We address the problem of active logistic regression in the realizable setting. It is well known that active learning can require exponentially fewer label queries compared to passive learning, in some cases using $\log \frac{1}{\eps}$ rather than $\poly(1/\eps)$ labels to get error $\eps$ larger than the optimum. We present the first algorithm that is polynomially competitive with the optimal algorithm on every input instance, up to a factor $d^2$ and factors polylogarithmic in the error and domain size. In particular, on a simple family of logistic threshold instances with a uniform distribution, our algorithm uses $\polylog(1/\eps)$ labels, whereas every passive learner requires $\Omega(1/\eps^2)$ labels. Our algorithm is based on sampling and can be extended to learn more general class of functions. We further support our theoretical results with experiments demonstrating performance gains for logistic regression compared to existing active learning algorithms.
In rapidly evolving e-commerce industry, the capability of selecting high-quality data for model training is essential. This study introduces the High-Utility Sequential Pattern Mining using SHAP values (HUSPM-SHAP) model, a utility mining-based active learning strategy to tackle this challenge. We found that the parameter settings for positive and negative SHAP values impact the model's mining outcomes, introducing a key consideration into the active learning framework. Through extensive experiments aimed at predicting behaviors that do lead to purchases or not, the designed HUSPM-SHAP model demonstrates its superiority across diverse scenarios. The model's ability to mitigate labeling needs while maintaining high predictive performance is highlighted. Our findings demonstrate the model's capability to refine e-commerce data processing, steering towards more streamlined, cost-effective prediction modeling.
For some hypothesis classes and input distributions, active agnostic learning needs exponentially fewer samples than passive learning; for other classes and distributions, it offers little to no improvement. The most popular algorithms for agnostic active learning express their performance in terms of a parameter called the disagreement coefficient, but it is known that these algorithms are inefficient on some inputs. We take a different approach to agnostic active learning, getting an algorithm that is competitive with the optimal algorithm for any binary hypothesis class $H$ and distribution $D_X$ over $X$. In particular, if any algorithm can use $m^*$ queries to get $O(\eta)$ error, then our algorithm uses $O(m^* \log |H|)$ queries to get $O(\eta)$ error. Our algorithm lies in the vein of the splitting-based approach of Dasgupta [2004], which gets a similar result for the realizable ($\eta = 0$) setting. We also show that it is NP-hard to do better than our algorithm's $O(\log |H|)$ overhead in general.