We thank the reviewers for their valuable input on how to improve our manuscript. We use our evaluation procedure ( 4) since we will not have ground-truth outcomes. The revision will provide this discussion with relevant citations. We would like to clarify that Theorem 3.1 describes the conditions under which our method is optimal. The RF estimation error dominates the confounding error.

Despite their growing popularity, there remains a prevalent misconception among practitioners about the equivalence in performance between parametric and non-parametric methods.

The type of information that these tools need to convey is often counterfactual in nature. Decision-makers need to know what is likely to happen if they choose to take a particular action.

We thank the reviewers for their valuable input on how to improve our manuscript. We use our evaluation procedure ( 4) since we will not have ground-truth outcomes. The revision will provide this discussion with relevant citations. We would like to clarify that Theorem 3.1 describes the conditions under which our method is optimal. The RF estimation error dominates the confounding error.

Cross-modal embeddings form the foundation for multi-modal models. However, visualization methods for interpreting cross-modal embeddings have been primarily confined to traditional dimensionality reduction (DR) techniques like PCA and t-SNE. These DR methods primarily focus on feature distributions within a single modality, whilst failing to incorporate metrics (e.g., CLIPScore) across multiple modalities. This paper introduces AKRMap, a new DR technique designed to visualize cross-modal embeddings metric with enhanced accuracy by learning kernel regression of the metric landscape in the projection space. Specifically, AKRMap constructs a supervised projection network guided by a post-projection kernel regression loss, and employs adaptive generalized kernels that can be jointly optimized with the projection. This approach enables AKRMap to efficiently generate visualizations that capture complex metric distributions, while also supporting interactive features such as zoom and overlay for deeper exploration. Quantitative experiments demonstrate that AKRMap outperforms existing DR methods in generating more accurate and trustworthy visualizations. We further showcase the effectiveness of AKRMap in visualizing and comparing cross-modal embeddings for text-to-image models. Code and demo are available at https://github.com/yilinye/AKRMap.

Dimension reduction (DR) algorithms have proven to be extremely useful for gaining insight into large-scale high-dimensional datasets, particularly finding clusters in transcriptomic data. The initial phase of these DR methods often involves converting the original high-dimensional data into a graph. In this graph, each edge represents the similarity or dissimilarity between pairs of data points. However, this graph is frequently suboptimal due to unreliable high-dimensional distances and the limited information extracted from the high-dimensional data. This problem is exacerbated as the dataset size increases. If we reduce the size of the dataset by selecting points for a specific sections of the embeddings, the clusters observed through DR are more separable since the extracted subgraphs are more reliable. In this paper, we introduce LocalMAP, a new dimensionality reduction algorithm that dynamically and locally adjusts the graph to address this challenge. By dynamically extracting subgraphs and updating the graph on-the-fly, LocalMAP is capable of identifying and separating real clusters within the data that other DR methods may overlook or combine. We demonstrate the benefits of LocalMAP through a case study on biological datasets, highlighting its utility in helping users more accurately identify clusters for real-world problems.