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A Latent Variable Framework for Scaling Laws in Large Language Models
Peiyao Cai, Chengyu Cui, Felipe Maia Polo +6
We propose a statistical framework built on latent variable modeling for scaling laws of large language models (LLMs). Our work is motivated by the rapid emergence of numerous new…
Online Price Competition under Generalized Linear Demands
Daniele Bracale, Moulinath Banerjee, Cong Shi +1
We study a sequential price competition among sellers, each influenced by the pricing decisions of their rivals. Specifically, the demand function for each seller follows t…
The Root Finding Problem Revisited: Beyond the Robbins-Monro procedure
Yue Yu, Moulinath Banerjee, Ya'acov Ritov
We introduce Sequential Probability Ratio Bisection (SPRB), a novel stochastic approximation algorithm that adapts to the local behavior of the (regression) function of interest ar…
Bridging Human and LLM Judgments: Understanding and Narrowing the Gap
Felipe Maia Polo, Xinhe Wang, Mikhail Yurochkin +3
Large language models are increasingly used as judges (LLM-as-a-judge) to evaluate model outputs at scale, but their assessments often diverge systematically from human judgments.…
Optimal Intervention for Self-triggering Spatial Networks with Application to Urban Crime Analytics
Pramit Das, Moulinath Banerjee, Yuekai Sun
In many network systems, events at one node trigger further activity at other nodes, e.g., social media users reacting to each other's posts or the clustering of criminal activity…
Estimation and Inference for the Average Treatment Effect in a Score-Explained Heterogeneous Treatment Effect Model
Kevin Christian Wibisono, Debarghya Mukherjee, Moulinath Banerjee +1
In many practical situations, randomly assigning treatments to subjects is uncommon due to feasibility constraints. For example, economic aid programs and merit-based scholarships…
Revenue Maximization Under Sequential Price Competition Via The Estimation Of s-Concave Demand Functions
Daniele Bracale, Moulinath Banerjee, Cong Shi +1
We consider price competition among multiple sellers over a selling horizon of periods. In each period, sellers simultaneously offer their prices (which are made public) and su…
Likelihood-Free Estimation for Spatiotemporal Hawkes processes with missing data and application to predictive policing
Pramit Das, Moulinath Banerjee, Yuekai Sun
With the growing use of AI technology, many police departments use forecasting software to predict probable crime hotspots and allocate patrolling resources effectively for crime p…
Dynamic Pricing in the Linear Valuation Model using Shape Constraints
Daniele Bracale, Moulinath Banerjee, Yuekai Sun +2
We propose a shape-constrained approach to dynamic pricing for censored data in the linear valuation model eliminating the need for tuning parameters commonly required by existing…