This study verified the effectiveness of Donald Trump's Twitter campaign in guiding agen-da-setting and deflecting political risk and examined Trump's Twitter communication strategy and explores the communication effects of his tweet content during Covid-19 pandemic. We collected all tweets posted by Trump on the Twitter platform from January 1, 2020 to December 31, 2020.We used Ordinary Least Squares (OLS) regression analysis with a fixed effects model to analyze the existence of the Twitter strategy. The correlation between the number of con-firmed daily Covid-19 diagnoses and the number of particular thematic tweets was investigated using time series analysis. Empirical analysis revealed Twitter's strategy is used to divert public attention from negative Covid-19 reports during the epidemic, and it posts a powerful political communication effect on Twitter. However, findings suggest that Trump did not use false claims to divert political risk and shape public opinion.

Current practice in interpretable machine learning often focuses on explaining the final model trained from data, e.g., by using the Shapley additive explanations (SHAP) method. The recently developed Shapley variable importance cloud (ShapleyVIC) extends the current practice to a group of "nearly optimal models" to provide comprehensive and robust variable importance assessments, with estimated uncertainty intervals for a more complete understanding of variable contributions to predictions. ShapleyVIC was initially developed for applications with traditional regression models, and the benefits of ShapleyVIC inference have been demonstrated in real-life prediction tasks using the logistic regression model. However, as a model-agnostic approach, ShapleyVIC application is not limited to such scenarios. In this work, we extend ShapleyVIC implementation for machine learning models to enable wider applications, and propose it as a useful complement to the current SHAP analysis to enable more trustworthy applications of these black-box models.

Outlier-robust estimation is a fundamental problem and has been extensively investigated by statisticians and practitioners. The last few years have seen a convergence across research fields towards "algorithmic robust statistics", which focuses on developing tractable outlier-robust techniques for high-dimensional estimation problems. Despite this convergence, research efforts across fields have been mostly disconnected from one another. This monograph bridges recent work on certifiable outlier-robust estimation for geometric perception in robotics and computer vision with parallel work in robust statistics. In particular, we adapt and extend recent results on robust linear regression (applicable to the low-outlier regime with << 50% outliers) and list-decodable regression (applicable to the high-outlier regime with >> 50% outliers) to the setup commonly found in robotics and vision, where (i) variables (e.g., rotations, poses) belong to a non-convex domain, (ii) measurements are vector-valued, and (iii) the number of outliers is not known a priori. The emphasis here is on performance guarantees: rather than proposing radically new algorithms, we provide conditions on the input measurements under which modern estimation algorithms (possibly after small modifications) are guaranteed to recover an estimate close to the ground truth in the presence of outliers. These conditions are what we call an "estimation contract". Besides the proposed extensions of existing results, we believe the main contributions of this monograph are (i) to unify parallel research lines by pointing out commonalities and differences, (ii) to introduce advanced material (e.g., sum-of-squares proofs) in an accessible and self-contained presentation for the practitioner, and (iii) to point out a few immediate opportunities and open questions in outlier-robust geometric perception.

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Neural networks (NN) play a central role in modern Artificial intelligence (AI) technology and has been successfully used in areas such as natural language processing and image recognition. While majority of NN applications focus on prediction and classification, there are increasing interests in studying statistical inference of neural networks. The study of NN statistical inference can enhance our understanding of NN statistical proprieties. Moreover, it can facilitate the NN-based hypothesis testing that can be applied to hypothesis-driven clinical and biomedical research. In this paper, we propose a sieve quasi-likelihood ratio test based on NN with one hidden layer for testing complex associations. The test statistic has asymptotic chi-squared distribution, and therefore it is computationally efficient and easy for implementation in real data analysis. The validity of the asymptotic distribution is investigated via simulations. Finally, we demonstrate the use of the proposed test by performing a genetic association analysis of the sequencing data from Alzheimer's Disease Neuroimaging Initiative (ADNI).

Flooding is one of the most disastrous natural hazards, responsible for substantial economic losses. A predictive model for flood-induced financial damages is useful for many applications such as climate change adaptation planning and insurance underwriting. This research assesses the predictive capability of regressors constructed on the National Flood Insurance Program (NFIP) dataset using neural networks (Conditional Generative Adversarial Networks), decision trees (Extreme Gradient Boosting), and kernel-based regressors (Gaussian Process). The assessment highlights the most informative predictors for regression. The distribution for claims amount inference is modeled with a Burr distribution permitting the introduction of a bias correction scheme and increasing the regressor's predictive capability. Aiming to study the interaction with physical variables, we incorporate Daymet rainfall estimation to NFIP as an additional predictor. A study on the coastal counties in the eight US South-West states resulted in an $R^2=0.807$. Further analysis of 11 counties with a significant number of claims in the NFIP dataset reveals that Extreme Gradient Boosting provides the best results, that bias correction significantly improves the similarity with the reference distribution, and that the rainfall predictor strengthens the regressor performance.

The geographically weighted regression (GWR) is an essential tool for estimating the spatial variation of relationships between dependent and independent variables in geographical contexts. However, GWR suffers from the problem that classical linear regressions, which compose the GWR model, are more prone to be underfitting, especially for significant volume and complex nonlinear data, causing inferior comparative performance. Nevertheless, some advanced models, such as the decision tree and the support vector machine, can learn features from complex data more effectively while they cannot provide explainable quantification for the spatial variation of localized relationships. To address the above issues, we propose a geographically gradient boosting weighted regression model, GWRBoost, that applies the localized additive model and gradient boosting optimization method to alleviate underfitting problems and retains explainable quantification capability for spatially-varying relationships between geographically located variables. Furthermore, we formulate the computation method of the Akaike information score for the proposed model to conduct the comparative analysis with the classic GWR algorithm. Simulation experiments and the empirical case study are applied to prove the efficient performance and practical value of GWRBoost. The results show that our proposed model can reduce the RMSE by 18.3% in parameter estimation accuracy and AICc by 67.3% in the goodness of fit.

Hydrocarbon prospect risking is a critical application in geophysics predicting well outcomes from a variety of data including geological, geophysical, and other information modalities. Traditional routines require interpreters to go through a long process to arrive at the probability of success of specific outcomes. AI has the capability to automate the process but its adoption has been limited thus far owing to a lack of transparency in the way complicated, black box models generate decisions. We demonstrate how LIME -- a model-agnostic explanation technique -- can be used to inject trust in model decisions by uncovering the model's reasoning process for individual predictions. It generates these explanations by fitting interpretable models in the local neighborhood of specific datapoints being queried. On a dataset of well outcomes and corresponding geophysical attribute data, we show how LIME can induce trust in model's decisions by revealing the decision-making process to be aligned to domain knowledge. Further, it has the potential to debug mispredictions made due to anomalous patterns in the data or faulty training datasets.

In a high dimensional linear predictive regression where the number of potential predictors can be larger than the sample size, we consider using LASSO, a popular L1-penalized regression method, to estimate the sparse coefficients when many unit root regressors are present. Consistency of LASSO relies on two building blocks: the deviation bound of the cross product of the regressors and the error term, and the restricted eigenvalue of the Gram matrix of the regressors. In our setting where unit root regressors are driven by temporal dependent non-Gaussian innovations, we establish original probabilistic bounds for these two building blocks. The bounds imply that the rates of convergence of LASSO are different from those in the familiar cross sectional case. In practical applications given a mixture of stationary and nonstationary predictors, asymptotic guarantee of LASSO is preserved if all predictors are scale-standardized. In an empirical example of forecasting the unemployment rate with many macroeconomic time series, strong performance is delivered by LASSO when the initial specification is guided by macroeconomic domain expertise.

Most regularized tensor regression research focuses on tensors predictors with scalars responses or vectors predictors to tensors responses. We consider the sparse low rank tensor on tensor regression where predictors $\mathcal{X}$ and responses $\mathcal{Y}$ are both high-dimensional tensors. By demonstrating that the general inner product or the contracted product on a unit rank tensor can be decomposed into standard inner products and outer products, the problem can be simply transformed into a tensor to scalar regression followed by a tensor decomposition. So we propose a fast solution based on stagewise search composed by contraction part and generation part which are optimized alternatively. We successfully demonstrate our method can out perform current methods in terms of accuracy and predictors selection by effectively incorporating the structural information.