliability of FC, it has been shown that reasonable reliability can be achieved with sufficient scan length and that this reliability can be improved when multiple sessions of FC are used (Birn et al., 2013;Noble et al., 2017;. Studies have also shown that FC reliability is different across the brain, with larger cortical nodes displaying the most reliability and within network connections exhibiting greater reliability than between network connections (Noble et al., 2017). Several studies have also shown that frequently used 6 min fMRI acquisitions do not have adequate reliability at the edge level, posing significant issues on numerous available clinical fMRI datasets when performing subject level associations. In terms of inter-subject differentiability, recent efforts have shown that individuals can be reasonably distinguished from each other using FC, as measured by identification rate (Amico & Goñi, 2018;Finn et al., 2015Finn et al., , 2017, perfect separability rate (Finn et al., 2015Noble et al., 2017), or differential identifiability (Amico & Goñi, 2018). Furthermore, it has been shown that individual level fingerprinting improves with longer scan length (Amico & Goñi, 2018;Noble et al., 2017) and when subjects are performing specific tasks . Finally, there is evidence that FC fingerprint is reduced in individuals with neurologic or psychiatric conditions (Kaufmann et al., 2017(Kaufmann et al., , 2018Svaldi et al., 2018), making association of FC with disease related phenotypes more difficult.
Evidence for fingerprint in FC has opened the door for efforts to improve prediction of cognition and behavior from FC Shen et al., 2017;Yahata et al., 2017;Yamada et al., 2017;Yoo et al., 2018). Predictive pipelines typically involve: (a) feature reduction to find FC features that are associated with specific cognitive outcomes, (b) training of a predictive model using these features to predict cognitive outcomes, and (c) evaluation of the accuracy and generalizability of resulting models on external data. It has been demonstrated that using multiple connectomes across sessions or connectomes from different tasks improves predictive power (Gao, Greene, Constable, & Scheinost, 2019). However, how test/retest reliability of FC features affects their contribution to predicting cognition or behavior is still under debate. One study found no association between the test/retest reliability of a given functional edge and the predictive value of the edge in external data (Noble et al., 2017). However, another study (Amico & Goñi, 2018) showed increased prediction accuracy when edges were chosen based on correlation to cognitive outcome and test/retest reliability, after using PCA to optimize differential identifiability to uncover FC fingerprints.
Though strategies such as increased scan length, multiple acquisitions and adding task-based fMRI may be useful for improving prediction of relevant outcomes, they may not be feasible in clinical settings.
Reasons include the associated cost of increased scan time, diminished tolerance in patient populations to long scan times, and impaired ability of patients in performing tasks. Additionally, there are numerous available datasets (Abbas et al., 2015;Amico et al., 2017;Contreras et al., 2017;Petersen et al., 2010;Xiao et al., 2017) with acquisition protocols that do not have adequate reliability (Noble et al., 2017) for subject level prediction. Finally, prediction of cognitive outcomes in neurologic and psychiatric populations remains a challenge as these subjects appear to have a reduced fingerprint (Kaufmann et al., 2017(Kaufmann et al., , 2018. To address such issues, Amico and Goñi proposed the differential identifiability framework (fÞ (Amico & Goñi, 2018), which is a principal component analysis (PCA) based denoising algorithm to uncover fingerprints in FC and improve betweensubject differentiability at the same time. Using data from 100 unrelated subjects in the Human Connectome Project, they demonstrated improvements in FC fingerprint beyond what could be achieved by increasing scan length (Amico & Goñi, 2018). This improvement was also observed in FC data from the Alzheimer's Disease Neuroimaging Initiative (ADNI), a dataset with more traditional acquisition consisting of 140 volumes (7 min scan) split in half to mimic a test/retest setting (Svaldi et al., 2018). Thus, the f framework demonstrated improvements in fingerprinting in a "traditional" acquisition performed on a clinical population. However, there is still conflicting evidence on whether increasing FC fingerprint subsequently improves prediction of clinically relevant outcomes. It is important to note that the abovementioned studies specifically assessed whether the test/retest reliability of a functional edge affected the predictive value of that edge in external subjects. Hence, two important questions remain open (a) the level of agreement in feature selection between test and retest data from the same subjects and (b) whether a model built on test data would generalize to re-test data from the same subjects. These two questions are critical, since good performance of predictive models in a test/retest setting is a minimum standard that should be met before testing on external data. Lack of agreement in feature selection between test and retest data indicates a model that overfits the training data and is not generalizable, even to a new session of the same training subjects. Even if this model is somewhat generalizable to external subjects, if it lacks test-retest agreement in feature selection, the model is likely overparametrized and selecting arbitrary features.
In this work, we test the effect of the differential f on key properties of models predicting cognitive outcomes related to AD from FC data. We assess performance of the models in both a test/retest setting and in generalization to validation data. When choosing key properties to assess the quality of predictive models for the purposes of predicting and understanding cognitive associations to the brain, it is important to keep in mind that interpretation of anatomical locations of the cognitive correlates of FC are as relevant as the accuracy of prediction. Hence, confirming robustness in the identification of FC features should precede model fitting and assessments of model accuracy. Further, it is important to note that the robustness of both feature selection and coefficient estimation can significantly influence model accuracy and generalizability. Therefore, we propose to evaluate three critical properties for well-behaved FC-based predictive models: (a) stability of feature selection in a test/retest setting, (b) specificity of edge selection, and (c) generalizability of the prediction to new data from the same subjects and to validation data.

| Opportunities in AD
We chose to evaluate these effects in data from the ADNI2, which consists of subjects spanning the AD spectrum. The heterogeneous, gradual progression of cognitive deficits in AD is particularly amenable to study the quality of models predicting cognition from FC. Briefly, in the stage of mild cognitive impairment (MCI) subjects typically manifest episodic memory decline, which is later accompanied by subtle deficits in other domains, and ultimately results in progressive functional impairment as the subject transitions through the mild, moderate and severe stages of dementia (Aggarwal, Wilson, Beck, Bienias, & Bennett, 2005;Cloutier, Chertkow, Kergoat, Gauthier, & Belleville, 2015;Lambon Ralph, Patterson, Graham, Dawson, & Hodges, 2003;Zhao et al., 2014). Within the AD spectrum there is much individual heterogeneity in terms of disease presentation and progression over time (Lambon Ralph et al., 2003), making predictive modeling at the subject level important.
The association between FC changes and cognitive deficits in AD has been subject of intense study to date (Contreras et al., 2017;Wook Yoo et al., 2015;Zhan et al., 2016). Changes in functional networks, primarily the default mode and frontoparietal networks, have been consistently replicated between diagnostic groups (Buckner et al., 2005Seeley, Crawford, Zhou, Miller, & Greicius, 2009).
Recent studies indicate that FC data can predict subject level diagnostic status (Vogel et al., 2018) and global cognitive decline (Lin et al., 2018) with reasonable accuracy. Several studies also show relationships between FC data and deficits in specific cognitive domains associated with AD (Contreras et al., 2017;Duchek et al., 2013;Zhan et al., 2016).
In this work, beyond assessing group level associations to specific cognitive domains or individual level prediction of cognitive status (impaired vs. non-impaired), we present a framework that improves the ability of FC to predict subject level deficits from different cognitive domains. This additionally enables us to assess which RSNs are globally associated to cognition in AD versus RSNs associated to specific deficits observed in AD. In this work, resting state fMRI and neurocognitive testing data from the second phase of the ADNI2/GO were used. Our analyses included 82 participants from the original 164 ADNI2/GO individuals with resting state fMRI scans. Subjects were excluded if (a) their amyloid status was not available, (b) they were cognitively impaired, but showed no evidence of amyloid-beta (Aß) deposition, and/or (c) they had over 30% of fMRI time points censored due to artifacts or head motion (see Section 2.2 for details). Aß status was determined using either mean PET Florbetapir standard uptake value ratio cutoff (Florbetapir >1.1; UC Berkeley) or CSF Aß level ≤ 192 pg/ml [5]. The rationale for excluding Aß-cognitively impaired participants was to ensure that all impaired subjects had underlying AD pathology, in an attempt to keep the pathological substrates of cognitive impairment as homogenous as possible in the sample.
Subjects were stratified into five categories based on their diagnosis and Aß status (Table 1)

| fMRI data processing
We used T1-weighted MPRAGE scans and EPI fMRI scans from the initial visit in ADNI2/GO (Philips Platforms, TR/TE = 3000/30 ms, 140 volumes, 3.3 mm thickness, see www.adni-info.org for detailed protocols) for estimation of whole-brain FCs. fMRI scans were processed with an in-house MATLAB and FSL based pipeline . This For purposes of evaluating reproducibility, we split the processed fMRI time series into halves (mimicking test and retest) and assigned each half for each subject as "restA" or "restB" randomly to avoid biases related to first versus second half of the scan. We obtained two FC matrices from the restA and restB halves of the fMRI time-series for each subject. FC nodes were defined using a 278 region parcellation (Shen, Tokoglu, Papademetris, & Constable, 2013), as previously detailed , with a modified more fine grained subcortical parcellation (Mawlawi et al., 2001), for a total of 286 Gy matter regions. We estimated single session FC matrices by calculating the Pearson correlation coefficient (K. Pearson, 1901)

| Differential f
We applied f which uses group level PCA (Hotelling, 1933) to find the optimal FC reconstruction point for simultaneous optimization of restA and restB FC reproducibility and between-subject differentiability, measured using differential identifiability (I diff , Figure 1) (Amico & Goñi, 2018). This section describes the general steps in the framework, while the cohorts on which the data was applied are described in Section 2.4. In this framework, the "identifiability matrix" I is defined as the matrix of pairwise correlations (square, non-symmetric) between the subjects' FC restA and FC restB . The dimension of I is N 2 where N is the number of subjects in the cohort. Self-identifiability, (I self , Equation 1), is defined as the average of the main diagonal elements of I, consisting of correlations between FC restA and FC restB from the same subjects. I others (Equation 2), is defined as average of the off-diagonal elements of matrix I, consisting of correlations between FC restA and FC restB of different subjects. Differential identifiability (I diff , Equation 3) is defined as the difference between I self and I others .
Group level PCA is then applied in the FC domain, on a data matrix (Figure 1a Finally, an external evaluation of the performance of these models was carried out using the validation cohort. Such evaluation was done by comparing the performance of models built/tested on original FCs (reconstructed using the full range of PCs) to the performance of models built/tested on FCs optimally reconstructed for I diff (see Section 2.5 last paragraph).
2.5 | Assessment of differential identifiability pipeline on connectome predictive modeling  2.6 | Effect of pre-processing on f-CPM workflow As a supplementary analysis, we split the timeseries prior to preprocessing for evaluation of the effect of splitting data prior to versus after pre-processing on the f -CPM workflow. We were not able to implement the splitting of the time series directly in half prior to preprocessing as such change greatly compromised the resulting FC, as expected, due to the short scanning length (7 min). Thus, we followed previously proposed guidelines (Horien et al., 2018) and split the time series by taking interleaved time points (as if TR = 6 s). We then repeated the entire scheme described above on connectomes generated from time series split prior to pre-processing. As such we generated f-CPM workflow results using two different approaches: (1) by processing the entire timeseries then splitting the pre-processed time series in half and (2) by splitting the timeseries in an interleaved fashion then pre-processing the split time series separately.
To test the effect of pre-processing on the FC matrices, we performed pairwise correlations on restA-restB averaged matrices from (1) versus (2) ( Figure S9a). This allowed us to compare how similar restA and restB connectomes when generated using (1) versus (2).
We also performed a permutation test (α = .05, 1,000 permutations) on the I self values in the main diagonal of the original I matrices (average across 1,000 repetitions) generated for (1) versus (2). This allowed us to test whether splitting the data prior to pre-processing versus splitting the data after pre-processing affected the initial similarity between restA FCs and restB FCs from the same subjects ( Figure 3 vs. S9b). To elaborate on the effect of pre-processing on the entire f -CPM workflow, we report qualitative comparisons of the behavior across the range of PCs of f, edge selection, and model generalizability in CPM for (1) versus (2) (Figures 4-6 vs. S9c-f).

| Association of resting-state networks to cognitive outcomes
Final masks for each outcome measure were defined by edges that appeared in at least 95% of the 1,000 repetitions. We used binomial tests (α = .05, uncorrected) for each outcome measure to assess whether specific RSNs (e.g., DMN-DMN), or their interactions (e.g., DMN-FP), were overrepresented in these masks beyond what could be expected from an equal number of edges chosen at random.  (Figures 3 and S1). Such increase in whole-brain differential identifiability also increased the fingerprint at the functional edge level, as shown when using mean ICC ( Figure S2).

| Training data: Test-retest generalizability
At the model fitting step, the performance of models built on restA data was evaluated on restA and restB FCs from the same subjects.
For restA connectomes, on which the models were built, correlation between the predicted and estimated outcomes increased as the number of PCs increased, though at a slower rate after the optimal reconstruction point for I diff (Figure 5 left). In contrast, correlation between the predicted and estimated outcomes peaked at the optimal reconstruction point for I diff in the training data (41 PCs

| DISCUSSION
Our work provides a comprehensive whole brain and whole cognitive spectrum view on the relationship between resting-state functional connectivity and cognition in AD and makes progress toward making subject level predictions of cognition from FC biomarkers. We accomplished that by improving the robustness of connectome predictive models of AD using f , which improved test/retest generalizability of these models and allowed for significantly improved predictions of cognition from external FC data for all seven outcomes evaluated.
Finally, robust edge selection allowed for identification of RSN motifs associated with cognitive deficits in AD.

| Differential identifiability
The use of FC as a biomarker in clinical settings requires major advancements in subject level identifiability of FC. In this work, we improve subject level FC identifiability, as measured using differential input data is twice the number of subjects (due to inclusion of test and retest data), the subject dimensionality of the data is the cutoff for a more accurate representation of individual FC, when considering small-moderate sample sizes. Additionally, we observe a very sharp drop-off after the peak in I diff as was also observed by (Amico & Goñi, 2018) when f was performed on FCs generated from split time series. Finally, as shown previously (Amico & Goñi, 2018), optimizing I diff , a coarse whole brain measure (Figure 3 blue line showing I diff and Figure S1), also robustly increased test-retest reliability at the level of individual edges ( Figure S2). Optimally reconstructed FCs retained 80% of the variance in the from the original FC data (Figure 3 black dashed line), indicating that around 20% of variance present in original FC estimates is not representative of robust individual characteristics, despite the extensive preprocessing of BOLD time series used here and described in detail in . It is important to note that splitting an fMRI session mimics the most ideal test-retest scenario where all conditions are maintained as homogenously as possible, including scan conditions, mental state, and motion artifacts. Therefore, we would hypothesize self-identifiability for these subjects to be very high even for original FCs reconstructed using the full range of PCs. However, the average I self for original FCs is only 60%, in comparison to 81% for optimally reconstructed FCs. Thus, using the f framework allows us to obtain two "quality" individual FC reconstructions from the same acquisition where we previously obtained one. Finally, we observed that the optimal I diff for this dataset is much higher than what we saw in previous data where I diff was optimized by splitting the resting state time series in half (Amico & Goñi, 2018). We speculate that these more dramatic improvements indicate that datasets with coarse temporal acquisition or datasets including clinical populations may benefit to a greater degree from this group level PCA cleaning technique in order to improve individual level estimates of FC. However, this remains to be confirmed in additional similar datasets and across clinical diseases.

| Effect of differential identifiability on connectome predictive modeling
When assessing clinical populations with CPM, one of the ultimate goals is to identify critical functional subcircuits associated with specific cognitive deficits. Therefore, a minimum criterion that must be met is that edge selection should be robust between test/retest data (e.g., fMRI runs or sessions) from the same subjects. Thus, we took advantage of previous splitting of fMRI data into restA and restB for purposes of uncovering connectome fingerprinting to compare edge selection performed separately on for restA versus restB FCs. Using f , we were able to improve the robustness of CPM in identifying functional subcircuits associated to specific cognitive deficits. Stability of edge selection displayed an optimal regime (12-41 PCs), after which it exponentially worsened for all outcome measures (Figure 4; see colored lines). Overlap between restA and restB edge selection (Figure 4) for optimally reconstructed data increased by an average of 30% from raw data, with an average peak overlap of 65% across outcome measures.
f did not affect the relative specificity in edge selection across outcome measures (Figure 4, black lines). Frobenius norm between outcomes remained constant around 40 and mask overlap remained constant at around 30%. This implies that the "distance" between mappings of different outcomes is preserved across PCs whereas the distance between restA-restB mappings for a single outcome is reduced as we move from original FCs to optimally reconstructed FCs (1/2 total number of PCs). It is noteworthy that for original FCs In addition to improving robustness of edge selection, we also modestly improved prediction of cognitive and behavioral outcomes in new FC data from the same subjects using f . More importantly, the addition of a test/restest validation step to CPM showed that reconstructing FC at the optimal point for I diff reduces overfitting to the training data as evidenced by a continued increase in model performance after 41 PCs for restA data from Training subjects versus a decrease after 41 PC for restB data. However, as optimally reconstructed restA and restB FCs come from the same orthogonal bases, it could be argued that their independence is further reduced upon implementation of the f , thus the improved prediction. By taking advantage of having two good quality FCs for each subject at the optimal reconstruction point, we showed that optimal reconstruction of FC significantly improved the generalization of models from the training cohorts to the validation cohorts for 5/7 the cognitive outcomes ( Figure 6), although variable performance was observed across repetitions. Note that the differential identifiability pipeline was run separately on the training and validation cohorts at each repetition, thus fully maintaining the independence of training data and validation data.
We showed that splitting the timeseries prior to pre-processing did not significantly affect the impact of f on CPM ( Figure S9). Splitting the time after pre-processing versus before pre-processing produced similar FCs, though there was variability in subject-wise FC similarity using the two approaches ( Figure S9a). Similarity between restA and restB connectomes from the same subjects, as measured by I self , was not significantly different between the two pre-processing approaches (Figure 3 vs. S9b). Similarly, f affected CPM equivalently for both pre-processing approaches (Figures 4-6 vs. S9c-e). This indicates that the effects of f on CPM are robust to separate preprocessing. However, testing of the effect of f on CPM when splitting the timeseries directly in half or when using FCs generated from two independent sessions, still needs to be directly assessed.

| Association of resting state networks to cognitive outcomes
Previous literature making predictions from ADNI fMRI data focused solely on prediction of global cognitive status (Lin et al., 2018) or diagnostic status (Dadi et al., 2019). In contrast, we assessed the involve-

Associations of within RSN interactions and cognitive function
showed strong coherence to previous literature regarding the roles of RSNs in cognition and AD. We found within SAL network connectivity to be predictive of performance in immediate recall. This association is anatomically coherent as the primary role of the SAL network is in detecting salient stimuli (in this case words being spoken) and recruitment other networks to integrate these stimuli (Peters, Dunlop, & Downar, 2016). Disruption of the salience network has been found in MCI subjects in a previous study (Chand, Wu, Hajjar, & Qiu, 2017). Additionally, we found within VIS connectivity to be predictive of performance in the Boston Naming task. The involvement of the visual system in this task is obvious as it consists of confrontational word retrieval from pictures (Kaplan, Goodlass, & Weintraub, 1983). We found within network EC connectivity to be predictive of performance in MOCA and Trail Making B, both of which contain a significant executive functioning component (Arbuthnott & Frank, 2000;Nasreddine et al., 2005). The EC network is known to play a role in working memory and in the organization of goal oriented behavior (Mansouri, Rosa, & Atapour, 2015).  (Chand et al., 2017). We also identified that interactions between the VIS network and other RSNs were consistently associated with tasks that required item generation in the context of verbal memory retrieval (i.e., AVLT immediate and delayed recall, Boston Naming Test) or spontaneous generation of items belonging to a given category (i.e., animal fluency). This finding suggests an interactive role of the visual system with other functional subcircuits when executing tasks requiring semantic organization and imagery. This role of the visual system is supported by other studies identifying activation of the visual cortex and cognitive networks in imagery and semantic association tasks (Cattaneo, Vecchi, Pascual-Leone, & Silvanto, 2009;J. Pearson, Naselaris, Holmes, & Kosslyn, 2015). Additionally, the visual cortex has also been implicated in visual short term memory and working memory (Cattaneo et al., 2009). Furthermore, in AD, connectivity of the visual system has been previously associated to neurofibrillary tangle deposition (Jones et al., 2016) and with cognitive complaints in cognitively normal or MCI subjects (Contreras et al., 2017). We identified interactions of the SM network with the EC network in the Clock Drawing task, reflecting the need for organizational planning of movement associated with the task. The involvement of these networks in the clock drawing task was also found in previous fMRI experiments using the clock drawing task on healthy aging subjects (Talwar et al., 2019).
We furthermore consistently saw a significant role of cerebellar connectivity in tasks with significant motor components. Intra-cerebellar network connectivity in Trail Making B and between network cerebellar connections were associated with performance on Trail Making B as well as MOCA (Note: the Trail Making B task is a subset of the MOCA battery) (Nasreddine et al., 2005).
Overall, findings of RSN associations consistent with previously reported roles of these RSNs in cognition and AD indicates that our unified framework not only produces robust prediction, but also produces anatomically coherent mapping of cognitive deficits to resting state functional connectivity. In depth analysis of whole brain associations between FC and cognition furthers the understanding of how changes in FC impact cognition in AD.

| Limitations and future work
The unified identifiability-CPM framework proposed here provides many opportunities for improving the clinical utility of FC. However, an important and necessary step to improve the clinical utility of FC is to evaluate results obtained using this unified framework on a completely external dataset such as ADNI3, which includes similar acquisition from different scanner types. This will require the estimation of final hyper parameters from the ensemble of those estimated here using the entire ADNI2 cohort and the edges appearing in the final masks. In addition to external validation of the framework, our results indicate that there are other opportunities to improve both edge selection and predictive capability of FC. Despite showing significant improvement in robustness of edge selection using our framework, we were still under 80% test/retest overlap in edge selection for all outcome measures. Edge selection may potentially be improved by taking into account the network relationship between edges, as opposed to using edgewise correlation with thresholding which treats edges as univariate independent entities. This has been previously done using methods such as partial least squares regression . One could also incorporate concepts from the Network Based Statistics framework to control for spurious, small connected components (Zalesky, Fornito, & Bullmore, 2010). Controlling for such components would allow the edge selection step to be thought of as the identification of the functional subcircuits associated with a given outcome, enabling the use of network science measurements (Avena-Koenigsberger et al., 2017;Bullmore & Sporns, 2009;Sporns, 2013) which may provide additional predictive power and provide further insight into the mechanisms of cognition and behavior. Thus, incorporating such methodologies may provide additional improvements in prediction to those shown here. As within and between network connections tend to have different properties (Noble et al., 2017), another avenue to test could be estimating separate masks and coefficients for within and between RSN connections. Finally, CPM may also prove useful in predicting change in cognitive outcomes over time (Pena-Nogales et al., 2018), thus assessing the effect of differential identifiability on connectome predictive of longitudinal outcomes in AD would be a worthy contribution toward improving FC utility as a clinical biomarker.

| CONCLUSIONS
Our framework improved the robustness of individual level prediction of cognition from FC, which is the first step toward clinical use of FC and better understanding of how functional connectivity supports cognition in AD. We showed that the joint framework of differential identifiability with connectome predictive modeling improves the quality of models obtained from CPM in terms of stability of edge selection, test/retest generalizability, and generalizability to external data. Additionally, we showed that the use of two FC sessions from each subject provides a unique perspective when assessing and validating connectome predictive models. Finally, improving the robustness of edge selection allowed for reliable assessment of the associations between functional connectivity and cognitive deficits in AD. Our findings indicate both specific and global associations of resting state functional connectivity with cognitive deficits in AD which are consistent with previous literature regarding the roles resting state networks play in both cognition and AD.