arXiv subjects

Anchit Jain

Publications and source records attributed to Anchit Jain.

3 recordsLinked to original sources

arXiv2026

Isotonic Survival Regression: Calibrated Survival Distributions from Deep Cox Models

Time-to-event data is widespread across the life sciences and engineering, but it is typically encountered together with censoring, which complicates the application of standard machine learning methods. Deep Cox models have emerged as a popular method for analyzing time-to-event data because they gracefully handle censoring and can be used with unstructured data such as clinical text reports, genomic sequences, and pathology images. However, their predicted survival probabilities are often poorly calibrated, thus limiting their practical utility. In this paper, we propose a novel post hoc calibration method for Deep Cox models that uses isotonic regression to refine predicted survival probabilities without affecting discriminative power. We establish favorable theoretical guarantees, including a double-robustness property and asymptotic calibration. Experiments on synthetic and real-world clinical data demonstrate the empirical effectiveness of our method.

stat.ML↗

arXiv2025

Deep Ensembles for Epistemic Uncertainty: A Frequentist Perspective

Decomposing prediction uncertainty into aleatoric (irreducible) and epistemic (reducible) components is critical for the reliable deployment of machine learning systems. While the mutual information between the response variable and model parameters is a principled measure for epistemic uncertainty, it requires access to the parameter posterior, which is computationally challenging to approximate. Consequently, practitioners often rely on probabilistic predictions from deep ensembles to quantify uncertainty, which have demonstrated strong empirical performance. However, a theoretical understanding of their success from a frequentist perspective remains limited. We address this gap by first considering a bootstrap-based estimator for epistemic uncertainty, which we prove is asymptotically correct. Next, we connect deep ensembles to the bootstrap estimator by decomposing it into data variability and training stochasticity; specifically, we show that deep ensembles capture the training stochasticity component. Through empirical studies, we show that this stochasticity component constitutes the majority of epistemic uncertainty, thereby explaining the effectiveness of deep ensembles.

stat.ML↗

arXiv2024

Bias in Motion: Theoretical Insights into the Dynamics of Bias in SGD Training

Machine learning systems often acquire biases by leveraging undesired features in the data, impacting accuracy variably across different sub-populations. Current understanding of bias formation mostly focuses on the initial and final stages of learning, leaving a gap in knowledge regarding the transient dynamics. To address this gap, this paper explores the evolution of bias in a teacher-student setup modeling different data sub-populations with a Gaussian-mixture model. We provide an analytical description of the stochastic gradient descent dynamics of a linear classifier in this setting, which we prove to be exact in high dimension. Notably, our analysis reveals how different properties of sub-populations influence bias at different timescales, showing a shifting preference of the classifier during training. Applying our findings to fairness and robustness, we delineate how and when heterogeneous data and spurious features can generate and amplify bias. We empirically validate our results in more complex scenarios by training deeper networks on synthetic and real datasets, including CIFAR10, MNIST, and CelebA.

cs.LG↗