Measuring the Algorithmic Convergence of Randomized Ensembles: The Regression Setting

Estimating the Algorithmic Variance of Randomized Ensembles via the Bootstrap

Although the methods of bagging and random forests are some of the most widely used prediction methods, relatively little is known about their algorithmic convergence. In particular, there are not many theoretical guarantees for deciding when an ensemble is "large enough" --- so that its accuracy is close to that of an ideal infinite ensemble. Due to the fact that bagging and random forests are randomized algorithms, the choice of ensemble size is closely related to the notion of "algorithmic variance" (i.e. the variance of prediction error due only to the training algorithm). In the present w…

包含算法随机性的两阶段观测模型中的统计推断

Statistical inference in two-stage observation models including algorithmic randomness

针对含算法随机性的两阶段观测模型的统计推断难题，提出次随机化框架，通过多规模运行随机算法近似误差分布，无需估计冗余参数，在两类标准方法失效的场景中实现有效推断。

Estimating a sharp convergence bound for randomized ensembles

When randomized ensembles such as bagging or random forests are used for binary classification, the prediction error of the ensemble tends to decrease and stabilize as the number of classifiers increases. However, the precise relationship between prediction error and ensemble size is unknown in practice. In the standard case when classifiers are aggregated by majority vote, the present work offers a way to quantify this convergence in terms of "algorithmic variance," i.e. the variance of prediction error due only to the randomized training algorithm. Specifically, we study a theoretical upper …

Improved Policy Evaluation for Randomized Trials of Algorithmic Resource Allocation

We consider the task of evaluating policies of algorithmic resource allocation through randomized controlled trials (RCTs). Such policies are tasked with optimizing the utilization of limited intervention resources, with the goal of maximizing the benefits derived. Evaluation of such allocation policies through RCTs proves difficult, notwithstanding the scale of the trial, because the individuals' outcomes are inextricably interlinked through resource constraints controlling the policy decisions. Our key contribution is to present a new estimator leveraging our proposed novel concept, that inv…

Algorithmic Connections Between Active Learning and Stochastic Convex Optimization

Interesting theoretical associations have been established by recent papers between the fields of active learning and stochastic convex optimization due to the common role of feedback in sequential querying mechanisms. In this paper, we continue this thread in two parts by exploiting these relations for the first time to yield novel algorithms in both fields, further motivating the study of their intersection. First, inspired by a recent optimization algorithm that was adaptive to unknown uniform convexity parameters, we present a new active learning algorithm for one-dimensional thresholds th…

Statistical and Algorithmic Perspectives on Randomized Sketching for Ordinary Least-Squares -- ICML

We consider statistical and algorithmic aspects of solving large-scale least-squares (LS) problems using randomized sketching algorithms. Prior results show that, from an \emph{algorithmic perspective}, when using sketching matrices constructed from random projections and leverage-score sampling, if the number of samples $r$ much smaller than the original sample size $n$, then the worst-case (WC) error is the same as solving the original problem, up to a very small relative error. From a \emph{statistical perspective}, one typically considers the mean-squared error performance of randomized sk…