Henry Lam

Huajie Qian, Donghao Ying, Henry Lam et al.

Ensemble learning is a popular technique to improve the accuracy of machine learning models. It traditionally hinges on the rationale that aggregating multiple weak models can lead to better models with lower variance and hence higher stability, especially for discontinuous base learners. In this paper, we provide a new perspective on ensembling. By selecting the best model trained on subsamples via majority voting, we can attain exponentially decaying tails for the excess risk, even if the base learner suffers from slow (i.e., polynomial) decay rates. This tail enhancement power of ensembling is agnostic to the underlying base learner and is stronger than variance reduction in the sense of exhibiting rate improvement. We demonstrate how our ensemble methods can substantially improve out-of-sample performances in a range of numerical examples involving heavy-tailed data or intrinsically slow rates. Code for the proposed methods is available at https://github.com/mickeyhqian/VoteEnsemble.

Fengpei Li, Haoxian Chen, Jiahe Lin et al.

For many complex simulation tasks spanning areas such as healthcare, engineering, and finance, Monte Carlo (MC) methods are invaluable due to their unbiased estimates and precise error quantification. Nevertheless, Monte Carlo simulations often become computationally prohibitive, especially for nested, multi-level, or path-dependent evaluations lacking effective variance reduction techniques. While machine learning (ML) surrogates appear as natural alternatives, naive replacements typically introduce unquantifiable biases. We address this challenge by introducing Prediction-Enhanced Monte Carlo (PEMC), a framework that leverages modern ML models as learned predictors, using cheap and parallelizable simulation as features, to output unbiased evaluation with reduced variance and runtime. PEMC can also be viewed as a "modernized" view of control variates, where we consider the overall computation-cost-aware variance reduction instead of per-replication reduction, while bypassing the closed-form mean function requirement and maintaining the advantageous unbiasedness and uncertainty quantifiability of Monte Carlo. We illustrate PEMC's broader efficacy and versatility through three examples: first, equity derivatives such as variance swaps under stochastic local volatility models; second, interest rate derivatives such as swaption pricing under the Heath-Jarrow-Morton (HJM) interest-rate model. Finally, we showcase PEMC in a socially significant context - ambulance dispatch and hospital load balancing - where accurate mortality rate estimates are key for ethically sensitive decision-making. Across these diverse scenarios, PEMC consistently reduces variance while preserving unbiasedness, highlighting its potential as a powerful enhancement to standard Monte Carlo baselines.

Yu Chen, Fengpei Li, Anderson Schneider et al.

Many event sequence data exhibit mutually exciting or inhibiting patterns. Reliable detection of such temporal dependency is crucial for scientific investigation. The de facto model is the Multivariate Hawkes Process (MHP), whose impact function naturally encodes a causal structure in Granger causality. However, the vast majority of existing methods use direct or nonlinear transform of standard MHP intensity with constant baseline, inconsistent with real-world data. Under irregular and unknown heterogeneous intensity, capturing temporal dependency is hard as one struggles to distinguish the effect of mutual interaction from that of intensity fluctuation. In this paper, we address the short-term temporal dependency detection issue. We show the maximum likelihood estimation (MLE) for cross-impact from MHP has an error that can not be eliminated but may be reduced by order of magnitude, using heterogeneous intensity not of the target HP but of the interacting HP. Then we proposed a robust and computationally-efficient method modified from MLE that does not rely on the prior estimation of the heterogeneous intensity and is thus applicable in a data-limited regime (e.g., few-shot, no repeated observations). Extensive experiments on various datasets show that our method outperforms existing ones by notable margins, with highlighted novel applications in neuroscience.

Yuanlu Bai, Henry Lam, Svitlana Vyetrenko et al.

Multi-agent simulation is commonly used across multiple disciplines, specifically in artificial intelligence in recent years, which creates an environment for downstream machine learning or reinforcement learning tasks. In many practical scenarios, however, only the output series that result from the interactions of simulation agents are observable. Therefore, simulators need to be calibrated so that the simulated output series resemble historical -- which amounts to solving a complex simulation optimization problem. In this paper, we propose a simple and efficient framework for calibrating simulator parameters from historical output series observations. First, we consider a novel concept of eligibility set to bypass the potential non-identifiability issue. Second, we generalize the two-sample Kolmogorov-Smirnov (K-S) test with Bonferroni correction to test the similarity between two high-dimensional distributions, which gives a simple yet effective distance metric between the output series sample sets. Third, we suggest using Bayesian optimization (BO) and trust-region BO (TuRBO) to minimize the aforementioned distance metric. Finally, we demonstrate the efficiency of our framework using numerical experiments both on a multi-agent financial market simulator.