The proposed representation learning approach can be effectively extended to handle high-dimensional or structured covariates, such as images or text data, by leveraging advanced neural network architectures specifically designed for these data types. For instance, convolutional neural networks (CNNs) can be employed for image data to automatically learn hierarchical representations that capture spatial features, while recurrent neural networks (RNNs) or transformers can be utilized for text data to capture sequential dependencies and contextual information.
To adapt the representation learning framework, one can integrate these specialized architectures into the representation function ( \\phi(x; \ heta_\\phi) ). The neural network can be trained to minimize the AutoDML loss, which allows for the estimation of weights without requiring outcome information. By doing so, the model can learn a low-dimensional representation that retains essential information from the high-dimensional input, thereby mitigating the curse of dimensionality.
Moreover, techniques such as transfer learning can be employed, where pre-trained models on large datasets are fine-tuned on the specific task at hand. This approach not only enhances the model's ability to generalize but also reduces the amount of labeled data required for training. Additionally, regularization techniques can be incorporated to prevent overfitting, ensuring that the learned representations are robust and generalizable across different datasets.