The seminal work of Cohen and Peng introduced Lewis weight sampling to the theoretical computer science community, yielding fast row sampling algorithms for approximating $d$-dimensional subspaces of $\ell_p$ up to $(1+\epsilon)$ error. Several works have extended this important primitive to other settings, including the online coreset and sliding window models. However, these results are only for $p\in\{1,2\}$, and results for $p=1$ require a suboptimal $\tilde O(d^2/\epsilon^2)$ samples. In this work, we design the first nearly optimal $\ell_p$ subspace embeddings for all $p\in(0,\infty)$ in the online coreset and sliding window models. In both models, our algorithms store $\tilde O(d^{1\lor(p/2)}/\epsilon^2)$ rows. This answers a substantial generalization of the main open question of [BDMMUWZ2020], and gives the first results for all $p\notin\{1,2\}$. Towards our result, we give the first analysis of "one-shot'' Lewis weight sampling of sampling rows proportionally to their Lewis weights, with sample complexity $\tilde O(d^{p/2}/\epsilon^2)$ for $p>2$. Previously, this scheme was only known to have sample complexity $\tilde O(d^{p/2}/\epsilon^5)$, whereas $\tilde O(d^{p/2}/\epsilon^2)$ is known if a more sophisticated recursive sampling is used. The recursive sampling cannot be implemented online, thus necessitating an analysis of one-shot Lewis weight sampling. Our analysis uses a novel connection to online numerical linear algebra. As an application, we obtain the first one-pass streaming coreset algorithms for $(1+\epsilon)$ approximation of important generalized linear models, such as logistic regression and $p$-probit regression. Our upper bounds are parameterized by a complexity parameter $\mu$ introduced by [MSSW2018], and we show the first lower bounds showing that a linear dependence on $\mu$ is necessary.

Adapting upper-limb impedance (i.e., stiffness, damping, inertia) is essential for humans interacting with dynamic environments for executing grasping or manipulation tasks. On the other hand, control methods designed for state-of-the-art upper-limb prostheses infer motor intent from surface electromyography (sEMG) signals in terms of joint kinematics, but they fail to infer and use the underlying impedance properties of the limb. We present a framework that allows a human user to simultaneously control the kinematics, stiffness, and damping of a simulated robot through wrist's flexion-extension. The framework includes muscle-tendon units and a forward dynamics block to estimate the motor intent from sEMG signals, and a variable impedance controller that implements the estimated intent on the robot, allowing the user to adapt the robot's kinematics and dynamics online. We evaluate our framework with 8 able-bodied subjects and an amputee during reaching tasks performed in free space, and in the presence of unexpected external perturbations that require adaptation of the wrist impedance to ensure stable interaction with the environment. We experimentally demonstrate that our approach outperforms a data-driven baseline in terms of its ability to adapt to external perturbations, overall controllability, and feedback from participants.

In many high-dimensional prediction or classification tasks, complementary data on the features are available, e.g. prior biological knowledge on (epi)genetic markers. Here we consider tasks with numerical prior information that provide an insight into the importance (weight) and the direction (sign) of the feature effects, e.g. regression coefficients from previous studies. We propose an approach for integrating multiple sources of such prior information into penalised regression. If suitable co-data are available, this improves the predictive performance, as shown by simulation and application. The proposed method is implemented in the R package `transreg' (https://github.com/lcsb-bds/transreg).

We extend best-subset selection to linear Multi-Task Learning (MTL), where a set of linear models are jointly trained on a collection of datasets (``tasks''). Allowing the regression coefficients of tasks to have different sparsity patterns (i.e., different supports), we propose a modeling framework for MTL that encourages models to share information across tasks, for a given covariate, through separately 1) shrinking the coefficient supports together, and/or 2) shrinking the coefficient values together. This allows models to borrow strength during variable selection even when the coefficient values differ markedly between tasks. We express our modeling framework as a Mixed-Integer Program, and propose efficient and scalable algorithms based on block coordinate descent and combinatorial local search. We show our estimator achieves statistically optimal prediction rates. Importantly, our theory characterizes how our estimator leverages the shared support information across tasks to achieve better variable selection performance. We evaluate the performance of our method in simulations and two biology applications. Our proposed approaches outperform other sparse MTL methods in variable selection and prediction accuracy. Interestingly, penalties that shrink the supports together often outperform penalties that shrink the coefficient values together. We will release an R package implementing our methods.

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.