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The Koopman operator enables simplified representations for nonlinear systems in data-driven optimal control, but the accompanying uncertainties inevitably induce deviations in the optimal controller and associated value function. This…

The Kalman filter (KF) and the extended Kalman filter (EKF) are well established techniques for state estimation. However, the choice of the filter tuning parameters still poses a major challenge for the engineers [1]. In the present work,…

Searching for new effective risk factors on stock returns is an important research topic in asset pricing. Factor modeling is an active research topic in statistics and econometrics, with many new advances. However, these new methods have…

Accurate estimation of power system dynamics is very important for the enhancement of power system reliability, resilience, security, and stability of power system. With the increasing integration of inverter-based distributed energy…

This paper analyses the forecasting performance of a new class of factor models with martingale difference errors (FMMDE) recently introduced by Lee and Shao (2018). The FMMDE makes it possible to retrieve a transformation of the original…

In this work, we present a new derivative-free optimization method and investigate its use for training neural networks. Our method is motivated by the Ensemble Kalman Filter (EnKF), which has been used successfully for solving optimization…

Language agents increasingly improve by reusing \emph{skills} -- structured procedural artifacts distilled from past experience. In particular, \emph{domain-level} and \emph{model-generated} skills are especially promising. They offer fast…

This paper makes a selective survey on the recent development of the factor model and its application on statistical learnings. We focus on the perspective of the low-rank structure of factor models, and particularly draws attentions to…

We study a novel large dimensional approximate factor model with regime changes in the loadings driven by a latent first order Markov process. By exploiting the equivalent linear representation of the model, we first recover the latent…

Recent advancements in large language models (LLMs) have shifted focus toward scaling inference-time compute, improving performance without retraining the model. A common approach is to sample multiple outputs in parallel, and select one of…

Quantile Factor Models (QFM) represent a new class of factor models for high-dimensional panel data. Unlike Approximate Factor Models (AFM), where only location-shifting factors can be extracted, QFM also allow to recover unobserved factors…

We review Quasi Maximum Likelihood estimation of factor models for high-dimensional panels of time series. We consider two cases: (1) estimation when no dynamic model for the factors is specified (Bai and Li, 2012, 2016); (2) estimation…

This paper develops a new nonlinear filter, called Moment-based Kalman Filter (MKF), using the exact moment propagation method. Existing state estimation methods use linearization techniques or sampling points to compute approximate values…

Model-based filtering is often carried out while subject to an imperfect model, as learning partially-observable stochastic systems remains a challenge. Recent work on Bayesian inference found that tempering the likelihood or full posterior…

Factor models are a class of powerful statistical models that have been widely used to deal with dependent measurements that arise frequently from various applications from genomics and neuroscience to economics and finance. As data are…

A Kalman filter based sequential estimator is presented in the present work. The estimator is integrated in the structure of segregated solvers for the analysis of incompressible flows. This technique provides an augmented flow state…

Forward and inverse models are used throughout different engineering fields to predict and understand the behaviour of systems and to find parameters from a set of observations. These models use root-finding and minimisation techniques…

This research presents a method that utilizes explainability techniques to amplify the performance of machine learning (ML) models in forecasting the quality of milling processes, as demonstrated in this paper through a manufacturing use…

This paper develops a set of simplified dynamical models with which to explore the conditions under which division of labor leads to optimized system output, as measured by the rate of production of a given product. We consider two models:…

We use statistical learning methods to construct an adaptive state estimator for nonlinear stochastic systems. Optimal state estimation, in the form of a Kalman filter, requires knowledge of the system's process and measurement uncertainty.…