This research project delves into the intricacies of road traffic accidents severity in the UK, employing a potent combination of machine learning algorithms, econometric techniques, and traditional statistical methods to analyse longitudinal historical data. Our robust analysis framework includes descriptive, inferential, bivariate, and multivariate methodologies, correlation analysis: Pearson's and Spearman's Rank Correlation Coefficient, multiple and logistic regression models, Multicollinearity Assessment, and Model Validation. In addressing heteroscedasticity or autocorrelation in error terms, we've advanced the precision and reliability of our regression analyses using the Generalized Method of Moments (GMM). Additionally, our application of the Vector Autoregressive (VAR) model and the Autoregressive Integrated Moving Average (ARIMA) models have enabled accurate time-series forecasting. With this approach, we've achieved superior predictive accuracy, marked by a Mean Absolute Scaled Error (MASE) of 0.800 and a Mean Error (ME) of -73.80 compared to a naive forecast.

Prediction is a classic challenge in spatial statistics and the inclusion of spatial covariates can greatly improve predictive performance when incorporated into a model with latent spatial effects. It is desirable to develop flexible regression models that allow for nonlinearities and interactions in the covariate structure. Machine learning models have been suggested in the spatial context, allowing for spatial dependence in the residuals, but fail to provide reliable uncertainty estimates. In this paper, we investigate a novel combination of a Gaussian process spatial model and a Bayesian Additive Regression Tree (BART) model. The computational burden of the approach is reduced by combining Markov chain Monte Carlo (MCMC) with the Integrated Nested Laplace Approximation (INLA) technique. We study the performance of the method via simulations and use the model to predict anthropometric responses, collected via household cluster samples in Kenya.

In this paper we consider the setting where machine learning models are retrained on updated datasets in order to incorporate the most up-to-date information or reflect distribution shifts. We investigate whether one can infer information about these updates in the training data (e.g., changes to attribute values of records). Here, the adversary has access to snapshots of the machine learning model before and after the change in the dataset occurs. Contrary to the existing literature, we assume that an attribute of a single or multiple training data points are changed rather than entire data records are removed or added. We propose attacks based on the difference in the prediction confidence of the original model and the updated model. We evaluate our attack methods on two public datasets along with multi-layer perceptron and logistic regression models. We validate that two snapshots of the model can result in higher information leakage in comparison to having access to only the updated model. Moreover, we observe that data records with rare values are more vulnerable to attacks, which points to the disparate vulnerability of privacy attacks in the update setting. When multiple records with the same original attribute value are updated to the same new value (i.e., repeated changes), the attacker is more likely to correctly guess the updated values since repeated changes leave a larger footprint on the trained model. These observations point to vulnerability of machine learning models to attribute inference attacks in the update setting.

We investigate the problem of performing logistic regression on data collected from privacy-sensitive sellers. Since the data is private, sellers must be incentivized through payments to provide their data. Thus, the goal is to design a mechanism that optimizes a weighted combination of test loss, seller privacy, and payment, i.e., strikes a balance between multiple objectives of interest. We solve the problem by combining ideas from game theory, statistical learning theory, and differential privacy. The buyer's objective function can be highly non-convex. However, we show that, under certain conditions on the problem parameters, the problem can be convexified by using a change of variables. We also provide asymptotic results characterizing the buyer's test error and payments when the number of sellers becomes large. Finally, we demonstrate our ideas by applying them to a real healthcare data set.

Safe deployment of AI models requires proactive detection of potential prediction failures to prevent costly errors. While failure detection in classification problems has received significant attention, characterizing failure modes in regression tasks is more complicated and less explored. Existing approaches rely on epistemic uncertainties or feature inconsistency with the training distribution to characterize model risk. However, we show that uncertainties are necessary but insufficient to accurately characterize failure, owing to the various sources of error. In this paper, we propose PAGER (Principled Analysis of Generalization Errors in Regressors), a framework to systematically detect and characterize failures in deep regression models. Built upon the recently proposed idea of anchoring in deep models, PAGER unifies both epistemic uncertainties and novel, complementary non-conformity scores to organize samples into different risk regimes, thereby providing a comprehensive analysis of model errors. Additionally, we introduce novel metrics for evaluating failure detectors in regression tasks. We demonstrate the effectiveness of PAGER on synthetic and real-world benchmarks. Our results highlight the capability of PAGER to identify regions of accurate generalization and detect failure cases in out-of-distribution and out-of-support scenarios.

Differential privacy (DP) is the state-of-the-art framework for guaranteeing privacy for individuals when releasing aggregated statistics or building statistical/machine learning models from data. We develop the open-source R package DPpack that provides a large toolkit of differentially private analysis. The current version of DPpack implements three popular mechanisms for ensuring DP: Laplace, Gaussian, and exponential. Beyond that, DPpack provides a large toolkit of easily accessible privacy-preserving descriptive statistics functions. These include mean, variance, covariance, and quantiles, as well as histograms and contingency tables. Finally, DPpack provides user-friendly implementation of privacy-preserving versions of logistic regression, SVM, and linear regression, as well as differentially private hyperparameter tuning for each of these models. This extensive collection of implemented differentially private statistics and models permits hassle-free utilization of differential privacy principles in commonly performed statistical analysis. We plan to continue developing DPpack and make it more comprehensive by including more differentially private machine learning techniques, statistical modeling and inference in the future.

In conventional statistical and machine learning methods, it is typically assumed that the test data are identically distributed with the training data. However, this assumption does not always hold, especially in applications where the target population are not well-represented in the training data. This is a notable issue in health-related studies, where specific ethnic populations may be underrepresented, posing a significant challenge for researchers aiming to make statistical inferences about these minority groups. In this work, we present a novel approach to addressing this challenge in linear regression models. We organize the model parameters for all the sub-populations into a tensor. By studying a structured tensor completion problem, we can achieve robust domain generalization, i.e., learning about sub-populations with limited or no available data. Our method novelly leverages the structure of group labels and it can produce more reliable and interpretable generalization results. We establish rigorous theoretical guarantees for the proposed method and demonstrate its minimax optimality. To validate the effectiveness of our approach, we conduct extensive numerical experiments and a real data study focused on education level prediction for multiple ethnic groups, comparing our results with those obtained using other existing methods.

PD is linked to faster brain aging. Sex is recognized as an important factor in PD, such that males are twice as likely as females to have the disease and have more severe symptoms and a faster progression rate. Despite previous research, there remains a significant gap in understanding the function of sex in the process of brain aging in PD patients. The T1-weighted MRI-driven brain-predicted age difference was computed in a group of 373 PD patients from the PPMI database using a robust brain-age estimation framework that was trained on 949 healthy subjects. Linear regression models were used to investigate the association between brain-PAD and clinical variables in PD, stratified by sex. All female PD patients were used in the correlational analysis while the same number of males were selected based on propensity score matching method considering age, education level, age of symptom onset, and clinical symptom severity. Despite both patient groups being matched for demographics, motor and non-motor symptoms, it was observed that males with Parkinson's disease exhibited a significantly higher mean brain age-delta than their female counterparts . In the propensity score-matched PD male group, brain-PAD was found to be associated with a decline in general cognition, a worse degree of sleep behavior disorder, reduced visuospatial acuity, and caudate atrophy. Conversely, no significant links were observed between these factors and brain-PAD in the PD female group.

In recent years, there has been a growing interest in statistical methods that exhibit robust performance under distribution changes between training and test data. While most of the related research focuses on point predictions with the squared error loss, this article turns the focus towards probabilistic predictions, which aim to comprehensively quantify the uncertainty of an outcome variable given covariates. Within a causality-inspired framework, we investigate the invariance and robustness of probabilistic predictions with respect to proper scoring rules. We show that arbitrary distribution shifts do not, in general, admit invariant and robust probabilistic predictions, in contrast to the setting of point prediction. We illustrate how to choose evaluation metrics and restrict the class of distribution shifts to allow for identifiability and invariance in the prototypical Gaussian heteroscedastic linear model. Motivated by these findings, we propose a method to yield invariant probabilistic predictions, called IPP, and study the consistency of the underlying parameters. Finally, we demonstrate the empirical performance of our proposed procedure on simulated as well as on single-cell data.

We consider the problem of predicting an individual's identity from accelerometry data collected during walking. In a previous paper we introduced an approach that transforms the accelerometry time series into an image by constructing its complete empirical autocorrelation distribution. Predictors derived by partitioning this image into grid cells were used in logistic regression to predict individuals. Here we: (1) implement machine learning methods for prediction using the grid cell-derived predictors; (2) derive inferential methods to screen for the most predictive grid cells; and (3) develop a novel multivariate functional regression model that avoids partitioning of the predictor space into cells. Prediction methods are compared on two open source data sets: (1) accelerometry data collected from $32$ individuals walking on a $1.06$ kilometer path; and (2) accelerometry data collected from six repetitions of walking on a $20$ meter path on two separate occasions at least one week apart for $153$ study participants. In the $32$-individual study, all methods achieve at least $95$% rank-1 accuracy, while in the $153$-individual study, accuracy varies from $41$% to $98$%, depending on the method and prediction task. Methods provide insights into why some individuals are easier to predict than others.