We consider the stochastic linear contextual bandit problem with high-dimensional features. We analyze the Thompson sampling (TS) algorithm, using special classes of sparsity-inducing priors (e.g. spike-and-slab) to model the unknown parameter, and provide a nearly optimal upper bound on the expected cumulative regret. To the best of our knowledge, this is the first work that provides theoretical guarantees of Thompson sampling in high dimensional and sparse contextual bandits. For faster computation, we use spike-and-slab prior to model the unknown parameter and variational inference instead of MCMC to approximate the posterior distribution. Extensive simulations demonstrate improved performance of our proposed algorithm over existing ones.

基于中心的聚类算法的最新进展通过隐式退火来打击贫穷的本地最小值，并使用一系列普遍的手段来打击。这些方法是劳埃德（Lloyd）著名的$ k $ -MEANS算法的变体，最适合于球形簇，例如由高斯数据引起的簇。在本文中，我们将这些算法的进步桥接为布雷格曼（Bregman）差异下的硬聚类的经典工作，这些工作享有指数级家庭分布的培养，因此非常适合由数据生成机制的广度引起的聚类对象。布雷格曼分歧的优雅特性使我们能够以简单透明的算法维护封闭的表单更新，此外，还引发了新的理论论点，以建立有限的样本范围，以放松在现有的艺术状态下做出的有限支持假设。此外，我们考虑对模拟实验进行彻底的经验分析和降雨数据的案例研究，发现所提出的方法在各种非高斯数据设置中都优于现有的同行方法。

在漂亮的广义框架下，过去的世纪已经广泛研究了线性预测问题。强大的统计文献中的最新进展允许我们通过手工（MOM）中位数的棱镜分析古典线性模型的强大版本。以零碎的方式结合这些方法可能导致临时程序，以及限制每个个人捐款的受限制理论结论可能不再有效。为了完全应对这些挑战，在这项研究中，我们提供了一个统一的强大框架，包括在希尔伯特空间上具有广泛的线性预测问题，与通用丢失功能相结合。值得注意的是，我们不需要对偏远数据点的分布（$ \ mathcal {o} $）的任何假设，也不需要依赖于依赖的支持的紧凑性（$ \ mathcal {i} $）。在双规范的温和条件下，我们展示了用于拼盘级别$ \ epsilon $，这些估算器达到$ O（\ max \ left \ {| \ mathcal {o} | ^ {1/2} n ^ {-1/2}，| \ mathcal {i} | ^ {1/2} n ^ {-1} n ^ { - 1} \ rick \} + \ epsilon）$，匹配文献中最着名的速率。此速率比$ O的经典速率略慢（n ^ { - 1/2}）$，表明我们需要在错误率方面支付价格以获得强大的估计。此外，我们表明，在额外的假设下，可以提高该速率以实现所​​谓的“快速速率”。

Lifelong learning aims to create AI systems that continuously and incrementally learn during a lifetime, similar to biological learning. Attempts so far have met problems, including catastrophic forgetting, interference among tasks, and the inability to exploit previous knowledge. While considerable research has focused on learning multiple input distributions, typically in classification, lifelong reinforcement learning (LRL) must also deal with variations in the state and transition distributions, and in the reward functions. Modulating masks, recently developed for classification, are particularly suitable to deal with such a large spectrum of task variations. In this paper, we adapted modulating masks to work with deep LRL, specifically PPO and IMPALA agents. The comparison with LRL baselines in both discrete and continuous RL tasks shows competitive performance. We further investigated the use of a linear combination of previously learned masks to exploit previous knowledge when learning new tasks: not only is learning faster, the algorithm solves tasks that we could not otherwise solve from scratch due to extremely sparse rewards. The results suggest that RL with modulating masks is a promising approach to lifelong learning, to the composition of knowledge to learn increasingly complex tasks, and to knowledge reuse for efficient and faster learning.

A framework for creating and updating digital twins for dynamical systems from a library of physics-based functions is proposed. The sparse Bayesian machine learning is used to update and derive an interpretable expression for the digital twin. Two approaches for updating the digital twin are proposed. The first approach makes use of both the input and output information from a dynamical system, whereas the second approach utilizes output-only observations to update the digital twin. Both methods use a library of candidate functions representing certain physics to infer new perturbation terms in the existing digital twin model. In both cases, the resulting expressions of updated digital twins are identical, and in addition, the epistemic uncertainties are quantified. In the first approach, the regression problem is derived from a state-space model, whereas in the latter case, the output-only information is treated as a stochastic process. The concepts of It\^o calculus and Kramers-Moyal expansion are being utilized to derive the regression equation. The performance of the proposed approaches is demonstrated using highly nonlinear dynamical systems such as the crack-degradation problem. Numerical results demonstrated in this paper almost exactly identify the correct perturbation terms along with their associated parameters in the dynamical system. The probabilistic nature of the proposed approach also helps in quantifying the uncertainties associated with updated models. The proposed approaches provide an exact and explainable description of the perturbations in digital twin models, which can be directly used for better cyber-physical integration, long-term future predictions, degradation monitoring, and model-agnostic control.

Dengue fever is a virulent disease spreading over 100 tropical and subtropical countries in Africa, the Americas, and Asia. This arboviral disease affects around 400 million people globally, severely distressing the healthcare systems. The unavailability of a specific drug and ready-to-use vaccine makes the situation worse. Hence, policymakers must rely on early warning systems to control intervention-related decisions. Forecasts routinely provide critical information for dangerous epidemic events. However, the available forecasting models (e.g., weather-driven mechanistic, statistical time series, and machine learning models) lack a clear understanding of different components to improve prediction accuracy and often provide unstable and unreliable forecasts. This study proposes an ensemble wavelet neural network with exogenous factor(s) (XEWNet) model that can produce reliable estimates for dengue outbreak prediction for three geographical regions, namely San Juan, Iquitos, and Ahmedabad. The proposed XEWNet model is flexible and can easily incorporate exogenous climate variable(s) confirmed by statistical causality tests in its scalable framework. The proposed model is an integrated approach that uses wavelet transformation into an ensemble neural network framework that helps in generating more reliable long-term forecasts. The proposed XEWNet allows complex non-linear relationships between the dengue incidence cases and rainfall; however, mathematically interpretable, fast in execution, and easily comprehensible. The proposal's competitiveness is measured using computational experiments based on various statistical metrics and several statistical comparison tests. In comparison with statistical, machine learning, and deep learning methods, our proposed XEWNet performs better in 75% of the cases for short-term and long-term forecasting of dengue incidence.

We propose a novel model agnostic data-driven reliability analysis framework for time-dependent reliability analysis. The proposed approach -- referred to as MAntRA -- combines interpretable machine learning, Bayesian statistics, and identifying stochastic dynamic equation to evaluate reliability of stochastically-excited dynamical systems for which the governing physics is \textit{apriori} unknown. A two-stage approach is adopted: in the first stage, an efficient variational Bayesian equation discovery algorithm is developed to determine the governing physics of an underlying stochastic differential equation (SDE) from measured output data. The developed algorithm is efficient and accounts for epistemic uncertainty due to limited and noisy data, and aleatoric uncertainty because of environmental effect and external excitation. In the second stage, the discovered SDE is solved using a stochastic integration scheme and the probability failure is computed. The efficacy of the proposed approach is illustrated on three numerical examples. The results obtained indicate the possible application of the proposed approach for reliability analysis of in-situ and heritage structures from on-site measurements.

Transformer layers, which use an alternating pattern of multi-head attention and multi-layer perceptron (MLP) layers, provide an effective tool for a variety of machine learning problems. As the transformer layers use residual connections to avoid the problem of vanishing gradients, they can be viewed as the numerical integration of a differential equation. In this extended abstract, we build upon this connection and propose a modification of the internal architecture of a transformer layer. The proposed model places the multi-head attention sublayer and the MLP sublayer parallel to each other. Our experiments show that this simple modification improves the performance of transformer networks in multiple tasks. Moreover, for the image classification task, we show that using neural ODE solvers with a sophisticated integration scheme further improves performance.

Consider a scenario in one-shot query-guided object localization where neither an image of the object nor the object category name is available as a query. In such a scenario, a hand-drawn sketch of the object could be a choice for a query. However, hand-drawn crude sketches alone, when used as queries, might be ambiguous for object localization, e.g., a sketch of a laptop could be confused for a sofa. On the other hand, a linguistic definition of the category, e.g., a small portable computer small enough to use in your lap" along with the sketch query, gives better visual and semantic cues for object localization. In this work, we present a multimodal query-guided object localization approach under the challenging open-set setting. In particular, we use queries from two modalities, namely, hand-drawn sketch and description of the object (also known as gloss), to perform object localization. Multimodal query-guided object localization is a challenging task, especially when a large domain gap exists between the queries and the natural images, as well as due to the challenge of combining the complementary and minimal information present across the queries. For example, hand-drawn crude sketches contain abstract shape information of an object, while the text descriptions often capture partial semantic information about a given object category. To address the aforementioned challenges, we present a novel cross-modal attention scheme that guides the region proposal network to generate object proposals relevant to the input queries and a novel orthogonal projection-based proposal scoring technique that scores each proposal with respect to the queries, thereby yielding the final localization results. ...

Labeling a module defective or non-defective is an expensive task. Hence, there are often limits on how much-labeled data is available for training. Semi-supervised classifiers use far fewer labels for training models, but there are numerous semi-supervised methods, including self-labeling, co-training, maximal-margin, and graph-based methods, to name a few. Only a handful of these methods have been tested in SE for (e.g.) predicting defects and even that, those tests have been on just a handful of projects. This paper takes a wide range of 55 semi-supervised learners and applies these to over 714 projects. We find that semi-supervised "co-training methods" work significantly better than other approaches. However, co-training needs to be used with caution since the specific choice of co-training methods needs to be carefully selected based on a user's specific goals. Also, we warn that a commonly-used co-training method ("multi-view"-- where different learners get different sets of columns) does not improve predictions (while adding too much to the run time costs 11 hours vs. 1.8 hours). Those cautions stated, we find using these "co-trainers," we can label just 2.5% of data, then make predictions that are competitive to those using 100% of the data. It is an open question worthy of future work to test if these reductions can be seen in other areas of software analytics. All the codes used and datasets analyzed during the current study are available in the https://GitHub.com/Suvodeep90/Semi_Supervised_Methods.