5 papers
Minimax Optimality of Shampoo for Nonstationary Stochastic Optimization
Abir Sarkar, Nirmalya Mandal, Martin T. Wells
We develop a comprehensive theoretical analysis of Matrix Shampoo for tracking time-varying optima in nonstationary stochastic optimization. We derive finite-horizon high-probabili…
Is There an AI Bubble? Robust Date-Stamping for Periods of Exuberance
Abir Sarkar, Martin T. Wells
The recent surge in valuations among AI related firms has renewed concerns that markets may be entering a new phase of speculative exuberance, especially in the technology and semi…
Adapt or Forget: Provable Tradeoffs Between Adam and SGD in Nonstationary Optimization
Sharan Sahu, Abir Sarkar, Cameron J. Hogan +1
We provide a theoretical analysis of Adam under non-stationary stochastic objectives, separating two regimes: Euclidean tracking under adaptive strong monotonicity of the Adam-prec…
Empirical Bayes Predictive Density Estimation under Covariate Shift in Large Imbalanced Linear Mixed Models
Abir Sarkar, Gourab Mukherjee, Keisuke Yano
We study empirical Bayes (EB) predictive density estimation in linear mixed models (LMMs) with large number of units, which induce a high dimensional random effects space. Focusing…
Double Local-to-Unity: Inference under Nearly Nonstationary Volatility
Abir Sarkar, Martin T. Wells
This article develops a moderate-deviation limit theory for autoregressive models with jointly persistent mean and volatility dynamics. The autoregressive coefficient is allowed to…