Note that lower values of ϵ and δ correspond to stronger privacy.

Selecting a suitable pretraining dataset is crucial for both general-domain (e.g., GPT -

Real-valued linear prediction is a fundamental problem in machine learning.

The NFM framework utilizes the classical idea of multiplicative frailty in survival analysis as a principled way of extending the proportional hazard assumption, at the same time being able to leverage the strong approximation power of neural architectures for handling nonlinear covariate dependence.

Over the last century, risk scores have been the most popular form of predictive model used in healthcare and criminal justice. Risk scores are sparse linear models with integer coefficients; often these models can be memorized or placed on an index card. Typically, risk scores have been created either without data or by rounding logistic regression coefficients, but these methods do not reliably produce high-quality risk scores. Recent work used mathematical programming, which is computationally slow. We introduce an approach for efficiently producing a collection of high-quality risk scores learned from data. Specifically, our approach produces a pool of almost-optimal sparse continuous solutions, each with a different support set, using a beam-search algorithm. Each of these continuous solutions is transformed into a separate risk score through a star ray search, where a range of multipliers are considered before rounding the coefficients sequentially to maintain low logistic loss. Our algorithm returns all of these high-quality risk scores for the user to consider. This method completes within minutes and can be valuable in a broad variety of applications.

We introduce a flexible empirical Bayes approach for fitting Bayesian generalized linear models. Specifically, we adopt a novel mean-field variational inference (VI) method and the prior is estimated within the VI algorithm, making the method tuning-free. Unlike traditional VI methods that optimize the posterior density function, our approach directly optimizes the posterior mean and prior parameters. This formulation reduces the number of parameters to optimize and enables the use of scalable algorithms such as L-BFGS and stochastic gradient descent. Furthermore, our method automatically determines the optimal posterior based on the prior and likelihood, distinguishing it from existing VI methods that often assume a Gaussian variational. Our approach represents a unified framework applicable to a wide range of exponential family distributions, removing the need to develop unique VI methods for each combination of likelihood and prior distributions. We apply the framework to solve sparse logistic regression and demonstrate the superior predictive performance of our method in extensive numerical studies, by comparing it to prevalent sparse logistic regression approaches.