Semi-supervised Predictive Clustering Trees for (Hierarchical) Multi-label Classification

Semi-supervised learning (SSL) is a common approach to learning predictive models using not only labeled examples, but also unlabeled examples. While SSL for the simple tasks of classification and regression has received a lot of attention from the research community, this is not properly investigated for complex prediction tasks with structurally dependent variables. This is the case of multi-label classification and hierarchical multi-label classification tasks, which may require additional information, possibly coming from the underlying distribution in the descriptive space provided by unlabeled examples, to better face the challenging task of predicting simultaneously multiple class labels. In this paper, we investigate this aspect and propose a (hierarchical) multi-label classification method based on semi-supervised learning of predictive clustering trees. We also extend the method towards ensemble learning and propose a method based on the random forest approach. Extensive experimental evaluation conducted on 23 datasets shows significant advantages of the proposed method and its extension with respect to their supervised counterparts. Moreover, the method preserves interpretability and reduces the time complexity of classical tree-based models

NCART: Neural Classification and Regression Tree for Tabular Data

Deep learning models have become popular in the analysis of tabular data, as they address the limitations of decision trees and enable valuable applications like semi-supervised learning, online learning, and transfer learning. However, these deep-learning approaches often encounter a trade-off. On one hand, they can be computationally expensive when dealing with large-scale or high-dimensional datasets. On the other hand, they may lack interpretability and may not be suitable for small-scale datasets. In this study, we propose a novel interpretable neural network called Neural Classification and Regression Tree (NCART) to overcome these challenges. NCART is a modified version of Residual Networks that replaces fully-connected layers with multiple differentiable oblivious decision trees. By integrating decision trees into the architecture, NCART maintains its interpretability while benefiting from the end-to-end capabilities of neural networks. The simplicity of the NCART architecture makes it well-suited for datasets of varying sizes and reduces computational costs compared to state-of-the-art deep learning models. Extensive numerical experiments demonstrate the superior performance of NCART compared to existing deep learning models, establishing it as a strong competitor to tree-based models

Semi-supervised Learning for Photometric Supernova Classification

We present a semi-supervised method for photometric supernova typing. Our approach is to first use the nonlinear dimension reduction technique diffusion map to detect structure in a database of supernova light curves and subsequently employ random forest classification on a spectroscopically confirmed training set to learn a model that can predict the type of each newly observed supernova. We demonstrate that this is an effective method for supernova typing. As supernova numbers increase, our semi-supervised method efficiently utilizes this information to improve classification, a property not enjoyed by template based methods. Applied to supernova data simulated by Kessler et al. (2010b) to mimic those of the Dark Energy Survey, our methods achieve (cross-validated) 95% Type Ia purity and 87% Type Ia efficiency on the spectroscopic sample, but only 50% Type Ia purity and 50% efficiency on the photometric sample due to their spectroscopic follow-up strategy. To improve the performance on the photometric sample, we search for better spectroscopic follow-up procedures by studying the sensitivity of our machine learned supernova classification on the specific strategy used to obtain training sets. With a fixed amount of spectroscopic follow-up time, we find that deeper magnitude-limited spectroscopic surveys are better for producing training sets. For supernova Ia (II-P) typing, we obtain a 44% (1%) increase in purity to 72% (87%) and 30% (162%) increase in efficiency to 65% (84%) of the sample using a 25th (24.5th) magnitude-limited survey instead of the shallower spectroscopic sample used in the original simulations. When redshift information is available, we incorporate it into our analysis using a novel method of altering the diffusion map representation of the supernovae. Incorporating host redshifts leads to a 5% improvement in Type Ia purity and 13% improvement in Type Ia efficiency.Comment: 16 pages, 11 figures, accepted for publication in MNRA