In many practical machine learning problems, the acquisition of labeled data is often expensive and/or time consuming. This motivates us to study a problem as follows: given a label budget, how to select data points to label such that the learning performance is optimized. We propose a selective labeling method by analyzing the out-of-sample error of Laplacian regularized Least Squares (LapRLS). In particular, we derive a deterministic out-of-sample error bound for LapRLS trained on subsampled data, and propose to select a subset of data points to label by minimizing this upper bound. Since the minimization is a combinational problem, we relax it into continuous domain and solve it by projected gradient descent. Experiments on benchmark datasets show that the proposed method outperforms the state-of-the-art methods.

In many practical machine learning problems, the acquisition of labeled data is often expensive and/or time consuming. This motivates us to study a problem as follows: given a label budget, how to select data points to label such that the learning performance is optimized. We propose a selective labeling method by analyzing the generalization error of Laplacian regularized Least Squares (LapRLS). In particular, we derive a deterministic generalization error bound for LapRLS trained on subsampled data, and propose to select a subset of data points to label by minimizing this upper bound. Since the minimization is a combinational problem, we relax it into continuous domain and solve it by projected gradient descent.

In many practical machine learning problems, the acquisition of labeled data is often expensive and/or time consuming. This motivates us to study a problem as follows: given a label budget, how to select data points to label such that the learning performance is optimized. We propose a selective labeling method by analyzing the out-of-sample error of Laplacian regularized Least Squares (LapRLS). In particular, we derive a deterministic out-of-sample error bound for LapRLS trained on subsampled data, and propose to select a subset of data points to label by minimizing this upper bound. Since the minimization is a combinational problem, we relax it into continuous domain and solve it by projected gradient descent. Experiments on benchmark datasets show that the proposed method outperforms the state-of-the-art methods.

In many practical machine learning problems, the acquisition of labeled data is often expensive and/or time consuming. This motivates us to study a problem as follows: given a label budget, how to select data points to label such that the learning performance is optimized. We propose a selective labeling method by analyzing the generalization error of Laplacian regularized Least Squares (LapRLS). In particular, we derive a deterministic generalization error bound for LapRLS trained on subsampled data, and propose to select a subset of data points to label by minimizing this upper bound. Since the minimization is a combinational problem, we relax it into continuous domain and solve it by projected gradient descent.

The smoothness hypothesis is critical for graph-based semi-supervised learning. This paper defines local smoothness, based on which a new algorithm, Reliable Label Inference via Smoothness Hypothesis (ReLISH), is proposed. ReLISH has produced smoother labels than some existing methods for both labeled and unlabeled examples. Theoretical analyses demonstrate good stability and generalizability of ReLISH. Using real-world datasets, our empirical analyses reveal that ReLISH is promising for both transductive and inductive tasks, when compared with representative algorithms, including Harmonic Functions, Local and Global Consistency, Constraint Metric Learning, Linear Neighborhood Propagation, and Manifold Regularization.

In many practical machine learning problems, the acquisition of labeled data is often expensive and/or time consuming. This motivates us to study a problem as follows: given a label budget, how to select data points to label such that the learning performance is optimized. We propose a selective labeling method by analyzing the generalization error of Laplacian regularized Least Squares (LapRLS). In particular, we derive a deterministic generalization error bound for LapRLS trained on subsampled data, and propose to select a subset of data points to label by minimizing this upper bound. Since the minimization is a combinational problem, we relax it into continuous domain and solve it by projected gradient descent. Experiments on benchmark datasets show that the proposed method outperforms the state-of-the-art methods.

In many real world applications, labeled data are usually expensive to get, while there may be a large amount of unlabeled data. To reduce the labeling cost, active learning attempts to discover the most informative data points for labeling. Recently, Optimal Experimental Design (OED) techniques have attracted an increasing amount of attention. OED is concerned with the design of experiments that minimizes variances of a parameterized model. Typical design criteria include D-, A-, and E-optimality. However, all these criteria are based on an ordinary linear regression model which aims to minimize the empirical error whereas the geometrical structure of the data space is not well respected. In this paper, we propose a novel optimal experimental design approach for active learning, called Laplacian G-Optimal Design (LapGOD), which considers both discriminating and geometrical structures. By using Laplacian Regularized Least Squares which incorporates manifold regularization into linear regression, our proposed algorithm selects those data points that minimizes the maximum variance of the predicted values on the data manifold. We also extend our algorithm to nonlinear case by using kernel trick. The experimental results on various image databases have shown that our proposed LapGOD active learning algorithm can significantly enhance the classification accuracy if the selected data points are used as training data.