RSQTAO (Randomized Subspace Quasi Taylor Order Analysis)
The Randomized Subspace Quasi Taylor-Order Analysis (RSQTOA) framework is a novel approach that addresses the challenge of high-dimensional regression modeling by reducing the dimensionality of multivariate scalar functions. The framework employs the concept of "Quasi-Separability" to identify dimensions that can be approximated independently of the rest. It combines this technique with machine learning algorithms, such as Artificial Neural Networks, to approximate the non-separable dimensions. By reducing the dimensionality of the problem, the RSQTOA framework improves computational efficiency and reduces the time and resources required for modeling. It provides a flexible and robust method for developing surrogate models that accurately represent complex relationships between input features and the target variable
The framework comprises three primary components: the sampling, the Quasi-Separability detection, and the subdomain splitting. The framework adopts an automatic approach that partitions the domain into smaller subdomains and identifies subspaces that exhibit Quasi-Separability. To accomplish this task, a tree-based structure is utilized to traverse the domain. To fit or represent a dimension using an approximate model, the framework relies on the Quasi-Separability regressor. Consequently, the framework depends on sampling to obtain a representative sample that can help the regressor identify the underlying structure and relationships between the feature and target variables. For more detailed description of frameworks implementation and background please refer to Simon L. Märtens, 2022.
Usage Examples: Function based experiments
In order to extend the capabilities of the RSQTOA framework, which focuses on producing approximate models for multivariate scalar functions, we conduct a consequent research aimed to enhance the framework’s compatibility with generating approximate models using datasets. The current framework operates on functions as input, where scalar regressions for each dimension are obtained through domain and dimension sampling. This process involves acquiring target values from the function, performing regressions, and validating the error against predefined criteria. However, when dealing with datasets instead of actual functions, we face the challenge of having limited data points available. To overcome this challenge, two approaches are proposed. Firstly, we suggest representing the dataset in a functional form using interpolators, which can then be utilized as input to the framework. Secondly, we introduce a multidimensional grid-based sampling approach to address the limitations posed by the dataset.
Consequently, a comparative analysis was conducted to evaluate the performance of the RSQTOA framework with interpolation and grid sampling approaches, in comparison to Artificial Neural Networks (ANNs) as baseline models. This evaluation aimed to assess the effectiveness of the proposed framework in various scenarios. Two experiments were utilized for this purpose. Firstly, a Synthetic Dataset was generated using a simple mathematical function, enabling a controlled environment for evaluating the performance of the RSQTOA-based approaches. Additionally, the Yelp Dataset was employed, which encompassed diverse features related to review content, reviewer characteristics, and business attributes. The comparative analysis of these datasets allowed for a comprehensive evaluation of the RSQTOA framework, providing valuable insights into its performance, accuracy, and scalability in different contexts. The findings from this analysis contribute to a better understanding of the advantages and limitations of the framework compared to traditional ANN-based models. For more detailed description of frameworks implementation and background please refer to Ashish Rajani, 2023.
Usage Examples: Data based experiments
The framework is compatible with python 3.7. Furthermore, for the dependencies please refer to requirements.txt. In
order to install dependencies. Create and activate a new virtual environment if needed and execute the following command:
pip3 install -r requirements.txt
For detailed description and usage guidance please refer to experiments. The code published with the experiments provide a good idea of how the framework in different settings can be used. Its worth noting that the framework is still under development, please refer to the detailed report by Simon L. Märtens, 2022 and Ashish Rajani, 2023.