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 called 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 method called the Generalized Low-Rank Update (GLRU) 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 SVM 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 amount of dataset 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

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 substructures, 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 (SPP) 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

Increased Level of Pericardial Insulin-Like Growth Factor-1 in Patients With Left Ventricular Dysfunction and Advanced Heart Failure

ObjectivesTo test the hypothesis that the cardiac insulin-like growth factor-1 (IGF-1) system is up-regulated in the failing heart, we measured the pericardial (cardiac) and plasma (circulating) IGF-1 levels in coronary artery disease patients.BackgroundLocal IGF-1 systems are regulated differently from the systemic IGF-1 system. The cardiac IGF-1 system is up-regulated by the increased left ventricular (LV) wall stress. However, it remains unknown how this system is affected in LV dysfunction and heart failure.MethodsWe measured the plasma and pericardial fluid levels of IGF-1 and brain natriuretic peptide (BNP) in 87 coronary artery disease patients undergoing cardiac surgery, and examined their relationships with LV function and heart failure severity. The expressions of IGF-1 and IGF-1 receptor proteins were examined in endomyocardial biopsies obtained from other patients with normal or impaired LV function.ResultsThe pericardial IGF-1 and BNP levels were positively correlated with the plasma BNP level (both p < 0.001). The pericardial IGF-1 level was increased in heart failure patients, whereas the plasma IGF-1 level was rather decreased. The pericardial IGF-1 level was inversely correlated with the LV ejection fraction (p < 0.001), whereas the plasma IGF-1 level was not. Positive immunostaining for IGF-1 and IGF-1 receptor proteins was enhanced in myocardial biopsies from failing hearts compared with those from nonfailing hearts.ConclusionsThe pericardial IGF-1 level was increased in patients with LV dysfunction and heart failure, whereas the plasma IGF-1 level was decreased. These results may indicate that up-regulation of the cardiac IGF-1 system serves as a compensatory mechanism for LV dysfunction