reviews: 
Comments: This paper proposes an active learning (AL) approach for survival analysis data, where the AL is constrained to a budget. The proposed approach is essentially an extension/adaptation of the BatchBALD algorithm (Kirsch et al., 2019) to account for survival data and a limited budget. The main motivation and application comes from the medical domain, where the proposed approach aims to identify which patients to follow up with to maximize the mutual information criterium of BatchBALD. The empirical results based on 3 real-world datasets in the medical domain show that the proposed approach can outperform standard BatchBALD, as well as 5 additional naive baselines.
Strengths: 1) The **problem addressed in this paper is relevant** and the existing research on the topic of AL for survival data is indeed limited. 
2) The proposed approach is **an original combination of existing ideas**, namely budgeted learning and BatchBALD for AL, with the latter being "tweaked" to work with survival data.
Weaknesses: 1) The **contributions are not very clear**. The authors should clearly state which contributions they are claiming. Is the extension of BatchBALD to a budget-constrained setting the central contribution? If so, why is the theoretical analysis included in the appendix rather than in the main text? Is the adaptation of BatchBALD to survival data the central contribution? Both? The narration is ambiguous with respect to this, thus unnecessarily increasing the difficulty of assessing novelty.
2) The **novelty is unfortunately low**. It is not clear how the proposed approach for accounting for the budget constraint is different from the existing approaches for budgeted learning from the literature. The adaptation of BatchBALD proposed for survival data is also very incremental and not adequately grounded. The authors also mention that "so far no method has been developed looking at
budgeted learning with survival data" - however, there are other works in the literature looking at applying BALD for right-censored data (see e.g., https://arxiv.org/pdf/2402.11973). How does the proposed approach relate to these works?  
3) There are **several concerns regarding the soundness** of the proposed approach. The extension of BatchBALD to a budget-constrained setting is not clearly described and is not adequately grounded. The proposed approach is an adaptation of the algorithm proposed in (Khuller et al., 1999) "by omitting the first two lines". However, it is not clear what lines the authors refer to and, most importantly, what are the theoretical grounds for doing so. Similarly, the adaptions of BatchBALD for survival data are essentially presented as "algorithmic tweaks" (e.g., setting probabilities to zero and renormalizing) without a proper theoretical justification. Lastly, it is not clear how the authors handle the fact that the queried instances can still be censored - are the censored times assumed to be known a priori before querying? If so, how limiting is that assumption in terms of the applicability of the proposed approach? 
4) The **limited application scope** of the proposed approach is also a topic of concern. Although I agree with the authors that AL for survival data is a topic worth investigating, and the literature is indeed lacking on this, the application scope is, in my opinion, broader than the medical domain application presented in the paper. This limits the target audience of the paper quite a lot. I would encourage the authors to consider revising their presentation to broaden the scope of application to other domains as well. For example, the authors mention applications in finance and engineering in the abstract - it would be interesting to discuss those as well. Lastly, the authors consider only approaches where time is discretized into bins (they use Multi-Task Logistic Regression as the underlying survival model), and the proposed adaptation of BatchBALD to handle survival data in Section 5 relies on this assumption, which can be quite limiting. This should be discussed in the paper. 
5) The presented **claims are not adequately supported by empirical evidence**. Looking at the results in Table 1, the improvements over standard BatchBALD are very marginal. However, the text claims that "BBsurv outperforms other algorithms when budget is equal to 20 across all 3 real world datasets", which does not seem to always be the case. In fact, even "Entropy" seems to perform quite comparably - did the authors perform a statistical significance test? Confusingly, the Table 1 caption states that "Budget = 10", which is inconsistent with the text. Moreover, the results in Table 1 seem to be inconsistent with Figures 1 and 2. If one considered a vertical line at Budget = 10 (or 20, whichever it is), shouldn't the values and relative order of the approaches be consistent with Table 1?
6) The **presentation can be significantly improved**. There are several typos, poorly constructed sentences, incorrect grammar usage, sentences that are too informal for scientific paper, etc. I strongly encourage the authors to carefully revise the writing and overall presentation of the paper. Other aspects of the presentation, such as mathematical derivations, can be significantly improved. For example, the authors should include numbers for the equations. Similarly, it is unclear how the authors transition from the eq. of the mutual information at the beginning of Section 4.1 to the computation of its right-most term 2 equations below. The right term is an expected entropy, while 2 equations below only the entropy is considered. Can you clarify?
Recommendation: 3
Reviewer confidence: 4
Soundness/correctness: 1
Clarity: 2