Rahul Shah

Purba Mukherjee, Rahul Shah, Arko Bhaumik et al.

We study the prospects of Gaussian processes (GP), a machine learning (ML) algorithm, as a tool to reconstruct the Hubble parameter $H(z)$ with two upcoming gravitational wave missions, namely the evolved Laser Interferometer Space Antenna (eLISA) and the Einstein Telescope (ET). Assuming various background cosmological models, the Hubble parameter has been reconstructed in a non-parametric manner with the help of GP using realistically generated catalogs for each mission. The effects of early-time and late-time priors on the reconstruction of $H(z)$, and hence on the Hubble constant ($H_0$), have also been focused on separately. Our analysis reveals that GP is quite robust in reconstructing the expansion history of the Universe within the observational window of the specific missions under consideration. We further confirm that both eLISA and ET would be able to provide constraints on $H(z)$ and $H_0$ which would be competitive to those inferred from current datasets. In particular, we observe that an eLISA run of $\sim10$-year duration with $\sim80$ detected bright siren events would be able to constrain $H_0$ as good as a $\sim3$-year ET run assuming $\sim 1000$ bright siren event detections. Further improvement in precision is expected for longer eLISA mission durations such as a $\sim15$-year time-frame having $\sim120$ events. Lastly, we discuss the possible role of these future gravitational wave missions in addressing the Hubble tension, for each model, on a case-by-case basis.

Mihran Miroyan, Shiny Weng, Rahul Shah et al.

In today's rapidly evolving educational landscape, traditional modes of passive information delivery are giving way to transformative pedagogical approaches that prioritize active student engagement. Within the context of large-scale hybrid classrooms, the challenge lies in fostering meaningful and active interaction between students and course content. This study delves into the significance of measuring students' earnestness during interactive lecture participation exercises. By analyzing students' responses to interactive lecture poll questions, establishing a clear rubric for evaluating earnestness, and conducting a comprehensive assessment, we introduce EIT (Earnest Insight Toolkit), a tool designed to assess students' engagement within interactive lecture participation exercises - particularly in the context of large-scale hybrid classrooms. Through the utilization of EIT, our objective is to equip educators with valuable means of identifying at-risk students for enhancing intervention and support strategies, as well as measuring students' levels of engagement with course content.

Rahul Shah, Soumadeep Saha, Purba Mukherjee et al.

We investigate the prospect of reconstructing the ''cosmic distance ladder'' of the Universe using a novel deep learning framework called LADDER - Learning Algorithm for Deep Distance Estimation and Reconstruction. LADDER is trained on the apparent magnitude data from the Pantheon Type Ia supernovae compilation, incorporating the full covariance information among data points, to produce predictions along with corresponding errors. After employing several validation tests with a number of deep learning models, we pick LADDER as the best performing one. We then demonstrate applications of our method in the cosmological context, including serving as a model-independent tool for consistency checks for other datasets like baryon acoustic oscillations, calibration of high-redshift datasets such as gamma ray bursts, and use as a model-independent mock catalog generator for future probes. Our analysis advocates for careful consideration of machine learning techniques applied to cosmological contexts.

Rahul Shah, Purba Mukherjee, Soumadeep Saha et al.

Conventional calibration of Baryon Acoustic Oscillations (BAO) data relies on estimation of the sound horizon at drag epoch $r_d$ from early universe observations by assuming a cosmological model. We present a recalibration of two independent BAO datasets, SDSS and DESI, by employing deep learning techniques for model-independent estimation of $r_d$, and explore the impacts on $Λ$CDM cosmological parameters. Significant reductions in both Hubble ($H_0$) and clustering ($S_8$) tensions are observed for both the recalibrated datasets. Moderate shifts in some other parameters hint towards further exploration of such data-driven approaches.

Shane Waxler, Paul Blazek, Davis White et al.

Realizing personalized medicine at scale calls for methods that distill insights from longitudinal patient journeys, which can be viewed as a sequence of medical events. Foundation models pretrained on large-scale medical event data represent a promising direction for scaling real-world evidence generation and generalizing to diverse downstream tasks. Using Epic Cosmos, a dataset with medical events from de-identified longitudinal health records for 16.3 billion encounters over 300 million unique patient records from 310 health systems, we introduce the Curiosity models, a family of decoder-only transformer models pretrained on 118 million patients representing 115 billion discrete medical events (151 billion tokens). We present the largest scaling-law study of medical event data, establishing a methodology for pretraining and revealing power-law scaling relationships for compute, tokens, and model size. Consequently, we pretrained a series of compute-optimal models with up to 1 billion parameters. Conditioned on a patient's real-world history, Curiosity autoregressively predicts the next medical event to simulate patient health timelines. We studied 78 real-world tasks, including diagnosis prediction, disease prognosis, and healthcare operations. Remarkably for a foundation model with generic pretraining and simulation-based inference, Curiosity generally outperformed or matched task-specific supervised models on these tasks, without requiring task-specific fine-tuning or few-shot examples. Curiosity's predictive power consistently improves as the model and pretraining scale. Our results show that Curiosity, a generative medical event foundation model, can effectively capture complex clinical dynamics, providing an extensible and generalizable framework to support clinical decision-making, streamline healthcare operations, and improve patient outcomes.

Jathin Korrapati, Tanish Baranwal, Rahul Shah

This work explores the theoretical and practical foundations of denoising diffusion probabilistic models (DDPMs) and score-based generative models, which leverage stochastic processes and Brownian motion to model complex data distributions. These models employ forward and reverse diffusion processes defined through stochastic differential equations (SDEs) to iteratively add and remove noise, enabling high-quality data generation. By analyzing the performance bounds of these models, we demonstrate how score estimation errors propagate through the reverse process and bound the total variation distance using discrete Girsanov transformations, Pinsker's inequality, and the data processing inequality (DPI) for an information theoretic lens.