We introduce an amortized variational inference algorithm and structured variational approximation for state-space models with nonlinear dynamics driven by Gaussian noise. Importantly, the proposed framework allows for efficient evaluation of the ELBO and low-variance stochastic gradient estimates without resorting to diagonal Gaussian approximations by exploiting (i) the low-rank structure of Monte-Carlo approximations to marginalize the latent state through the dynamics (ii) an inference network that approximates the update step with low-rank precision matrix updates (iii) encoding current and future observations into pseudo observations -- transforming the approximate smoothing problem into an (easier) approximate filtering problem. Overall, the necessary statistics and ELBO can be computed in $O(TL(Sr + S^2 + r^2))$ time where $T$ is the series length, $L$ is the state-space dimensionality, $S$ are the number of samples used to approximate the predict step statistics, and $r$ is the rank of the approximate precision matrix update in the update step (which can be made of much lower dimension than $L$).

The Evidential regression network (ENet) estimates a continuous target and its predictive uncertainty without costly Bayesian model averaging. However, it is possible that the target is inaccurately predicted due to the gradient shrinkage problem of the original loss function of the ENet, the negative log marginal likelihood (NLL) loss. In this paper, the objective is to improve the prediction accuracy of the ENet while maintaining its efficient uncertainty estimation by resolving the gradient shrinkage problem. A multi-task learning (MTL) framework, referred to as MT-ENet, is proposed to accomplish this aim. In the MTL, we define the Lipschitz modified mean squared error (MSE) loss function as another loss and add it to the existing NLL loss. The Lipschitz modified MSE loss is designed to mitigate the gradient conflict with the NLL loss by dynamically adjusting its Lipschitz constant. By doing so, the Lipschitz MSE loss does not disturb the uncertainty estimation of the NLL loss. The MT-ENet enhances the predictive accuracy of the ENet without losing uncertainty estimation capability on the synthetic dataset and real-world benchmarks, including drug-target affinity (DTA) regression. Furthermore, the MT-ENet shows remarkable calibration and out-of-distribution detection capability on the DTA benchmarks.

Motivating study and statistical approaches Crohn's disease (CD) is a chronic debilitating condition characterized by periods of inflammatory activity in the bowel that causes symptoms such as abdominal pain, diarrhea, andweight loss. Pharmacologic treatment for CD includes medications such as steroids, immunomodulating drugs, and biological therapy. Despite these available medications, many people with CD are escalated to surgical interventions from small to extensive resections of the bowel or colon (Gomollón et al., 2016). Previous studies have estimated that up to 50% of patients with CD undergo surgery within 10 years after diagnosis; however, surgical rates have decreased over time, possibly due to the introduction of modern treatments such as thiopurines and anti-TNF (Lakatos et al., 2012; Ramadas et al., 2010). The aim of this study is to determine whether clinical and demographic characteristics observed at the time of diagnosis can be used to predict the occurrence of major abdominal surgery within 5 years, with the goal of personalized disease management.

We propose a multi-armed bandit algorithm that explores based on randomizing its history. The key idea is to estimate the value of the arm from the bootstrap sample of its history, where we add pseudo observations after each pull of the arm. The pseudo observations seem to be harmful. But on the contrary, they guarantee that the bootstrap sample is optimistic with a high probability. Because of this, we call our algorithm Giro, which is an abbreviation for garbage in, reward out. We analyze Giro in a $K$-armed Bernoulli bandit and prove a $O(K \Delta^{-1} \log n)$ bound on its $n$-round regret, where $\Delta$ denotes the difference in the expected rewards of the optimal and best suboptimal arms. The main advantage of our exploration strategy is that it can be applied to any reward function generalization, such as neural networks. We evaluate Giro and its contextual variant on multiple synthetic and real-world problems, and observe that Giro is comparable to or better than state-of-the-art algorithms.

This paper presents a new approach for Gaussian process (GP) regression for large datasets. The approach involves partitioning the regression input domain into multiple local regions with a different local GP model fitted in each region. Unlike existing local partitioned GP approaches, we introduce a technique for patching together the local GP models nearly seamlessly to ensure that the local GP models for two neighboring regions produce nearly the same response prediction and prediction error variance on the boundary between the two regions. This effectively solves the well-known discontinuity problem that degrades the boundary accuracy of existing local partitioned GP methods. Our main innovation is to represent the continuity conditions as additional pseudo-observations that the differences between neighboring GP responses are identically zero at an appropriately chosen set of boundary input locations. To predict the response at any input location, we simply augment the actual response observations with the pseudo-observations and apply standard GP prediction methods to the augmented data. In contrast to heuristic continuity adjustments, this has an advantage of working within a formal GP framework, so that the GP-based predictive uncertainty quantification remains valid. Our approach also inherits a sparse block-like structure for the sample covariance matrix, which results in computationally efficient closed-form expressions for the predictive mean and variance. In addition, we provide a new spatial partitioning scheme based on a recursive space partitioning along local principal component directions, which makes the proposed approach applicable for regression domains having more than two dimensions. Using three spatial datasets and three higher dimensional datasets, we investigate the numerical performance of the approach and compare it to several state-of-the-art approaches.