Policy optimization is a core component of reinforcement learning (RL), and most existing RL methods directly optimize parameters of a policy based on maximizing the expected total reward, or its surrogate. Though often achieving encouraging empirical success, its underlying mathematical principle on {\em policy-distribution} optimization is unclear. We place policy optimization into the space of probability measures, and interpret it as Wasserstein gradient flows. On the probability-measure space, under specified circumstances, policy optimization becomes a convex problem in terms of distribution optimization. To make optimization feasible, we develop efficient algorithms by numerically solving the corresponding discrete gradient flows. Our technique is applicable to several RL settings, and is related to many state-of-the-art policy-optimization algorithms. Empirical results verify the effectiveness of our framework, often obtaining better performance compared to related algorithms.

Hamiltonian Monte Carlo (HMC) is a very popular and generic collection of Markov chain Monte Carlo (MCMC) algorithms. One explanation for the popularity of HMC algorithms is their excellent performance as the dimension $d$ of the target becomes large: under conditions that are satisfied for many common statistical models, optimally-tuned HMC algorithms have a running time that scales like $d^{0.25}$. In stark contrast, the running time of the usual Random-Walk Metropolis (RWM) algorithm, optimally tuned, scales like $d$. This superior scaling of the HMC algorithm with dimension is attributed to the fact that it, unlike RWM, incorporates the gradient information in the proposal distribution. In this paper, we investigate a different scaling question: does HMC beat RWM for highly $\textit{multimodal}$ targets? We find that the answer is often $\textit{no}$. We compute the spectral gaps for both the algorithms for a specific class of multimodal target densities, and show that they are identical. The key reason is that, within one mode, the gradient is effectively ignorant about other modes, thus negating the advantage the HMC algorithm enjoys in unimodal targets. We also give heuristic arguments suggesting that the above observation may hold quite generally. Our main tool for answering this question is a novel simple formula for the conductance of HMC using Liouville's theorem. This result allows us to compute the spectral gap of HMC algorithms, for both the classical HMC with isotropic momentum and the recent Riemannian HMC, for multimodal targets.

Fuzzy clustering methods identify naturally occurring clusters in a dataset, where the extent to which different clusters are overlapped can differ. Most methods have a parameter to fix the level of fuzziness. However, the appropriate level of fuzziness depends on the application at hand. This paper presents Entropy $c$-Means (ECM), a method of fuzzy clustering that simultaneously optimizes two contradictory objective functions, resulting in the creation of fuzzy clusters with different levels of fuzziness. This allows ECM to identify clusters with different degrees of overlap. ECM optimizes the two objective functions using two multi-objective optimization methods, Non-dominated Sorting Genetic Algorithm II (NSGA-II), and Multiobjective Evolutionary Algorithm based on Decomposition (MOEA/D). We also propose a method to select a suitable trade-off clustering from the Pareto front. Experiments on challenging synthetic datasets as well as real-world datasets show that ECM leads to better cluster detection compared to the conventional fuzzy clustering methods as well as previously used multi-objective methods for fuzzy clustering.

Electronic phenotyping, which is the task of ascertaining whether an individual has a medical condition of interest by analyzing their medical records, is a foundational task in clinical informatics. Increasingly, electronic phenotyping is performed via supervised learning. We investigate the effectiveness of multitask learning for phenotyping using electronic health records (EHR) data. Multitask learning aims to improve model performance on a target task by jointly learning additional auxiliary tasks, and has been used to good effect in disparate areas of machine learning. However, its utility when applied to EHR data has not been established, and prior work suggests that its benefits are inconsistent. Here we present experiments that elucidate when multitask learning with neural networks can improve performance for electronic phenotyping using EHR data relative to well-tuned single task neural networks. We find that multitask networks consistently outperform single task networks for rare phenotypes but underperform for more common phenotypes. The effect size increases as more auxiliary tasks are added.

Motivated by applications in hyperspectral imaging we investigate methods for approximating a high-dimensional non-negative matrix $\mathbf{\mathit{Y}}$ by a product of two lower-dimensional, non-negative matrices $\mathbf{\mathit{K}}$ and $\mathbf{\mathit{X}}.$ This so-called non-negative matrix factorization is based on defining suitable Tikhonov functionals, which combine a discrepancy measure for $\mathbf{\mathit{Y}}\approx\mathbf{\mathit{KX}}$ with penalty terms for enforcing additional properties of $\mathbf{\mathit{K}}$ and $\mathbf{\mathit{X}}$. The minimization is based on alternating minimization with respect to $\mathbf{\mathit{K}}$ or $\mathbf{\mathit{X}}$, where in each iteration step one replaces the original Tikhonov functional by a locally defined surrogate functional. The choice of surrogate functionals is crucial: It should allow a comparatively simple minimization and simultaneously its first order optimality condition should lead to multiplicative update rules, which automatically preserve non-negativity of the iterates. We review the most standard construction principles for surrogate functionals for Frobenius-norm and Kullback-Leibler discrepancy measures. We extend the known surrogate constructions by a general framework, which allows to add a large variety of penalty terms. The paper finishes by deriving the corresponding alternating minimization schemes explicitely and by applying these methods to MALDI imaging data.

Primary care serves as patients' first point of contact with the healthcare system and is a continuing focal point of comprehensive, accessible, and community-based care [1]. More than just a gate-keeping process for specialist referrals, it has been widely recognized for its focus on caring for the longterm health of patients rather than solely for treating specific diseases or conditions. As such, primary care helps deliver more equitable health outcomes across populations and meets 80-90% of individuals' health needs throughout their lives [2]. To this end, a recent special report from the Economist stated that "good primary care is an essential precondition for a decent healthcare system" [3]. The World Health Organization (WHO) emphasized several defining features for effective and socially productive primary care, including comprehensiveness, person-centeredness, and continuity of care [4]. In particular, person-centeredness refers to the "clinical method of participatory democracy" that allows patients to participate in decisions that affect their health.

Predictive models can fail to generalize from training to deployment environments because of dataset shift, posing a threat to model reliability and the safety of downstream decisions made in practice. Instead of using samples from the target distribution to reactively correct dataset shift, we use graphical knowledge of the causal mechanisms relating variables in a prediction problem to proactively remove relationships that do not generalize across environments, even when these relationships may depend on unobserved variables (violations of the "no unobserved confounders" assumption). To accomplish this, we identify variables with unstable paths of statistical influence and remove them from the model. We also augment the causal graph with latent counterfactual variables that isolate unstable paths of statistical influence, allowing us to retain stable paths that would otherwise be removed. Our experiments demonstrate that models that remove vulnerable variables and use estimates of the latent variables transfer better, often outperforming in the target domain despite some accuracy loss in the training domain.

Zhilin Zhang Abstract Multi-valued data are commonly found in many real applications. During the process of clustering multi-valued data, most existing methods use sampling or aggregation mechanisms that cannot reflect the real distribution of objects and their instances and thus fail to obtain high-quality clusters. In this paper, a concept ofα -approximation distance is introduced to measure the connectivity between multi-valued objects by taking account of the distribution of the instances. An α -approximation density-based clustering algorithm (DBCMO) is proposed to efficiently cluster the multi-valued objects by using global and local R* tree structures. To speed up the algorithm, four pruning rules on the tree structures are implemented. Empirical studies on synthetic and real datasets demonstrate that DBCMO can efficiently and effectively discover the multi-valued object clusters. A comparison with two existing methods further shows that DBCMO can better handle a continuous decrease in the cluster density and detect clusters of varying density. Keywords Multi-valued objects· α -Approximation· Density-based· Clustering 1 Introduction Multi-valued data (Zhang et al. 2010), including multi-instance data and uncertain data, are commonly found in many real applications. The check-in data of location-based social networks are one example. Each user is an object, and he/she can have multiple check-in records associated with different temporal and spatial information. The observation data of dynamic objects, such as seismic activity, sea floor bathymetry, and sea height, are other examples. Since the states of observed objects change constantly, the limited observation data can only reveal the objects' states with a certain probability. The clustering of multi-valued objects is the process of grouping objects into different partitions based on similarity measurements or connectivity calculations. Based on the mechanism used for measuring similarity or connectivity, the clustering algorithms for multi-valued objects can be divided into two main categories: aggregation-based clustering and sampling-based clustering. Aggregation-based clustering methodology first transfers the multi-valued objects into single-valued objects with an aggregation function (e.g. the mean). After that, various traditional clustering algorithms can be applied directly. Sampling-based methods obtain a sequence of sample points for each object using sampling techniques. And then the distance density function or the expected distance of two objects can be computed with the multiple discrete distance values from the samples. Both aggregation and sampling are useful in reducing computational cost, especially when there is large number of values for objects. However, determination of a proper aggregation function or sampling strategy is not trivial.

Algorithm selection and hyperparameter tuning remain two of the most challenging tasks in machine learning. The number of machine learning applications is growing much faster than the number of machine learning experts, hence we see an increasing demand for efficient automation of learning processes. Here, we introduce OBOE, an algorithm for time-constrained model selection and hyperparameter tuning. Taking advantage of similarity between datasets, OBOE finds promising algorithm and hyperparameter configurations through collaborative filtering. Our system explores these models under time constraints, so that rapid initializations can be provided to warm-start more fine-grained optimization methods. One novel aspect of our approach is a new heuristic for active learning in time-constrained matrix completion based on optimal experiment design. Our experiments demonstrate that OBOE delivers state-of-the-art performance faster than competing approaches on a test bed of supervised learning problems.

We present a regression technique for data driven problems based on polynomial chaos expansion (PCE). PCE is a popular technique in the field of uncertainty quantification (UQ), where it is typically used to replace a runnable but expensive computational model subject to random inputs with an inexpensive-to-evaluate polynomial function. The metamodel obtained enables a reliable estimation of the statistics of the output, provided that a suitable probabilistic model of the input is available. In classical machine learning (ML) regression settings, however, the system is only known through observations of its inputs and output, and the interest lies in obtaining accurate pointwise predictions of the latter. Here, we show that a PCE metamodel purely trained on data can yield pointwise predictions whose accuracy is comparable to that of other ML regression models, such as neural networks and support vector machines. The comparisons are performed on benchmark datasets available from the literature. The methodology also enables the quantification of the output uncertainties and is robust to noise. Furthermore, it enjoys additional desirable properties, such as good performance for small training sets and simplicity of construction, with only little parameter tuning required. In the presence of statistically dependent inputs, we investigate two ways to build the PCE, and show through simulations that one approach is superior to the other in the stated settings.