Modeling and prediction of epidemic spread are critical to assist in policy-making for mitigation. Therefore, we present a new method based on Gaussian Process Regression to model and predict epidemics, and it quantifies prediction confidence through variance and high probability error bounds. Gaussian Process Regression excels in using small datasets and providing uncertainty bounds, and both of these properties are critical in modeling and predicting epidemic spreading processes with limited data. However, the derivation of formal uncertainty bounds remains lacking when using Gaussian Process Regression in the setting of epidemics, which limits its usefulness in guiding mitigation efforts. Therefore, in this work, we develop a novel bound on the variance of the prediction that quantifies the impact of the epidemic data on the predictions we make. Further, we develop a high probability error bound on the prediction, and we quantify how the epidemic spread, the infection data, and the length of the prediction horizon all affect this error bound. We also show that the error stays below a certain threshold based on the length of the prediction horizon. To illustrate this framework, we leverage Gaussian Process Regression to model and predict COVID-19 using real-world infection data from the United Kingdom.

In this paper we consider the adversarial contextual bandit problem in metric spaces. The paper "Nearest neighbour with bandit feedback" tackled this problem but when there are many contexts near the decision boundary of the comparator policy it suffers from a high regret. In this paper we eradicate this problem, designing an algorithm in which we can hold out any set of contexts when computing our regret term. Our algorithm builds on that of "Nearest neighbour with bandit feedback" and hence inherits its extreme computational efficiency.

Gaussian process regression is a classical kernel method for function estimation and data interpolation. In large data applications, computational costs can be reduced using low-rank or sparse approximations of the kernel. This paper investigates the effect of such kernel approximations on the interpolation error. We introduce a unified framework to analyze Gaussian process regression under important classes of computational misspecification: Karhunen-Lo\`eve expansions that result in low-rank kernel approximations, multiscale wavelet expansions that induce sparsity in the covariance matrix, and finite element representations that induce sparsity in the precision matrix. Our theory also accounts for epistemic misspecification in the choice of kernel parameters.

Clustering algorithms may unintentionally propagate or intensify existing disparities, leading to unfair representations or biased decision-making. Current fair clustering methods rely on notions of fairness that do not capture any information on the underlying causal mechanisms. We show that optimising for non-causal fairness notions can paradoxically induce direct discriminatory effects from a causal standpoint. We present a clustering approach that incorporates causal fairness metrics to provide a more nuanced approach to fairness in unsupervised learning. Our approach enables the specification of the causal fairness metrics that should be minimised. We demonstrate the efficacy of our methodology using datasets known to harbour unfair biases.

We propose a new method called the Metropolis-adjusted Mirror Langevin algorithm for approximate sampling from distributions whose support is a compact and convex set. This algorithm adds an accept-reject filter to the Markov chain induced by a single step of the mirror Langevin algorithm (Zhang et al., 2020), which is a basic discretisation of the mirror Langevin dynamics. Due to the inclusion of this filter, our method is unbiased relative to the target, while known discretisations of the mirror Langevin dynamics including the mirror Langevin algorithm have an asymptotic bias. We give upper bounds for the mixing time of the proposed algorithm when the potential is relatively smooth, convex, and Lipschitz with respect to a self-concordant mirror function. As a consequence of the reversibility of the Markov chain induced by the algorithm, we obtain an exponentially better dependence on the error tolerance for approximate sampling. We also present numerical experiments that corroborate our theoretical findings.

Stochastic optimal control, which has the goal of driving the behavior of noisy systems, is broadly applicable in science, engineering and artificial intelligence. Our work introduces Stochastic Optimal Control Matching (SOCM), a novel Iterative Diffusion Optimization (IDO) technique for stochastic optimal control that stems from the same philosophy as the conditional score matching loss for diffusion models. That is, the control is learned via a least squares problem by trying to fit a matching vector field. The training loss, which is closely connected to the cross-entropy loss, is optimized with respect to both the control function and a family of reparameterization matrices which appear in the matching vector field. The optimization with respect to the reparameterization matrices aims at minimizing the variance of the matching vector field. Experimentally, our algorithm achieves lower error than all the existing IDO techniques for stochastic optimal control for three out of four control problems, in some cases by an order of magnitude. The key idea underlying SOCM is the path-wise reparameterization trick, a novel technique that is of independent interest, e.g., for generative modeling. Code at https://github.com/facebookresearch/SOC-matching

Motivated by policy gradient methods in the context of reinforcement learning, we derive the first large deviation rate function for the iterates generated by stochastic gradient descent for possibly non-convex objectives satisfying a Polyak-Lojasiewicz condition. Leveraging the contraction principle from large deviations theory, we illustrate the potential of this result by showing how convergence properties of policy gradient with a softmax parametrization and an entropy regularized objective can be naturally extended to a wide spectrum of other policy parametrizations.

Theoretical guarantees in reinforcement learning (RL) are known to suffer multiplicative blow-up factors with respect to the misspecification error of function approximation. Yet, the nature of such \emph{approximation factors} -- especially their optimal form in a given learning problem -- is poorly understood. In this paper we study this question in linear off-policy value function estimation, where many open questions remain. We study the approximation factor in a broad spectrum of settings, such as with the weighted $L_2$-norm (where the weighting is the offline state distribution), the $L_\infty$ norm, the presence vs. absence of state aliasing, and full vs. partial coverage of the state space. We establish the optimal asymptotic approximation factors (up to constants) for all of these settings. In particular, our bounds identify two instance-dependent factors for the $L_2(\mu)$ norm and only one for the $L_\infty$ norm, which are shown to dictate the hardness of off-policy evaluation under misspecification.

This article intends to systematically identify and comparatively analyze state-of-the-art supply chain (SC) forecasting strategies and technologies. A novel framework has been proposed incorporating Big Data Analytics in SC Management (problem identification, data sources, exploratory data analysis, machine-learning model training, hyperparameter tuning, performance evaluation, and optimization), forecasting effects on human-workforce, inventory, and overall SC. Initially, the need to collect data according to SC strategy and how to collect them has been discussed. The article discusses the need for different types of forecasting according to the period or SC objective. The SC KPIs and the error-measurement systems have been recommended to optimize the top-performing model. The adverse effects of phantom inventory on forecasting and the dependence of managerial decisions on the SC KPIs for determining model performance parameters and improving operations management, transparency, and planning efficiency have been illustrated. The cyclic connection within the framework introduces preprocessing optimization based on the post-process KPIs, optimizing the overall control process (inventory management, workforce determination, cost, production and capacity planning). The contribution of this research lies in the standard SC process framework proposal, recommended forecasting data analysis, forecasting effects on SC performance, machine learning algorithms optimization followed, and in shedding light on future research.

Accurate estimation of sub-surface properties like moisture content and depth of layers is crucial for applications spanning sub-surface condition monitoring, precision agriculture, and effective wildfire risk assessment. Soil in nature is often covered by overlaying surface material, making its characterization using conventional methods challenging. In addition, the estimation of the properties of the overlaying layer is crucial for applications like wildfire assessment. This study thus proposes a Bayesian model-updating-based approach for ground penetrating radar (GPR) waveform inversion to predict sub-surface properties like the moisture contents and depths of the soil layer and overlaying material accumulated above the soil. The dielectric permittivity of material layers were predicted with the proposed method, along with other parameters, including depth and electrical conductivity of layers. The proposed Bayesian model updating approach yields probabilistic estimates of these parameters that can provide information about the confidence and uncertainty related to the estimates. The methodology was evaluated for a diverse range of experimental data collected through laboratory and field investigations. Laboratory investigations included variations in soil moisture values and depth of the top layer (or overlaying material), and the field investigation included measurement of field soil moisture for sixteen days. The results demonstrated predictions consistent with time-domain reflectometry (TDR) measurements and conventional gravimetric tests. The top layer depth could also be predicted with reasonable accuracy. The proposed method provides a promising approach for uncertainty-aware sub-surface parameter estimation that can enable decision-making for risk assessment across a wide range of applications.