The use of multiple drugs, termed polypharmacy, is common to treat patients with complex diseases or co-existing medical conditions. However, a major consequence of polypharmacy is a much higher risk of side effects for the patient. Polypharmacy side effects emerge because of drug interactions, in which activity of one drug may change, favorably or unfavorably, if taken with another drug. The knowledge of drug interactions is limited because these complex relationships are usually not observed in small clinical testing. Discovering polypharmacy side effects thus remains a challenge with significant implications for patient mortality and morbidity. Here we introduce Decagon, an approach for modeling polypharmacy side effects. The approach constructs a multimodal graph of protein-protein interactions, drug-protein interactions, and the polypharmacy side effects, which are represented as drug-drug interactions, where each side effect is an edge of a different type. Decagon is developed specifically to handle such multimodal graphs with a large number of edge types. Our approach develops a new graph convolutional neural network for multirelational link prediction in multimodal networks. Unlike approaches limited to predicting simple drug-drug interaction values, Decagon can predict the exact side effect, if any, through which a given drug combination manifests clinically. Decagon accurately predicts polypharmacy side effects, outperforming baselines by up to 69%. Furthermore, Decagon models particularly well side effects that have a strong molecular basis, while on predominantly non-molecular side effects, it achieves good performance because of effective sharing of model parameters across edge types. Decagon creates an opportunity to use large molecular and patient population data to flag and prioritize polypharmacy side effects for follow-up analysis via formal pharmacological studies.

Gaussian processes are rich distributions over functions, with generalization properties determined by a kernel function. When used for long-range extrapolation, predictions are particularly sensitive to the choice of kernel parameters. It is therefore critical to account for kernel uncertainty in our predictive distributions. We propose a distribution over kernels formed by modelling a spectral mixture density with a L\'evy process. The resulting distribution has support for all stationary covariances--including the popular RBF, periodic, and Mat\'ern kernels--combined with inductive biases which enable automatic and data efficient learning, long-range extrapolation, and state of the art predictive performance. The proposed model also presents an approach to spectral regularization, as the L\'evy process introduces a sparsity-inducing prior over mixture components, allowing automatic selection over model order and pruning of extraneous components. We exploit the algebraic structure of the proposed process for $\mathcal{O}(n)$ training and $\mathcal{O}(1)$ predictions. We perform extrapolations having reasonable uncertainty estimates on several benchmarks, show that the proposed model can recover flexible ground truth covariances and that it is robust to errors in initialization.

Predicting conversion rates (CVRs) in display advertising (e.g., predicting the proportion of users who purchase an item (i.e., a conversion) after its corresponding ad is clicked) is important when measuring the effects of ads shown to users and to understanding the interests of the users. There is generally a time delay (i.e., so-called {\it delayed feedback}) between the ad click and conversion. Owing to the delayed feedback, samples that are converted after an observation period may be treated as negative. To overcome this drawback, CVR prediction assuming that the time delay follows an exponential distribution has been proposed. In practice, however, there is no guarantee that the delay is generated from the exponential distribution, and the best distribution with which to represent the delay depends on the data. In this paper, we propose a nonparametric delayed feedback model for CVR prediction that represents the distribution of the time delay without assuming a parametric distribution, such as an exponential or Weibull distribution. Because the distribution of the time delay is modeled depending on the content of an ad and the features of a user, various shapes of the distribution can be represented potentially. In experiments, we show that the proposed model can capture the distribution for the time delay on a synthetic dataset, even when the distribution is complicated. Moreover, on a real dataset, we show that the proposed model outperforms the existing method that assumes an exponential distribution for the time delay in terms of conversion rate prediction.

In this paper, we propose a stochastic Primal-Dual Hybrid Gradient (PDHG) approach for solving a wide spectrum of regularized stochastic minimization problems, where the regularization term is composite with a linear function. It has been recognized that solving this kind of problem is challenging since the closed-form solution of the proximal mapping associated with the regularization term is not available due to the imposed linear composition, and the per-iteration cost of computing the full gradient of the expected objective function is extremely high when the number of input data samples is considerably large. Our new approach overcomes these issues by exploring the special structure of the regularization term and sampling a few data points at each iteration. Rather than analyzing the convergence in expectation, we provide the detailed iteration complexity analysis for the cases of both uniformly and non-uniformly averaged iterates with high probability. This strongly supports the good practical performance of the proposed approach. Numerical experiments demonstrate that the efficiency of stochastic PDHG, which outperforms other competing algorithms, as expected by the high-probability convergence analysis.

Support vector data description (SVDD) is a machine learning technique that is used for single-class classification and outlier detection. The idea of SVDD is to find a set of support vectors that defines a boundary around data. When dealing with online or large data, existing batch SVDD methods have to be rerun in each iteration. We propose an incremental learning algorithm for SVDD that uses the Gaussian kernel. This algorithm builds on the observation that all support vectors on the boundary have the same distance to the center of sphere in a higher-dimensional feature space as mapped by the Gaussian kernel function. Each iteration involves only the existing support vectors and the new data point. Moreover, the algorithm is based solely on matrix manipulations; the support vectors and their corresponding Lagrange multiplier $\alpha_i$'s are automatically selected and determined in each iteration. It can be seen that the complexity of our algorithm in each iteration is only $O(k^2)$, where $k$ is the number of support vectors. Experimental results on some real data sets indicate that FISVDD demonstrates significant gains in efficiency with almost no loss in either outlier detection accuracy or objective function value.

We consider a wide range of regularized stochastic minimization problems with two regularization terms, one of which is composed with a linear function. This optimization model abstracts a number of important applications in artificial intelligence and machine learning, such as fused Lasso, fused logistic regression, and a class of graph-guided regularized minimization. The computational challenges of this model are in two folds. On one hand, the closed-form solution of the proximal mapping associated with the composed regularization term or the expected objective function is not available. On the other hand, the calculation of the full gradient of the expectation in the objective is very expensive when the number of input data samples is considerably large. To address these issues, we propose a stochastic variant of extra-gradient type methods, namely \textsf{Stochastic Primal-Dual Proximal ExtraGradient descent (SPDPEG)}, and analyze its convergence property for both convex and strongly convex objectives. For general convex objectives, the uniformly average iterates generated by \textsf{SPDPEG} converge in expectation with $O(1/\sqrt{t})$ rate. While for strongly convex objectives, the uniformly and non-uniformly average iterates generated by \textsf{SPDPEG} converge with $O(\log(t)/t)$ and $O(1/t)$ rates, respectively. The order of the rate of the proposed algorithm is known to match the best convergence rate for first-order stochastic algorithms. Experiments on fused logistic regression and graph-guided regularized logistic regression problems show that the proposed algorithm performs very efficiently and consistently outperforms other competing algorithms.

Natural language processing often involves computations with semantic or syntactic graphs to facilitate sophisticated reasoning based on structural relationships. While convolution kernels provide a powerful tool for comparing graph structure based on node (word) level relationships, they are difficult to customize and can be computationally expensive. We propose a generalization of convolution kernels, with a nonstationary model, for better expressibility of natural languages in supervised settings. For a scalable learning of the parameters introduced with our model, we propose a novel algorithm that leverages stochastic sampling on k-nearest neighbor graphs, along with approximations based on locality-sensitive hashing. We demonstrate the advantages of our approach on a challenging real-world (structured inference) problem of automatically extracting biological models from the text of scientific papers.

Decision-makers are faced with the challenge of estimating what is likely to happen when they take an action. For instance, if I choose not to treat this patient, are they likely to die? Practitioners commonly use supervised learning algorithms to fit predictive models that help decision-makers reason about likely future outcomes, but we show that this approach is unreliable, and sometimes even dangerous. The key issue is that supervised learning algorithms are highly sensitive to the policy used to choose actions in the training data, which causes the model to capture relationships that do not generalize. We propose using a different learning objective that predicts counterfactuals instead of predicting outcomes under an existing action policy as in supervised learning. To support decision-making in temporal settings, we introduce the Counterfactual Gaussian Process (CGP) to predict the counterfactual future progression of continuous-time trajectories under sequences of future actions. We demonstrate the benefits of the CGP on two important decision-support tasks: risk prediction and "what if?" reasoning for individualized treatment planning.

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I'm not aware of a requirement to square a percentage variable. If I assume that the percentage is independent (i.e. it isn't a percentage of one of the other variables or of the dependent variable), then using a percent (0 to 100) is a simple linear transformation of the values of the orignal parameter, therefore there is no reason to square it. However, consider that your goal is to best model the dependent variable. If you find a transformation of one of the independent variables improves the results, then you should consider using it. Just be careful when using the model to ensure you properly transform the independent data.