Potassium Chloride Sodium Potassium & Sodium -5
-4
-3
-2
-1
0
1
2
3
4
5
Figure 4.14. Parallel coordinates visualization of the latent representations withL = 10in the Ion Channel dataset. Most dimensions separate at least one class from the others.
computations presented in this Chapter can be performed on a mid-range graphics card in a rea-sonable time. Figure 4.17 shows the runtime of GPU and CPU implementations as a function of the number of latent factors in a200×200matrix factorization problem. On an NVIDA Titan X graphics card, the speedup is found to be around30×as compared to the baseline CPU implementation, which utilized LAPACK and an Intel Core i7-4510U CPU. However, memory requirements in larger dimen-sions or with many latent factors still restrict the applicability of GPUs,i.e. scaling remains an open question. We developed a sparse implementation alongside the dense solver in order to decrease the memory footprint of the algorithm.
Although modern consumer-level GPUs provide excellent single precision performance, double precision performance typically lags far behind, around1/8−1/32, raising the issue of single preci-sion numerical stability. To address this issue, we also provide a QR factorization-based implementa-tion which is more stable but significantly slower than the default blocked Cholesky decomposiimplementa-tion method. The computational cost in VB-MK-LMF is dominated by the inversion in Eq. 4.19, which givesO(DL3max(I3, J3))for the total time complexity whereDis the number of iterations. Com-parison with the time complexity of NRLMF,O(DLIJ), clearly shows the burden of fully Bayesian inference and calls for the usage of approximative inversion techniques, which we consider as a future work.
an-0.0 2.5 5.0 7.5
1 2 3 4 5 6 7 8 9
# Targets
Expected value
Nuclear Receptor
0 10 20
0 5 10 15 20 25
# Targets
Expected value
GPCR
0 25 50 75 100 125
0 25 50 75 100 125
# Targets
Expected value
Ion Channel
0 25 50 75 100
0 25 50 75 100
# Targets
Expected value
Enzyme
0 10 20 30 40
0 10 20 30 40 50
# Targets
Expected value
Kinase
Figure 4.15. Number of known targets of each drug in the datasets (horizontal) vs. the expected number of interactions as predicted by VB-MK-LMF (vertical).
0 1 2 3 4 5
0 1 2 3 4
# Targets
# Predicted
Figure 4.16. Expected number of interactions as predicted by VB-MK-LMF for each drug in the GPCR dataset with a given number of known targets in a10×cross-validation setting.
alytic estimates or expert hints for the missing data, and extracting information from missingness patterns, whose effect is integrated consistently into the overall posterior.
We derived efficient Bayesian inference methods for both models, namely, variational approxi-mation and Gibbs sampling, respectively. The former is easy to parallelize and implement on the GPU, however, the computational complexity is dominated by the inversion of the precision matrix.
As a future work, we plan to investigate analytic and approximative solutions for inverting matrices with this special structure. The Gibbs sampling-based inference offers an efficient inference scheme in a practical dimension, but in general, scaling up is a difficult question due to the memory com-plexity of storing the kernels and the notoriously hard problem of scaling up Gibbs sampling itself.
We plan to investigate low-rank kernel approximations, alternative MCMC schemes and GPU-based implementations.
VB-MK-LMF and MK-BMF-MNAR achieved better predictive performance in standard bench-marks compared to other state-of-the-art methods. Although facilitating comparability, benchmark-ing the pure predictive performance on pre-defined datasets gives only a narrow view about real-world applicability. The possible utilizations of the DTI prediction methods in real-real-world scenarios are much more diverse; for example, the same algorithms could be applied in the quality control phase for anomaly detection, especially when merging different bioactivity values from public and private sources. Additional use-cases include screening design, hit triage and prioritization for further
vali-1 10 100
5 10 15 20
Latent factors
Time (s)
Device GPU CPU
Figure 4.17. Runtime of the GPU and CPU implementations in terms of the number of latent factors in a200×200matrix factorization task. The GPU implementation brings a30×speedup on an NVIDIA GTX Titan X graphics card.
dation [136], possibly in an active learning framework [20, 137]. Finally, DTI prediction methods may also provide important insights by supporting visualization and visual data analytics, as we demon-strated in a new range of dimensionality (10−20), which proved to be sufficient with our methods.
As a future work, we plan to utilize these tools to find plausible biochemical interpretations of the latent dimensions.
The explicit modeling of interaction probabilities in VB-MK-LMF allows the establishment of cred-ibility regions and the estimation of promiscuity and druggability through the expected number of hits in a dataset. In general, the predicted posteriors for the interactions can be utilized to develop new functionalities in post-processing, going beyond enrichment methods available for ranking meth-ods [92, 138]. To utilize the Bayesian predictions of our algorithms, we also plan to investigate their sequential, decision theoretic usage,e.g.in functional validations.
Further interesting research directions are the use of multiple instances of our models for context-specific, but overlapping DTI matrices, which are linked to each other by common observations, giv-ing rise to a multitask version of the algorithms, however, the availability of multiple interaction scores (i.e. multiple bioactivity data) and the selection of row-entities and column-entities (i.e. com-pounds and targets), remain open challenges.
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