The recent outbreak of the COVID-19 shocked humanity leading to the death of millions of people worldwide. To stave off the spread of the virus, the authorities in the US, employed different strategies including the mask mandate (MM) order issued by the states' governors. Although most of the previous studies pointed in the direction that MM can be effective in hindering the spread of viral infections, the effectiveness of MM in reducing the degree of exposure to the virus and, consequently, death rates remains indeterminate. Indeed, the extent to which the degree of exposure to COVID-19 takes part in the lethality of the virus remains unclear. In the current work, we defined a parameter called the average death ratio as the monthly average of the ratio of the number of daily deaths to the total number of daily cases. We utilized survey data provided by New York Times to quantify people's abidance to the MM order. Additionally, we implicitly addressed the extent to which people abide by the MM order that may depend on some parameters like population, income, and political inclination. Using different machine learning classification algorithms we investigated how the decrease or increase in death ratio for the counties in the US West Coast correlates with the input parameters. Our results showed a promising score as high as 0.94 with algorithms like XGBoost, Random Forest, and Naive Bayes. To verify the model, the best performing algorithms were then utilized to analyze other states (Arizona, New Jersey, New York and Texas) as test cases. The findings show an acceptable trend, further confirming usability of the chosen features for prediction of similar cases.

In the multi-armed bandit problem, a decision maker needs to sequentially decide between acting to reveal data about a system and acting to generate profit. The central idea of the multi-armed bandit is that the agent has K'options' or equivalently, a bandit with K arms, and must choose which arm to play at each time. Playing an arm results in a reward generated from a fixed but unknown distribution which must be inferred'on-the-fly'. In the classic multi-armed bandit problem, the reward of each arm is assumed to be independent of the others (Gittins and Jones [9], Agrawal [1], Lattimore and Szepesvári [13]) and it is the only observation obtained by the decision maker at each step. In practice, we often observe signals in addition to the rewards and there is often correlation between the distributions of outcomes for different choices. For example, in a dynamic pricing problem (Dubé and Misra [6], Misra et al. [14]), an agent wants to fix the price of a single product, from a finite set of prices {c

Model deficiency that results from incomplete training data is a form of structural blindness that leads to costly errors, oftentimes with high confidence. During the training of classification tasks, underrepresented class-conditional distributions that a given hypothesis space can recognize results in a mismatch between the model and the target space. To mitigate the consequences of this discrepancy, we propose Random Test Sampling and Cross-Validation (RTSCV) as a general algorithmic framework that aims to perform a post-training model rectification at deployment time in a supervised way. RTSCV extracts unknown unknowns (u.u.s), i.e., examples from the class-conditional distributions that a classifier is oblivious to, and works in combination with a diverse family of modern prediction models. RTSCV augments the training set with a sample of the test set (or deployment data) and uses this redefined class layout to discover u.u.s via cross-validation, without relying on active learning or budgeted queries to an oracle. We contribute a theoretical analysis that establishes performance guarantees based on the design bases of modern classifiers. Our experimental evaluation demonstrates RTSCV's effectiveness, using 7 benchmark tabular and computer vision datasets, by reducing a performance gap as large as 41% from the respective pre-rectification models. Last we show that RTSCV consistently outperforms state-of-the-art approaches.

By leveraging experience from previous tasks, meta-learning algorithms can achieve effective fast adaptation ability when encountering new tasks. However it is unclear how the generalization property applies to new tasks. Probably approximately correct (PAC) Bayes bound theory provides a theoretical framework to analyze the generalization performance for meta-learning. We derive three novel generalisation error bounds for meta-learning based on PAC-Bayes relative entropy bound. Furthermore, using the empirical risk minimization (ERM) method, a PAC-Bayes bound for meta-learning with data-dependent prior is developed. Experiments illustrate that the proposed three PAC-Bayes bounds for meta-learning guarantee a competitive generalization performance guarantee, and the extended PAC-Bayes bound with data-dependent prior can achieve rapid convergence ability.

We consider convolutional neural network (CNN) ensemble learning with the objective function inspired by least action principle; it includes resource consumption component. We teach an agent to perceive images through the set of pre-trained classifiers and want the resulting dynamically configured system to unfold the computational graph with the trajectory that refers to the minimal number of operations and maximal expected accuracy. The proposed agent's architecture implicitly approximates the required classifier selection function with the help of reinforcement learning. Our experimental results prove, that if the agent exploits the dynamic (and context-dependent) structure of computations, it outperforms conventional ensemble learning.

In this paper, we study the problem of inferring time-varying Markov random fields (MRF), where the underlying graphical model is both sparse and changes sparsely over time. Most of the existing methods for the inference of time-varying MRFs rely on the regularized maximum likelihood estimation (MLE), that typically suffer from weak statistical guarantees and high computational time. Instead, we introduce a new class of constrained optimization problems for the inference of sparsely-changing MRFs. The proposed optimization problem is formulated based on the exact $\ell_0$ regularization, and can be solved in near-linear time and memory. Moreover, we show that the proposed estimator enjoys a provably small estimation error. As a special case, we derive sharp statistical guarantees for the inference of sparsely-changing Gaussian MRFs (GMRF) in the high-dimensional regime, showing that such problems can be learned with as few as one sample per time. Our proposed method is extremely efficient in practice: it can accurately estimate sparsely-changing graphical models with more than 500 million variables in less than one hour.

The main objective of this paper is to outline a theoretical framework to analyse how humans' decision-making strategies under uncertainty manage the trade-off between information gathering (exploration) and reward seeking (exploitation). A key observation, motivating this line of research, is the awareness that human learners are amazingly fast and effective at adapting to unfamiliar environments and incorporating upcoming knowledge: this is an intriguing behaviour for cognitive sciences as well as an important challenge for Machine Learning. The target problem considered is active learning in a black-box optimization task and more specifically how the exploration/exploitation dilemma can be modelled within Gaussian Process based Bayesian Optimization framework, which is in turn based on uncertainty quantification. The main contribution is to analyse humans' decisions with respect to Pareto rationality where the two objectives are improvement expected and uncertainty quantification. According to this Pareto rationality model, if a decision set contains a Pareto efficient (dominant) strategy, a rational decision maker should always select the dominant strategy over its dominated alternatives. The distance from the Pareto frontier determines whether a choice is (Pareto) rational (i.e., lays on the frontier) or is associated to "exasperate" exploration. However, since the uncertainty is one of the two objectives defining the Pareto frontier, we have investigated three different uncertainty quantification measures and selected the one resulting more compliant with the Pareto rationality model proposed. The key result is an analytical framework to characterize how deviations from "rationality" depend on uncertainty quantifications and the evolution of the reward seeking process.

We propose a novel framework for modeling multiple multivariate point processes, each with heterogeneous event types that share an underlying space and obey the same generative mechanism. Focusing on Hawkes processes and their variants that are associated with Granger causality graphs, our model leverages an uncountable event type space and samples the graphs with different sizes from a nonparametric model called {\it graphon}. Given those graphs, we can generate the corresponding Hawkes processes and simulate event sequences. Learning this graphon-based Hawkes process model helps to 1) infer the underlying relations shared by different Hawkes processes; and 2) simulate event sequences with different event types but similar dynamics. We learn the proposed model by minimizing the hierarchical optimal transport distance between the generated event sequences and the observed ones, leading to a novel reward-augmented maximum likelihood estimation method. We analyze the properties of our model in-depth and demonstrate its rationality and effectiveness in both theory and experiments.

Missing values with mixed data types is a common problem in a large number of machine learning applications such as processing of surveys and in different medical applications. Recently, Gaussian copula models have been suggested as a means of performing imputation of missing values using a probabilistic framework. While the present Gaussian copula models have shown to yield state of the art performance, they have two limitations: they are based on an approximation that is fast but may be imprecise and they do not support unordered multinomial variables. We address the first limitation using direct and arbitrarily precise approximations both for model estimation and imputation by using randomized quasi-Monte Carlo procedures. The method we provide has lower errors for the estimated model parameters and the imputed values, compared to previously proposed methods. We also extend the previous Gaussian copula models to include unordered multinomial variables in addition to the present support of ordinal, binary, and continuous variables.

The 3D modelling of indoor environments and the generation of process simulations play an important role in factory and assembly planning. In brownfield planning cases existing data are often outdated and incomplete especially for older plants, which were mostly planned in 2D. Thus, current environment models cannot be generated directly on the basis of existing data and a holistic approach on how to build such a factory model in a highly automated fashion is mostly non-existent. Major steps in generating an environment model in a production plant include data collection and pre-processing, object identification as well as pose estimation. In this work, we elaborate a methodical workflow, which starts with the digitalization of large-scale indoor environments and ends with the generation of a static environment or simulation model. The object identification step is realized using a Bayesian neural network capable of point cloud segmentation. We elaborate how the information on network uncertainty generated by a Bayesian segmentation framework can be used in order to build up a more accurate environment model. The steps of data collection and point cloud segmentation as well as the resulting model accuracy are evaluated on a real-world data set collected at the assembly line of a large-scale automotive production plant. The segmentation network is further evaluated on the publicly available Stanford Large-Scale 3D Indoor Spaces data set. The Bayesian segmentation network clearly surpasses the performance of the frequentist baseline and allows us to increase the accuracy of the model placement in a simulation scene considerably.