I would like to address the concern regarding applying to program specialities based on admit chances as opposed to applying to programs of interest. I personally think students should apply strictly to programs they are interested in and are actually passionate about. In our conversations with colleagues who also serve as admission committee members for some of the top competitive programs like CMU, we found that having publications is not a hard requirement, even for PhD programs. In fact they shared that many students apply with publications in subpar journals which do not necessarily have expert reviewers. Such publications are not impressive and end up having little value for the admissions committee. Unless the publications are in top and respectable venues, they are sometimes not even counted in the evaluation process. The admissions committee needs evidence that you have trained in handling complex problems and can dive deeper into the subject matter to pitch and implement a solution to a hard practical problem. This evidence can come from your letters of recommendation from supervisors who can speak to your relevant problem-solving abilities. Your letters of recommendations are looked at carefully to assess how you are perceived by an academic, and how they attest to your ability to succeed in the graduate program.
Regarding the ‘profile-building’ aspect, I personally think this notion can confuse you because it implies you need to perfect all elements of your application. This can lead to loss in the quality or substance of your unique selling points. I think your focus should be, starting in your undergraduate, to try to best learn in your foundational courses and build a strong basis. Then you can proceed with more advanced coursework in your areas of interest moving forward. For example if your probability and statistics courses particularly intrigued you, you can take Machine learning, deep learning and generative AI courses to further build and explore your interest. Showcase that you followed and pursued your interests and committed to them, which can be done through good grades and your letters of recommendation. In fact, many times students have to go through long interviews for PhDs and Masters with funding and may be asked to showcase their technical acumen based on their course learnings through programming exercises and technical questions. It is therefore vital to cover your bases and have strong foundational knowledge in your areas of interest.