Synthesis of Ovarian Cancer Multi-Omics Datasets: A Biology-Informed Evaluation Framework

Déborah Boyenval; Alina Malyutina; Jaana Oikkonen; Sammeli Liikkanen; Sampsa Hautaniemi

Figure 4: Generation from the prior in a standard VAE and the three adaptations. (a) The VAE samples

z\sim p(z)

, then

x\sim p_{\theta}(x\mid z)

. (b) ISOMERIC samples independent

z

and

w

,

w

contributes to both profiles and

z

only to RNA. (c) TMO-Net decodes CNV from

z_{C}

, then uses the generated CNV to parameterize and sample

z_{X}=z_{C\rightarrow R}

before decoding RNA. (d) CustOmics decodes one central

z

into two representations, one for each modality, and then into RNA and CNV. White circles denote sampled Gaussian latents, the shaded circle denotes a sampled observation, and boxes denote deterministic decoder outputs. Arrows denote computational dependence rather than causality.

Figure 5: Training architectures: (a) ISOMERIC, (b) TMO-Net, and (c) CustOmics. Observed RNA and CNV profiles are denoted by

r

and

c

, hats denote reconstructions. Green boxes denote Gaussian approximate posteriors and circles denote reparameterized samples. Solid arrows show forward computations, orange dashed arrows show objective terms. See Section 2 for model definitions.

Gene	Real held-out	Model	Synthetic	Bias	Absolute error
FOLR1	$0.108\pm 0.041$	TMO-Net	$0.051\pm 0.030$	$-0.057\pm 0.059$	$0.059\pm 0.056$
		ISOMERIC	$0.003\pm 0.002$	$-0.105\pm 0.040$	$0.105\pm 0.040$
		CustOmics	$0.015\pm 0.010$	$-0.092\pm 0.045$	$0.092\pm 0.045$
ERBB2	$0.068\pm 0.019$	TMO-Net	$0.030\pm 0.018$	$-0.037\pm 0.035$	$0.039\pm 0.033$
		ISOMERIC	$0.001\pm 0.000$	$-0.067\pm 0.019$	$0.067\pm 0.019$
		CustOmics	$0.001\pm 0.001$	$-0.067\pm 0.018$	$0.067\pm 0.018$

Appendix

Table 4: Biomarker-level amplification G-scores for the before-treatment primary cohort. All 14 prespecified biomarkers are reported. Values are means

\pm

sample SD across three patient-disjoint outer folds. Within each fold, synthetic scores, signed biases, and absolute errors are averaged over three initializations, absolute errors are computed before averaging. Bias is synthetic minus held-out real G-score, positive values indicate overestimation. G-scores summarize event frequency and amplitude, so errors are in G-score units, not frequency percentage points. Lower absolute error indicates closer agreement.

Gene	Real held-out	Model	Synthetic	Bias	Absolute error
FOLR1	$0.009\pm 0.015$	TMO-Net	$0.001\pm 0.001$	$-0.008\pm 0.015$	$0.009\pm 0.014$
		ISOMERIC	$0.000\pm 0.000$	$-0.009\pm 0.015$	$0.009\pm 0.015$
		CustOmics	$0.000\pm 0.000$	$-0.009\pm 0.015$	$0.009\pm 0.015$
ERBB2	$0.205\pm 0.033$	TMO-Net	$0.192\pm 0.065$	$-0.013\pm 0.099$	$0.070\pm 0.051$
		ISOMERIC	$0.042\pm 0.033$	$-0.164\pm 0.059$	$0.164\pm 0.059$
		CustOmics	$0.105\pm 0.036$	$-0.100\pm 0.046$	$0.102\pm 0.043$

Appendix

Table 5: Biomarker-level deletion G-scores for the before-treatment primary cohort. All 14 prespecified biomarkers are reported. Values are means

\pm

sample SD across three patient-disjoint outer folds. Within each fold, synthetic scores, signed biases, and absolute errors are averaged over three initializations, absolute errors are computed before averaging. Bias is synthetic minus held-out real G-score, positive values indicate overestimation. G-scores summarize event frequency and amplitude, so errors are in G-score units, not frequency percentage points. Lower absolute error indicates closer agreement.

Gene	Real held-out	Model	Synthetic	Bias	Absolute error
FOLR1	$0.115\pm 0.062$	TMO-Net	$0.066\pm 0.023$	$-0.049\pm 0.084$	$0.069\pm 0.062$
		ISOMERIC	$0.019\pm 0.024$	$-0.096\pm 0.083$	$0.096\pm 0.083$
		CustOmics	$0.023\pm 0.029$	$-0.092\pm 0.086$	$0.095\pm 0.081$
ERBB2	$0.042\pm 0.044$	TMO-Net	$0.004\pm 0.004$	$-0.038\pm 0.048$	$0.044\pm 0.040$
		ISOMERIC	$0.000\pm 0.000$	$-0.042\pm 0.044$	$0.042\pm 0.044$
		CustOmics	$0.000\pm 0.000$	$-0.042\pm 0.044$	$0.042\pm 0.044$

Appendix

Table 6: Biomarker-level amplification G-scores for the after-treatment cohort. All 14 prespecified biomarkers are reported. Values are means

\pm

sample SD across three patient-disjoint outer folds. Within each fold, synthetic scores, signed biases, and absolute errors are averaged over three initializations, absolute errors are computed before averaging. Bias is synthetic minus held-out real G-score, positive values indicate overestimation. G-scores summarize event frequency and amplitude, so errors are in G-score units, not frequency percentage points. Lower absolute error indicates closer agreement.

Gene	Real held-out	Model	Synthetic	Bias	Absolute error
FOLR1	$0.006\pm 0.010$	TMO-Net	$0.004\pm 0.004$	$-0.002\pm 0.013$	$0.009\pm 0.007$
		ISOMERIC	$0.001\pm 0.002$	$-0.005\pm 0.011$	$0.006\pm 0.009$
		CustOmics	$0.001\pm 0.002$	$-0.004\pm 0.008$	$0.004\pm 0.008$
ERBB2	$0.153\pm 0.009$	TMO-Net	$0.088\pm 0.018$	$-0.065\pm 0.027$	$0.065\pm 0.027$
		ISOMERIC	$0.026\pm 0.020$	$-0.127\pm 0.027$	$0.127\pm 0.027$
		CustOmics	$0.059\pm 0.034$	$-0.094\pm 0.041$	$0.094\pm 0.041$

Appendix

Table 7: Biomarker-level deletion G-scores for the after-treatment cohort. All 14 prespecified biomarkers are reported. Values are means

\pm

sample SD across three patient-disjoint outer folds. Within each fold, synthetic scores, signed biases, and absolute errors are averaged over three initializations, absolute errors are computed before averaging. Bias is synthetic minus held-out real G-score, positive values indicate overestimation. G-scores summarize event frequency and amplitude, so errors are in G-score units, not frequency percentage points. Lower absolute error indicates closer agreement.

Metric	$A-B$	$\Delta_{0}$	$\Delta_{1}$	$\Delta_{2}$	Mean
RNA fidelity
Mean gene-wise $W_{1}$ $\downarrow$	T–I	$-0.0069$	$-0.0339$	$-0.0118$	$-0.0175$
	T–C	$+0.0142$	$-0.0242$	$-0.0474$	$-0.0191$
	I–C	$+0.0211$	$+0.0097$	$-0.0356$	$-0.0016$
Mean Jensen–Shannon distance $\downarrow$	T–I	$-0.0075$	$-0.0164$	$-0.0053$	$-0.0097$
	T–C	$+0.0038$	$-0.0096$	$-0.0180$	$-0.0079$

Appendix

Table 14: Before-treatment paired model differences. T: TMO-Net, I: ISOMERIC, C: CustOmics. Each contrast is the first model minus the second after averaging three training seeds within fold. Arrows indicate preferred directions or targets for the original scores, differences retain their original units. NN: nearest neighbor, AUC: area under the receiver operating characteristic curve.

Metric	$A-B$	$\Delta_{0}$	$\Delta_{1}$	$\Delta_{2}$	Mean
RNA fidelity
Mean gene-wise $W_{1}$ $\downarrow$	T–I	$-0.0354$	$-0.0295$	$+0.0012$	$-0.0212$
	T–C	$-0.0826$	$-0.0263$	$-0.0687$	$-0.0592$
	I–C	$-0.0473$	$+0.0032$	$-0.0699$	$-0.0380$
Mean Jensen–Shannon distance $\downarrow$	T–I	$-0.0093$	$-0.0081$	$-0.0023$	$-0.0066$
	T–C	$-0.0158$	$-0.0031$	$-0.0213$	$-0.0134$

Appendix

Table 15: After-treatment paired model differences. T: TMO-Net, I: ISOMERIC, C: CustOmics. Each contrast is the first model minus the second after averaging three training seeds within fold. Arrows indicate preferred directions or targets for the original scores, differences retain their original units. NN: nearest neighbor, AUC: area under the receiver operating characteristic curve.

Figure 6: Held-out evaluation in the after-treatment DECIDER cohort (139 paired samples from 89 patients). (g) Mean gene-wise RNA

W_{1}

, (h) correlation of same-gene RNA-CNV slopes, (i) distance to the closest paired training sample relative to the closest paired held-out sample, (j) amplification and deletion G-score correlations, and (k) paired membership AUC. Panel (l) reports RNA co-expression edge F1. Arrows and dashed lines indicate preferred directions, neutral targets, or real train-test references. Small points show individual outer folds, large markers and horizontal bars show the mean and sample standard deviation across the three folds. TMO-Net has the lowest RNA

W_{1}

and the highest co-expression edge F1 but also shows the strongest training preference. ISOMERIC leads the same-gene and G-score metrics. No architecture dominates overall.

Figure 7: After-treatment visual diagnostics. (e) RNA fidelity: Held-out real and ISOMERIC synthetic RNA profiles in a PCA space fitted on real training data. (f) CNV fidelity: Real and ISOMERIC synthetic G-scores for six HGSC genes, deletions are plotted below zero. Bars show mean G-scores across the three folds, error bars indicate sample SD. The CNV visualization uses the intersection of fold-specific evaluated genes (

n=1{,}230

), benchmark correlations use all 3,000 CNV genes per fold. (g) RNA-CNV association: For each gene, the linear association estimated in the held-out data is compared with the corresponding estimate from ISOMERIC synthetic and real-training data. Points near the diagonal indicate agreement. Panels (f,g) are ensemble visualizations: synthetic gene-level values are averaged across initializations within each fold. Their benchmark annotations use correlations computed separately per initialization, averaged within fold, then summarized as mean

\pm

sample SD across three folds. MAE denotes mean absolute error between synthetic and held-out G-scores across the 14 prespecified biomarkers. Amplification and deletion MAEs are reported in Table 3 . (h) RNA co-expression: The two subpanels compare Fisher-transformed gene-pair correlations in held-out real data (x-axis) with those in TMO-Net synthetic data and real training data (y-axes), using identical scales. Diagonals mark equality, dotted lines mark

r=0.70

. Grayscale hexbins show gene-pair density, colored markers show recovered (TP), missed (FN), and extra (FP) edges, with counts in the legends. Panel (h) is an illustrative example from one fold and initialization, its Fisher-

z

concordance (

C_{z}

) and edge F1 are example statistics. Models were selected separately for each property, so the panels are illustrative rather than an overall model ranking. The CNV criterion is the mean of amplification and deletion G-score correlations. Examples in (e,h) use the median fold and the initialization closest to its mean score (Appendix G ).

Figure 8: ISOMERIC: before-treatment visual diagnostics. (a) RNA PCA, (b) CNV G-scores, (c) same-gene RNA-CNV slopes, and (d) RNA co-expression. Panels (b,c) are ensemble visualizations, averaging synthetic gene-level values across initializations within each fold. The CNV plot uses 1,236 genes common to folds, benchmark correlations use all 3,000 CNV genes per fold. MAE denotes mean absolute error between synthetic and held-out G-scores across the 14 prespecified biomarkers. Amplification and deletion MAEs are reported in Table 3 . Benchmark correlations are computed per initialization, averaged within fold, then summarized as mean

\pm

sample SD across three folds. Panel (d) shows one illustrative fold and initialization, Fisher-

z

concordance (

C_{z}

) and edge F1 describe that example. Other plotting conventions follow Figure 3 .

Figure 9: TMO-Net: before-treatment visual diagnostics. (a) RNA PCA, (b) CNV G-scores, (c) same-gene RNA-CNV slopes, and (d) RNA co-expression. Panels (b,c) are ensemble visualizations, averaging synthetic gene-level values across initializations within each fold. The CNV plot uses 1,236 genes common to folds, benchmark correlations use all 3,000 CNV genes per fold. MAE denotes mean absolute error between synthetic and held-out G-scores across the 14 prespecified biomarkers. Amplification and deletion MAEs are reported in Table 3 . Benchmark correlations are computed per initialization, averaged within fold, then summarized as mean

\pm

sample SD across three folds. Panel (d) shows one illustrative fold and initialization, Fisher-

z

concordance (

C_{z}

) and edge F1 describe that example. Other plotting conventions follow Figure 3 .

Figure 10: CustOmics: before-treatment visual diagnostics. (a) RNA PCA, (b) CNV G-scores, (c) same-gene RNA-CNV slopes, and (d) RNA co-expression. Panels (b,c) are ensemble visualizations, averaging synthetic gene-level values across initializations within each fold. The CNV plot uses 1,236 genes common to folds, benchmark correlations use all 3,000 CNV genes per fold. MAE denotes mean absolute error between synthetic and held-out G-scores across the 14 prespecified biomarkers. Amplification and deletion MAEs are reported in Table 3 . Benchmark correlations are computed per initialization, averaged within fold, then summarized as mean

\pm

sample SD across three folds. Panel (d) shows one illustrative fold and initialization, Fisher-

z

concordance (

C_{z}

) and edge F1 describe that example. Other plotting conventions follow Figure 3 .

Figure 11: ISOMERIC: after-treatment visual diagnostics. (a) RNA PCA, (b) CNV G-scores, (c) same-gene RNA-CNV slopes, and (d) RNA co-expression. Panels (b,c) are ensemble visualizations, averaging synthetic gene-level values across initializations within each fold. The CNV plot uses 1,230 genes common to folds, benchmark correlations use all 3,000 CNV genes per fold. MAE denotes mean absolute error between synthetic and held-out G-scores across the 14 prespecified biomarkers. Amplification and deletion MAEs are reported in Table 3 . Benchmark correlations are computed per initialization, averaged within fold, then summarized as mean

\pm

sample SD across three folds. Panel (d) shows one illustrative fold and initialization, Fisher-

z

concordance (

C_{z}

) and edge F1 describe that example. Other plotting conventions follow Figure 7 .

Figure 12: TMO-Net: after-treatment visual diagnostics. (a) RNA PCA, (b) CNV G-scores, (c) same-gene RNA-CNV slopes, and (d) RNA co-expression. Panels (b,c) are ensemble visualizations, averaging synthetic gene-level values across initializations within each fold. The CNV plot uses 1,230 genes common to folds, benchmark correlations use all 3,000 CNV genes per fold. MAE denotes mean absolute error between synthetic and held-out G-scores across the 14 prespecified biomarkers. Amplification and deletion MAEs are reported in Table 3 . Benchmark correlations are computed per initialization, averaged within fold, then summarized as mean

\pm

sample SD across three folds. Panel (d) shows one illustrative fold and initialization, Fisher-

z

concordance (

C_{z}

) and edge F1 describe that example. Other plotting conventions follow Figure 7 .

Figure 13: CustOmics: after-treatment visual diagnostics. (a) RNA PCA, (b) CNV G-scores, (c) same-gene RNA-CNV slopes, and (d) RNA co-expression. Panels (b,c) are ensemble visualizations, averaging synthetic gene-level values across initializations within each fold. The CNV plot uses 1,230 genes common to folds, benchmark correlations use all 3,000 CNV genes per fold. MAE denotes mean absolute error between synthetic and held-out G-scores across the 14 prespecified biomarkers. Amplification and deletion MAEs are reported in Table 3 . Benchmark correlations are computed per initialization, averaged within fold, then summarized as mean

\pm

sample SD across three folds. Panel (d) shows one illustrative fold and initialization, Fisher-

z

concordance (

C_{z}

) and edge F1 describe that example. Other plotting conventions follow Figure 7 .

Figure 14: RNA residual-noise ablation before treatment. Decoder means (gray) and Gaussian residual noise (blue) share fitted models, sampling temperatures, latent draws, and CNV profiles. (a) Median gene-wise RNA variance ratio, (b) co-expression edge-density ratio (logarithmic axis), (c) edge F1. Ratios compare synthetic with held-out data and target one (dashed lines), higher F1 indicates greater edge agreement. Connected points show paired outer folds, diamonds and bars show arithmetic means

\pm

sample SD across three folds, using training seed 42 only.

Model	Condition	RNA variance ratio $\to 1$	Edge-density ratio $\to 1$	Edge $F_{1}\uparrow$
TMO-Net	Decoder mean	$0.667\pm 0.090$	$1.681\pm 0.417$	$0.499\pm 0.023$
	Gaussian	$0.714\pm 0.080$	$1.051\pm 0.302$	$0.519\pm 0.047$
	$\Delta$ (G $-$ D)	$+0.047\pm 0.011$	$-0.630\pm 0.209$	$+0.021\pm 0.027$
ISOMERIC	Decoder mean	$0.568\pm 0.094$	$2.535\pm 0.413$	$0.432\pm 0.022$
	Gaussian	$0.844\pm 0.103$	$0.190\pm 0.129$	$0.193\pm 0.059$
	$\Delta$ (G $-$ D)	$+0.277\pm 0.022$	$-2.345\pm 0.350$	$-0.239\pm 0.080$

Appendix

Table 16: Variance and co-expression under RNA residual noise. Before-treatment cohort, training seed 42, three patient-disjoint outer folds. Values are means

\pm

sample SD across folds. D denotes decoder means and G Gaussian residual noise,

\Delta=\mathrm{G}-\mathrm{D}

is computed within fold before summarizing. Both synthetic-to-held-out ratios target one, higher edge F1 indicates greater agreement. Weights, temperatures, latent draws, and CNV are fixed.

Model	Condition	$W_{1}\downarrow$	$\mathrm{MMD}^{2}\downarrow$	Fisher- $z$ Pearson $\uparrow$	$r_{\beta}\uparrow$	Median $\|\Delta\beta\|\downarrow$
TMO-Net	Decoder mean	$0.1620\pm 0.0180$	$0.01313\pm 0.00243$	$0.6925\pm 0.0341$	$0.5950\pm 0.0577$	$0.1463\pm 0.0087$
	Gaussian	$0.1566\pm 0.0145$	$0.01310\pm 0.00240$	$0.6861\pm 0.0349$	$0.5922\pm 0.0552$	$0.1479\pm 0.0134$
	$\Delta$ (G $-$ D)	$-0.0054\pm 0.0035$	$-0.00003\pm 0.00004$	$-0.0064\pm 0.0018$	$-0.0028\pm 0.0047$	$+0.0017\pm 0.0060$
ISOMERIC	Decoder mean	$0.1846\pm 0.0178$	$0.01370\pm 0.00370$	$0.6965\pm 0.0188$	$0.5463\pm 0.1238$	$0.1204\pm 0.0070$
	Gaussian	$0.1545\pm 0.0110$	$0.01369\pm 0.00378$	$0.6593\pm 0.0139$	$0.5386\pm 0.1232$	$0.1229\pm 0.0002$
	$\Delta$ (G $-$ D)	$-0.0301\pm 0.0167$	$-0.00002\pm 0.00010$	$-0.0373\pm 0.0092$	$-0.0077\pm 0.0207$	$+0.0025\pm 0.0069$

Appendix

Table 17: RNA fidelity and cis RNA–CNV association under residual noise. Before-treatment cohort, seed 42, means

\pm

sample SD across three patient-disjoint outer folds.

\Delta

summarizes paired Gaussian-minus-decoder-mean differences.

W_{1}

: mean gene-wise Wasserstein distance, MMD 2 : squared maximum mean discrepancy in PCA space, Fisher-

z

Pearson: RNA correlation concordance,

r_{\beta}

: slope Pearson correlation. Arrows indicate preferred directions against held-out data.

Model	Condition	RNA NN ratio	RNA AUC	Paired NN ratio	Paired AUC	Paired NN agreement
TMO-Net	Decoder mean	$0.8855\pm 0.0200$	$0.8142\pm 0.0321$	$0.9552\pm 0.0137$	$0.6691\pm 0.0419$	$0.0998\pm 0.0179$
	Gaussian	$0.8927\pm 0.0172$	$0.8136\pm 0.0325$	$0.9556\pm 0.0139$	$0.6687\pm 0.0422$	$0.0987\pm 0.0145$
	$\Delta$ (G $-$ D)	$+0.0072\pm 0.0028$	$-0.0006\pm 0.0007$	$+0.0003\pm 0.0003$	$-0.0004\pm 0.0005$	$-0.0011\pm 0.0035$
ISOMERIC	Decoder mean	$0.9498\pm 0.0117$	$0.6486\pm 0.0527$	$0.9932\pm 0.0142$	$0.4422\pm 0.0312$	$0.0301\pm 0.0098$
	Gaussian	$0.9627\pm 0.0091$	$0.6473\pm 0.0529$	$0.9946\pm 0.0127$	$0.4422\pm 0.0305$	$0.0332\pm 0.0097$
	$\Delta$ (G $-$ D)	$+0.0129\pm 0.0052$	$-0.0013\pm 0.0052$	$+0.0014\pm 0.0015$	$+0.0000\pm 0.0011$	$+0.0030\pm 0.0001$

Appendix

Table 18: Training proximity under RNA residual noise. Before-treatment cohort, seed 42, means

\pm

sample SD across three patient-disjoint outer folds.

\Delta

summarizes paired Gaussian-minus-decoder-mean differences. Nearest-neighbor (NN) ratios compare distances from synthetic profiles to equally sized training and held-out sets. Ratios below one or membership AUC above

0.5

indicate training preference. Paired NN agreement is the fraction whose closest training RNA and CNV profiles identify the same sample. These diagnostics do not establish privacy protection.

Cohort	Pairing	$r_{\beta}\uparrow$	$\operatorname{median}\|\Delta\beta\|\downarrow$	Sign agreement $\uparrow$
Before treatment	Intact	$0.742\pm 0.046$	$0.093\pm 0.006$	$0.958\pm 0.008$
	Shuffled	$0.013\pm 0.029$	$0.436\pm 0.021$	$0.480\pm 0.007$
After treatment	Intact	$0.410\pm 0.061$	$0.163\pm 0.017$	$0.922\pm 0.022$
	Shuffled	$0.005\pm 0.065$	$0.472\pm 0.037$	$0.464\pm 0.021$

Appendix

Table 19: Cis association scores for intact and shuffled held-out pairs against real-training slopes. Values are means

\pm

sample standard deviations across three outer folds. For shuffled pairs, the 100 permutation scores are first averaged within each fold.

r_{\beta}

is the Pearson correlation of same-gene slopes. Sign agreement excludes exact-zero slopes. Intact and shuffled comparisons use the same eligible held-out samples and fixed gene set in each fold. Arrows indicate closer agreement with the reference, the standard deviations are descriptive, not confidence intervals.

Figure 15: Sensitivity of cis RNA–CNV slope correlation to pair shuffling. The upper and lower panels show the before- and after-treatment cohorts. Orange diamonds show correlations between slopes from intact held-out pairs and slopes from the original real-training pairs. Teal points show the corresponding correlations after each of 100 CNV permutations in the held-out data. The training pairs remain unchanged in every comparison. Boxes show the median and interquartile range, whiskers extend to the most extreme values within 1.5 interquartile ranges of the box. Labels give the number of eligible held-out samples (

n

) and the fixed number of estimable genes (

G

). Folds are displayed separately. The spread describes variation among permutations and is not a confidence interval.

Before treatment
Method	RNA $W_{1}\downarrow$	Edge F1 $\uparrow$	$r_{\beta}\uparrow$	Paired AUC
ISOMERIC	$0.184\pm 0.020$	$0.412\pm 0.018$	$0.551\pm 0.101$	$0.446\pm 0.035$
TMO-Net	$0.166\pm 0.027$	$0.474\pm 0.010$	$0.600\pm 0.047$	$0.657\pm 0.043$
CustOmics	$0.185\pm 0.013$	$0.226\pm 0.034$	$0.567\pm 0.049$	$0.524\pm 0.046$
Independent marginals	$0.115\pm 0.007$	$0.546\pm 0.007$	$0.024\pm 0.031$	$0.876\pm 0.021$
After treatment

Appendix

Table 20: Independent empirical marginal baseline compared with the three learned generators. RNA

W_{1}

(R1), RNA co-expression edge F1 (R2), and same-gene slope correlation

r_{\beta}

(R3) compare generated and held-out real cohorts. Paired membership AUC (R4) measures training-versus-held-out separation,

0.5

denotes no separation and values above

0.5

indicate training preference. Each entry is the mean

\pm

sample standard deviation across three outer folds after averaging three replicates per fold. Replicates are sampling cohorts for Independent marginals and training initializations for the learned models. Arrows indicate closer held-out agreement. These four selected metrics do not summarize every property assessed by the complete R1–R4 evaluation.

Figure 16: Independent empirical marginals compared with the adapted VAEs. Panels a–d show the before-treatment cohort and e–h show the after-treatment cohort. RNA Wasserstein distance (R1), RNA co-expression edge F1 (R2), and same-gene slope correlation (R3) compare generated cohorts with held-out data. Arrows indicate the direction of closer agreement. Paired membership AUC (R4) measures training-versus-held-out separation:

0.5

denotes no separation, and higher values indicate training preference. Bars show means and error bars show sample SDs across three outer folds. Points show individual fold values after averaging three generated cohorts for the baseline or three training initializations for each VAE. The baseline combines favorable RNA-only scores with near-zero slope correlations. Table 20 reports the numerical values.

Figure 17: Co-expression threshold sensitivity before treatment. (A) Candidate/held-out network density ratio (one denotes equal density), (B–D) edge precision, recall, and F1 (higher indicates greater recovery of held-out edges). Colored curves compare synthetic RNA with held-out RNA, the gray dashed curve uses real-training RNA as the candidate. Points and bars show mean

\pm

sample standard deviation across three outer folds, after averaging metrics over three training seeds per fold.

$\tau$	Candidate	Density ratio	Precision	Recall	Edge F1
0.60	ISOMERIC	$2.620\pm 0.313$	$0.264\pm 0.025$	$0.677\pm 0.021$	$0.377\pm 0.022$
	TMO-Net	$1.882\pm 0.607$	$0.336\pm 0.051$	$0.596\pm 0.109$	$0.420\pm 0.009$
	CustOmics	$6.380\pm 1.749$	$0.131\pm 0.029$	$0.793\pm 0.056$	$0.224\pm 0.040$
	Real training	$0.952\pm 0.216$	$0.578\pm 0.052$	$0.542\pm 0.081$	$0.554\pm 0.024$
0.65	ISOMERIC	$2.587\pm 0.285$	$0.278\pm 0.019$	$0.705\pm 0.030$	$0.396\pm 0.014$
	TMO-Net	$1.833\pm 0.634$	$0.364\pm 0.059$	$0.623\pm 0.120$	$0.448\pm 0.009$

Appendix

Table 21: Edge metrics across correlation thresholds before treatment. Values are mean

\pm

sample SD across three outer folds, after averaging three training seeds within each fold. Each candidate is compared with held-out real RNA. The shared real-training reference appears once per threshold,

\tau=0.70

is the primary setting.

Synthesis of Ovarian Cancer Multi-Omics Datasets: A Biology-Informed Evaluation Framework

Abstract

Figures & tables

Appendix

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