Modeling a system's temporal behaviour in reaction to external stimuli is a fundamental problem in many areas. Pure Machine Learning (ML) approaches often fail in the small sample regime and cannot provide actionable insights beyond predictions. A promising modification has been to incorporate expert domain knowledge into ML models. The application we consider is predicting the progression of disease under medications, where a plethora of domain knowledge is available from pharmacology. Pharmacological models describe the dynamics of carefully-chosen medically meaningful variables in terms of systems of Ordinary Differential Equations (ODEs). However, these models only describe a limited collection of variables, and these variables are often not observable in clinical environments. To close this gap, we propose the latent hybridisation model (LHM) that integrates a system of expert-designed ODEs with machine-learned Neural ODEs to fully describe the dynamics of the system and to link the expert and latent variables to observable quantities. We evaluated LHM on synthetic data as well as real-world intensive care data of COVID-19 patients. LHM consistently outperforms previous works, especially when few training samples are available such as at the beginning of the pandemic.

Randomized Controlled Trials (RCTs) are the gold standard for comparing the effectiveness of a new treatment to the current one (the control). Most RCTs allocate the patients to the treatment group and the control group by uniform randomization. We show that this procedure can be highly sub-optimal (in terms of learning) if -- as is often the case -- patients can be recruited in cohorts (rather than all at once), the effects on each cohort can be observed before recruiting the next cohort, and the effects are heterogeneous across identifiable subgroups of patients. We formulate the patient allocation problem as a finite stage Markov Decision Process in which the objective is to minimize a given weighted combination of type-I and type-II errors. Because finding the exact solution to this Markov Decision Process is computationally intractable, we propose an algorithm -- \textit{Knowledge Gradient for Randomized Controlled Trials} (RCT-KG) -- that yields an approximate solution. We illustrate our algorithm on a synthetic dataset with Bernoulli outcomes and compare it with uniform randomization. For a given size of trial our method achieves significant reduction in error, and to achieve a prescribed level of confidence (in identifying whether the treatment is superior to the control), our method requires many fewer patients. Our approach uses what has been learned from the effects on previous cohorts to recruit patients to subgroups and allocate patients (to treatment/control) within subgroups in a way that promotes more efficient learning.

Machine Learning models have proved extremely successful for a wide variety of supervised learning problems, but the predictions of many of these models are difficult to interpret. A recent literature interprets the predictions of more general "black-box" machine learning models by approximating these models in terms of simpler models such as piecewise linear or piecewise constant models. Existing literature constructs these approximations in an ad-hoc manner. We provide a tractable dynamic programming algorithm that partitions the feature space into clusters in a principled way and then uses this partition to provide both piecewise constant and piecewise linear interpretations of an arbitrary "black-box" model. When loss is measured in terms of mean squared error, our approximation is optimal (under certain conditions); for more general loss functions, our interpretation is probably approximately optimal (in the sense of PAC learning). Experiments with real and synthetic data show that it continues to provide significant improvements (in terms of mean squared error) over competing approaches.

Survival analysis (time-to-event analysis) is widely used in economics and finance, engineering, medicine and many other areas. A fundamental problem is to understand the relationship between the covariates and the (distribution of) survival times(times-to-event). Much of the previous work has approached the problem by viewing the survival time as the first hitting time of a stochastic process, assuming a specific form for the underlying stochastic process, using available data to learn the relationship between the covariates and the parameters of the model, and then deducing the relationship between covariates and the distribution of first hitting times (the risk). However, previous models rely on strong parametric assumptions that are often violated. This paper proposes a very different approach to survival analysis, DeepHit, that uses a deep neural network to learn the distribution of survival times directly.DeepHit makes no assumptions about the underlying stochastic process and allows for the possibility that the relationship between covariates and risk(s) changes over time. Most importantly, DeepHit smoothly handles competing risks; i.e. settings in which there is more than one possible event of interest.Comparisons with previous models on the basis of real and synthetic datasets demonstrate that DeepHit achieves large and statistically significant performance improvements over previous state-of-the-art methods.

This paper proposes a novel approach for constructing effective personalized policies when the observed data lacks counter-factual information, is biased and possesses many features. The approach is applicable in a wide variety of settings from healthcare to advertising to education to finance. These settings have in common that the decision maker can observe, for each previous instance, an array of features of the instance, the action taken in that instance, and the reward realized -- but not the rewards of actions that were not taken: the counterfactual information. Learning in such settings is made even more difficult because the observed data is typically biased by the existing policy (that generated the data) and because the array of features that might affect the reward in a particular instance -- and hence should be taken into account in deciding on an action in each particular instance -- is often vast. The approach presented here estimates propensity scores for the observed data, infers counterfactuals, identifies a (relatively small) number of features that are (most) relevant for each possible action and instance, and prescribes a policy to be followed. Comparison of the proposed algorithm against the state-of-art algorithm on actual datasets demonstrates that the proposed algorithm achieves a significant improvement in performance.