Efficient model selection for predictive pattern mining model by safe pattern pruning.

Predictive pattern mining is an approach used to construct prediction models when the input is represented by structured data, such as sets, graphs, and sequences. The main idea behind predictive pattern mining is to build a prediction model by considering unified inconsistent notation sub-structures, such as subsets, subgraphs, and subsequences (referred to as patterns), present in the structured data as features of the model. The primary challenge in predictive pattern mining lies in the exponential growth of the number of patterns with the complexity of the structured data. In this study, we propose the safe pattern pruning method to address the explosion of pattern numbers in predictive pattern mining. We also discuss how it can be effectively employed throughout the entire model building process in practical data analysis. To demonstrate the effectiveness of the proposed method, we conduct numerical experiments on regression and classification problems involving sets, graphs, and sequences.

Generalized Low-Rank Update: Model Parameter Bounds for Low-Rank Training Data Modifications.

In this study, we have developed an incremental machine learning (ML) method that efficiently obtains the optimal model when a small number of instances or features are added or removed. This problem holds practical importance in model selection, such as cross-validation (CV) and feature selection. Among the class of ML methods known as linear estimators, there exists an efficient model update framework, the low-rank update, that can effectively handle changes in a small number of rows and columns within the data matrix. However, for ML methods beyond linear estimators, there is currently no comprehensive framework available to obtain knowledge about the updated solution within a specific computational complexity. In light of this, our study introduces a the generalized low-rank update (GLRU) method, which extends the low-rank update framework of linear estimators to ML methods formulated as a certain class of regularized empirical risk minimization, including commonly used methods such as support vector machines and logistic regression. The proposed GLRU method not only expands the range of its applicability but also provides information about the updated solutions with a computational complexity proportional to the number of data set changes. To demonstrate the effectiveness of the GLRU method, we conduct experiments showcasing its efficiency in performing cross-validation and feature selection compared to other baseline methods.