Online Active Linear Regression via Thresholding

We consider the problem of online active learning to collect data for regression modeling. Specifically, we consider a decision maker with a limited experimentation budget who must efficiently learn an underlying linear population model. Our main contribution is a novel threshold-based algorithm for selection of most informative observations; we characterize its performance and fundamental lower bounds. We extend the algorithm and its guarantees to sparse linear regression in high-dimensional settings. Simulations suggest the algorithm is remarkably robust: it provides significant benefits over passive random sampling in real-world datasets that exhibit high nonlinearity and high dimensionality --- significantly reducing both the mean and variance of the squared error.Comment: Published in AAAI 201

Optimal Sample Selection Through Uncertainty Estimation and Its Application in Deep Learning

Modern deep learning heavily relies on large labeled datasets, which often comse with high costs in terms of both manual labeling and computational resources. To mitigate these challenges, researchers have explored the use of informative subset selection techniques, including coreset selection and active learning. Specifically, coreset selection involves sampling data with both input (\bx) and output (\by), active learning focuses solely on the input data (\bx). In this study, we present a theoretically optimal solution for addressing both coreset selection and active learning within the context of linear softmax regression. Our proposed method, COPS (unCertainty based OPtimal Sub-sampling), is designed to minimize the expected loss of a model trained on subsampled data. Unlike existing approaches that rely on explicit calculations of the inverse covariance matrix, which are not easily applicable to deep learning scenarios, COPS leverages the model's logits to estimate the sampling ratio. This sampling ratio is closely associated with model uncertainty and can be effectively applied to deep learning tasks. Furthermore, we address the challenge of model sensitivity to misspecification by incorporating a down-weighting approach for low-density samples, drawing inspiration from previous works. To assess the effectiveness of our proposed method, we conducted extensive empirical experiments using deep neural networks on benchmark datasets. The results consistently showcase the superior performance of COPS compared to baseline methods, reaffirming its efficacy

S-Rocket: Selective Random Convolution Kernels for Time Series Classification

Random convolution kernel transform (Rocket) is a fast, efficient, and novel approach for time series feature extraction using a large number of independent randomly initialized 1-D convolution kernels of different configurations. The output of the convolution operation on each time series is represented by a partial positive value (PPV). A concatenation of PPVs from all kernels is the input feature vector to a Ridge regression classifier. Unlike typical deep learning models, the kernels are not trained and there is no weighted/trainable connection between kernels or concatenated features and the classifier. Since these kernels are generated randomly, a portion of these kernels may not positively contribute in performance of the model. Hence, selection of the most important kernels and pruning the redundant and less important ones is necessary to reduce computational complexity and accelerate inference of Rocket for applications on the edge devices. Selection of these kernels is a combinatorial optimization problem. In this paper, we propose a scheme for selecting these kernels while maintaining the classification performance. First, the original model is pre-trained at full capacity. Then, a population of binary candidate state vectors is initialized where each element of a vector represents the active/inactive status of a kernel. A population-based optimization algorithm evolves the population in order to find a best state vector which minimizes the number of active kernels while maximizing the accuracy of the classifier. This activation function is a linear combination of the total number of active kernels and the classification accuracy of the pre-trained classifier with the active kernels. Finally, the selected kernels in the best state vector are utilized to train the Ridge regression classifier with the selected kernels