Agents that assist people need to have well-initialized policies that can adapt quickly to align with their partners' reward functions. Initializing policies to maximize performance with unknown partners can be achieved by bootstrapping nonlinear models using imitation learning over large, offline datasets. Such policies can require prohibitive computation to fine-tune in-situ and therefore may miss critical run-time information about a partner's reward function as expressed through their immediate behavior. In contrast, online logistic regression using low-capacity models performs rapid inference and fine-tuning updates and thus can make effective use of immediate in-task behavior for reward function alignment. However, these low-capacity models cannot be bootstrapped as effectively by offline datasets and thus have poor initializations. We propose BLR-HAC, Bootstrapped Logistic Regression for Human Agent Collaboration, which bootstraps large nonlinear models to learn the parameters of a low-capacity model which then uses online logistic regression for updates during collaboration. We test BLR-HAC in a simulated surface rearrangement task and demonstrate that it achieves higher zero-shot accuracy than shallow methods and takes far less computation to adapt online while still achieving similar performance to fine-tuned, large nonlinear models. For code, please see our project page https://sites.google.com/view/blr-hac.

We introduce a model of online algorithms subject to strict constraints on data retention. An online learning algorithm encounters a stream of data points, one per round, generated by some stationary process. Crucially, each data point can request that it be removed from memory $m$ rounds after it arrives. To model the impact of removal, we do not allow the algorithm to store any information or calculations between rounds other than a subset of the data points (subject to the retention constraints). At the conclusion of the stream, the algorithm answers a statistical query about the full dataset. We ask: what level of performance can be guaranteed as a function of $m$? We illustrate this framework for multidimensional mean estimation and linear regression problems. We show it is possible to obtain an exponential improvement over a baseline algorithm that retains all data as long as possible. Specifically, we show that $m = \textsc{Poly}(d, \log(1/\epsilon))$ retention suffices to achieve mean squared error $\epsilon$ after observing $O(1/\epsilon)$ $d$-dimensional data points. This matches the error bound of the optimal, yet infeasible, algorithm that retains all data forever. We also show a nearly matching lower bound on the retention required to guarantee error $\epsilon$. One implication of our results is that data retention laws are insufficient to guarantee the right to be forgotten even in a non-adversarial world in which firms merely strive to (approximately) optimize the performance of their algorithms. Our approach makes use of recent developments in the multidimensional random subset sum problem to simulate the progression of stochastic gradient descent under a model of adversarial noise, which may be of independent interest.

This paper explores the field of semi-supervised Fr\'echet regression, driven by the significant costs associated with obtaining non-Euclidean labels. Methodologically, we propose two novel methods: semi-supervised NW Fr\'echet regression and semi-supervised kNN Fr\'echet regression, both based on graph distance acquired from all feature instances. These methods extend the scope of existing semi-supervised Euclidean regression methods. We establish their convergence rates with limited labeled data and large amounts of unlabeled data, taking into account the low-dimensional manifold structure of the feature space. Through comprehensive simulations across diverse settings and applications to real data, we demonstrate the superior performance of our methods over their supervised counterparts. This study addresses existing research gaps and paves the way for further exploration and advancements in the field of semi-supervised Fr\'echet regression.

Constrained learning has become increasingly important, especially in the realm of algorithmic fairness and machine learning. In these settings, predictive models are developed specifically to satisfy pre-defined notions of fairness. Here, we study the general problem of constrained statistical machine learning through a statistical functional lens. We consider learning a function-valued parameter of interest under the constraint that one or several pre-specified real-valued functional parameters equal zero or are otherwise bounded. We characterize the constrained functional parameter as the minimizer of a penalized risk criterion using a Lagrange multiplier formulation. We show that closed-form solutions for the optimal constrained parameter are often available, providing insight into mechanisms that drive fairness in predictive models. Our results also suggest natural estimators of the constrained parameter that can be constructed by combining estimates of unconstrained parameters of the data generating distribution. Thus, our estimation procedure for constructing fair machine learning algorithms can be applied in conjunction with any statistical learning approach and off-the-shelf software. We demonstrate the generality of our method by explicitly considering a number of examples of statistical fairness constraints and implementing the approach using several popular learning approaches.

This research employs Gaussian Process Regression (GPR) with an ensemble kernel, integrating Exponential Squared, Revised Mat\'ern, and Rational Quadratic kernels to analyze pharmaceutical sales data. Bayesian optimization was used to identify optimal kernel weights: 0.76 for Exponential Squared, 0.21 for Revised Mat\'ern, and 0.13 for Rational Quadratic. The ensemble kernel demonstrated superior performance in predictive accuracy, achieving an \( R^2 \) score near 1.0, and significantly lower values in Mean Squared Error (MSE), Mean Absolute Error (MAE), and Root Mean Squared Error (RMSE). These findings highlight the efficacy of ensemble kernels in GPR for predictive analytics in complex pharmaceutical sales datasets.

This article introduces differentially private log-location-scale (DP-LLS) regression models, which incorporate differential privacy into LLS regression through the functional mechanism. The proposed models are established by injecting noise into the log-likelihood function of LLS regression for perturbed parameter estimation. We will derive the sensitivities utilized to determine the magnitude of the injected noise and prove that the proposed DP-LLS models satisfy $\epsilon$-differential privacy. In addition, we will conduct simulations and case studies to evaluate the performance of the proposed models. The findings suggest that predictor dimension, training sample size, and privacy budget are three key factors impacting the performance of the proposed DP-LLS regression models. Moreover, the results indicate that a sufficiently large training dataset is needed to simultaneously ensure decent performance of the proposed models and achieve a satisfactory level of privacy protection.

Social science research often hinges on the relationship between categorical variables and outcomes. We introduce CAVIAR, a novel method for embedding categorical variables that assume values in a high-dimensional ambient space but are sampled from an underlying manifold. Our theoretical and numerical analyses outline challenges posed by such categorical variables in causal inference. Specifically, dynamically varying and sparse levels can lead to violations of the Donsker conditions and a failure of the estimation functionals to converge to a tight Gaussian process. Traditional approaches, including the exclusion of rare categorical levels and principled variable selection models like LASSO, fall short. CAVIAR embeds the data into a lower-dimensional global coordinate system. The mapping can be derived from both structured and unstructured data, and ensures stable and robust estimates through dimensionality reduction. In a dataset of direct-to-consumer apparel sales, we illustrate how high-dimensional categorical variables, such as zip codes, can be succinctly represented, facilitating inference and analysis.

This study examines the effects of de-globalization trends on international trade networks and their role in improving forecasts for economic growth. Using section-level trade data from nearly 200 countries from 2010 to 2022, we identify significant shifts in the network topology driven by rising trade policy uncertainty. Our analysis highlights key global players through centrality rankings, with the United States, China, and Germany maintaining consistent dominance. Using a horse race of supervised regressors, we find that network topology descriptors evaluated from section-specific trade networks substantially enhance the quality of a country's GDP growth forecast. We also find that non-linear models, such as Random Forest, XGBoost, and LightGBM, outperform traditional linear models used in the economics literature. Using SHAP values to interpret these non-linear model's predictions, we find that about half of most important features originate from the network descriptors, underscoring their vital role in refining forecasts. Moreover, this study emphasizes the significance of recent economic performance, population growth, and the primary sector's influence in shaping economic growth predictions, offering novel insights into the intricacies of economic growth forecasting.

An exponentially weighted moving model (EWMM) for a vector time series fits a new data model each time period, based on an exponentially fading loss function on past observed data. The well known and widely used exponentially weighted moving average (EWMA) is a special case that estimates the mean using a square loss function. For quadratic loss functions EWMMs can be fit using a simple recursion that updates the parameters of a quadratic function. For other loss functions, the entire past history must be stored, and the fitting problem grows in size as time increases. We propose a general method for computing an approximation of EWMM, which requires storing only a window of a fixed number of past samples, and uses an additional quadratic term to approximate the loss associated with the data before the window. This approximate EWMM relies on convex optimization, and solves problems that do not grow with time. We compare the estimates produced by our approximation with the estimates from the exact EWMM method.

We consider the problem of localizing change points in high-dimensional linear regression. We propose an Approximate Message Passing (AMP) algorithm for estimating both the signals and the change point locations. Assuming Gaussian covariates, we give an exact asymptotic characterization of its estimation performance in the limit where the number of samples grows proportionally to the signal dimension. Our algorithm can be tailored to exploit any prior information on the signal, noise, and change points. It also enables uncertainty quantification in the form of an efficiently computable approximate posterior distribution, whose asymptotic form we characterize exactly. We validate our theory via numerical experiments, and demonstrate the favorable performance of our estimators on both synthetic data and images.