We address the pre-image problem encountered in structured output prediction and the one of finding a string maximizing the prediction function of various kernel-based classifiers and regressors. We demonstrate that these problems reduce to a common combinatorial problem valid for many string kernels. For this problem, we propose an upper bound on the prediction function which has low computational complexity and which can be used in a branch and bound search algorithm to obtain optimal solutions. We also show that for many string kernels, the complexity of the problem increases significantly when the kernel is normalized. On the optical word recognition task, the exact solution of the pre-image problem is shown to significantly improve the prediction accuracy in comparison with an approximation found by the best known heuristic. On the task of finding a string maximizing the prediction function of kernel-based classifiers and regressors, we highlight that existing methods can be biased toward long strings that contain many repeated symbols. We demonstrate that this bias is removed when using normalized kernels. Finally, we present results for the discovery of lead compounds in drug discovery. The source code can be found at https://github.com/a-ro/preimage

The discovery of peptides possessing high biological activity is very challenging due to the enormous diversity for which only a minority have the desired properties. To lower cost and reduce the time to obtain promising peptides, machine learning approaches can greatly assist in the process and even partly replace expensive laboratory experiments by learning a predictor with existing data or with a smaller amount of data generation. Unfortunately, once the model is learned, selecting peptides having the greatest predicted bioactivity often requires a prohibitive amount of computational time. For this combinatorial problem, heuristics and stochastic optimization methods are not guaranteed to find adequate solutions. We focused on recent advances in kernel methods and machine learning to learn a predictive model with proven success. For this type of model, we propose an efficient algorithm based on graph theory, that is guaranteed to find the peptides for which the model predicts maximal bioactivity. We also present a second algorithm capable of sorting the peptides of maximal bioactivity. Extensive analyses demonstrate how these algorithms can be part of an iterative combinatorial chemistry procedure to speed up the discovery and the validation of peptide leads. Moreover, the proposed approach does not require the use of known ligands for the target protein since it can leverage recent multi-target machine learning predictors where ligands for similar targets can serve as initial training data. Finally, we validated the proposed approach in vitro with the discovery of new cationic antimicrobial peptides. Source code freely available at http://graal.ift.ulaval.ca/peptide-design/.

We provide rigorous guarantees for the regression approach to structured output prediction. We show that the quadratic regression loss is a convex surrogate of the prediction loss when the output kernel satisfies some condition with respect to the prediction loss. We provide two upper bounds of the prediction risk that depend on the empirical quadratic risk of the predictor. The minimizer of the first bound is the predictor proposed by Cortes et al. (2007) while the minimizer of the second bound is a predictor that has never been proposed so far. Both predictors are compared on practical tasks.

BACKGROUND: The cellular function of a vast majority of proteins is performed through physical interactions with other biomolecules, which, most of the time, are other proteins. Peptides represent templates of choice for mimicking a secondary structure in order to modulate protein-protein interaction. They are thus an interesting class of therapeutics since they also display strong activity, high selectivity, low toxicity and few drug-drug interactions. Furthermore, predicting peptides that would bind to a specific MHC alleles would be of tremendous benefit to improve vaccine based therapy and possibly generate antibodies with greater affinity. Modern computational methods have the potential to accelerate and lower the cost of drug and vaccine discovery by selecting potential compounds for testing in silico prior to biological validation. RESULTS: We propose a specialized string kernel for small bio-molecules, peptides and pseudo-sequences of binding interfaces. The kernel incorporates physico-chemical properties of amino acids and elegantly generalizes eight kernels, comprised of the Oligo, the Weighted Degree, the Blended Spectrum, and the Radial Basis Function. We provide a low complexity dynamic programming algorithm for the exact computation of the kernel and a linear time algorithm for it's approximation. Combined with kernel ridge regression and SupCK, a novel binding pocket kernel, the proposed kernel yields biologically relevant and good prediction accuracy on the PepX database. For the first time, a machine learning predictor is capable of predicting the binding affinity of any peptide to any protein with reasonable accuracy. The method was also applied to both single-target and pan-specific Major Histocompatibility Complex class II benchmark datasets and three Quantitative Structure Affinity Model benchmark datasets. CONCLUSION: On all benchmarks, our method significantly (p-value ≤ 0.057) outperforms the current state-of-the-art methods at predicting peptide-protein binding affinities. The proposed approach is flexible and can be applied to predict any quantitative biological activity. Moreover, generating reliable peptide-protein binding affinities will also improve system biology modelling of interaction pathways. Lastly, the method should be of value to a large segment of the research community with the potential to accelerate the discovery of peptide-based drugs and facilitate vaccine development. The proposed kernel is freely available at http://graal.ift.ulaval.ca/downloads/gs-kernel/.