Accurate occupancy information helps to improve building energy efficiency and occupant comfort. Occupancy detection methods based on CO2 sensors have received attention due to their low cost and low intrusiveness. In naturally ventilated buildings, the accuracy of CO2-based occupancy detection is generally low in related studies due to the complex ventilation behavior and the difficulty in measuring the actual air exchange through windows. In this study, we present two novel features for occupancy detection based on the spatial distribution of the CO2 concentration. After a quantitative analysis with Support Vector Machine (SVM) as classifier, it was found that the accuracy of occupancy state detection in naturally ventilated rooms could be improved by up to 14.8 percentage points compared to the baseline, reaching 83.2 % (F1 score 0.84) without any ventilation information. With ventilation information, the accuracy reached 87.6 % (F1 score 0.89). The performance of occupancy quantity detection was significantly improved by up to 25.3 percentage points versus baseline, reaching 56 %, with root mean square error (RMSE) of 11.44 occupants, using only CO2-related features. Additional ventilation information further enhanced the performance to 61.8 % (RMSE 9.02 occupants). By incorporating spatial features, the model using only CO2-related features revealed similar performance as the model containing additional ventilation information, resulting in a better low-cost occupancy detection method for naturally ventilated buildings.

Policy Mirror Descent (PMD) is a powerful and theoretically sound methodology for sequential decision-making. However, it is not directly applicable to Reinforcement Learning (RL) due to the inaccessibility of explicit action-value functions. We address this challenge by introducing a novel approach based on learning a world model of the environment using conditional mean embeddings. We then leverage the operatorial formulation of RL to express the action-value function in terms of this quantity in closed form via matrix operations. Combining these estimators with PMD leads to POWR, a new RL algorithm for which we prove convergence rates to the global optimum. Preliminary experiments in finite and infinite state settings support the effectiveness of our method.

Kernel learning forward backward SDE filter is an iterative and adaptive meshfree approach to solve the nonlinear filtering problem. I t builds from forward backward SDE for Fokker-Planker equation, which defines evol ving density for the state variable, and employs KDE to approximate density . This algorithm has shown more superior performance than mainstream particle filter me thod, in both convergence speed and efficiency of solving high dimension problems . However, this method has only been shown to converge empiric ally . In this paper, we present a rigorous analysis to demonstrate its local and g lobal convergence, and provide theoretical support for its empirical results.

Bayesian Additive Regression Trees (BART) is a popular Bayesian non-parametric regression model that is commonly used in causal inference and beyond. Its strong predictive performance is supported by theoretical guarantees that its posterior distribution concentrates around the true regression function at optimal rates under various data generative settings and for appropriate prior choices. In this paper, we show that the BART sampler often converges slowly, confirming empirical observations by other researchers. Assuming discrete covariates, we show that, while the BART posterior concentrates on a set comprising all optimal tree structures (smallest bias and complexity), the Markov chain's hitting time for this set increases with $n$ (training sample size), under several common data generative settings. As $n$ increases, the approximate BART posterior thus becomes increasingly different from the exact posterior (for the same number of MCMC samples), contrasting with earlier concentration results on the exact posterior. This contrast is highlighted by our simulations showing worsening frequentist undercoverage for approximate posterior intervals and a growing ratio between the MSE of the approximate posterior and that obtainable by artificially improving convergence via averaging multiple sampler chains. Finally, based on our theoretical insights, possibilities are discussed to improve the BART sampler convergence performance.

We propose a novel deep generative model, the Kolmogorov-Smirnov Generative Adversarial Network (KSGAN). Unlike existing approaches, KSGAN formulates the learning process as a minimization of the Kolmogorov-Smirnov (KS) distance, generalized to handle multivariate distributions. This distance is calculated using the quantile function, which acts as the critic in the adversarial training process. We formally demonstrate that minimizing the KS distance leads to the trained approximate distribution aligning with the target distribution. We propose an efficient implementation and evaluate its effectiveness through experiments. The results show that KSGAN performs on par with existing adversarial methods, exhibiting stability during training, resistance to mode dropping and collapse, and tolerance to variations in hyperparameter settings. Additionally, we review the literature on the Generalized KS test and discuss the connections between KSGAN and existing adversarial generative models.

Partially observed stochastic reaction network (SRN) modeling the dynamics of a population of interacting species, such as chemical molecules participating in multiple reactions, is the fundamental building block of multi-scale bioprocess mechanistic model characterizing the causal interdependences from molecular-to macro-kinetics. It plays a critical role to: (1) facilitate digital twin development and support mechanism learning for biomanufacturing processes; (2) allow us to probe critical latent state based on partially observed information; and (3) serve as a fundamental model for a biofoundry platform [1] that can integrate heterogeneous online and offline measures collected from different manufacturing processes and speed up the bioprocess development with much less experiments. Model inference on the SRN mechanistic model based on heterogeneous data also helps to strengthen the theoretical foundations of federated learning on bioprocess mechanisms, through which we can train and advance knowledge. The SRN mechanistic model has three key features that make the model inference challenging. First, the continuoustime state transition model, representing the evolution of concentration or number of molecules, is highly nonlinear.

To support interpretable predictions and optimal control of biomanfuacturing processes, in this paper, we develop a digital twin calibration approach for multi-scale bioprocess mechanistic model or Biological System-of-Systems (Bio-SoS) [Zheng et al., 2024] characterizing causal interdependence from molecular-to cellular-to macro-kinetics. Even though this study is motivated by cell culture process, it can be extended to calibrate general Bio-SoS with modular design. Basically, cell culture process dynamics and variations depend on the modules: (1) a single cell mechanistic model characterizing each living cell behaviors and their interactions with environment; (2) a metabolic shift model characterizing the change of cell metabolic phase and behaviors as a response to culture conditions and cell age; and (3) macro-kinetic model of a bioreactor system composed of many living cells under different metabolic phases. The benefits of considering the Bio-SoS mechanistic model with modular design include: a) support flexible manufacturing through assembling a system of modules to account for biomanufacturing processes under different conditions and inputs; and b) facilitate the integration of heterogeneous data from different production processes, such as 2D culture and 3D aggregate culture for Induced Pluripotent Stem Cells (iPSCs) [Wang et al., 2024, Zheng et al., 2024]. By incorporating the structure property of the Bio-SoS mechanistic model into the calibration method, we can quantify how the model uncertainties or approximation errors of different modules interact with each other and propagate through the reaction pathways to the prediction of outputs (e.g., yield and product quality attributes), which can guide interpretable and most informative Design of Experiments (DoEs) to efficiently improve model fidelity with less experiments. The model uncertainty quantification approaches for digital twin calibration can be divided into two main categories: Bayesian and frequentist approaches [Corlu et al., 2020]. Bayesian approaches treat unknown model parameters as random variables and quantify our belief by posterior distributions. It involves specifying prior distributions for model parameters and updating these distributions based on the information from observed data by applying Bayes' theorem.

The study of geometric extremes, where extremal dependence properties are inferred from the deterministic limiting shapes of scaled sample clouds, provides an exciting approach to modelling the extremes of multivariate data. These shapes, termed limit sets, link together several popular extremal dependence modelling frameworks. Although the geometric approach is becoming an increasingly popular modelling tool, current inference techniques are limited to a low dimensional setting (d < 4), and generally require rigid modelling assumptions. In this work, we propose a range of novel theoretical results to aid with the implementation of the geometric extremes framework and introduce the first approach to modelling limit sets using deep learning. By leveraging neural networks, we construct asymptotically-justified yet flexible semi-parametric models for extremal dependence of high-dimensional data. We showcase the efficacy of our deep approach by modelling the complex extremal dependencies between meteorological and oceanographic variables in the North Sea off the coast of the UK.

Large Language Models (LLMs) exhibit strong generalization capabilities to novel tasks when prompted with language instructions and in-context demos. Since this ability sensitively depends on the quality of prompts, various methods have been explored to automate the instruction design. While these methods demonstrated promising results, they also restricted the searched prompt to one instruction. Such simplification significantly limits their capacity, as a single demo-free instruction might not be able to cover the entire complex problem space of the targeted task. To alleviate this issue, we adopt the Mixture-of-Expert paradigm and divide the problem space into a set of sub-regions; Each sub-region is governed by a specialized expert, equipped with both an instruction and a set of demos. A two-phase process is developed to construct the specialized expert for each region: (1) demo assignment: Inspired by the theoretical connection between in-context learning and kernel regression, we group demos into experts based on their semantic similarity; (2) instruction assignment: A region-based joint search of an instruction per expert complements the demos assigned to it, yielding a synergistic effect. The resulting method, codenamed Mixture-of-Prompts (MoP), achieves an average win rate of 81% against prior arts across several major benchmarks.

A common issue in learning decision-making policies in data-rich settings is spurious correlations in the offline dataset, which can be caused by hidden confounders. Instrumental variable (IV) regression, which utilises a key unconfounded variable known as the instrument, is a standard technique for learning causal relationships between confounded action, outcome, and context variables. Most recent IV regression algorithms use a two-stage approach, where a deep neural network (DNN) estimator learnt in the first stage is directly plugged into the second stage, in which another DNN is used to estimate the causal effect. Naively plugging the estimator can cause heavy bias in the second stage, especially when regularisation bias is present in the first stage estimator. We propose DML-IV, a non-linear IV regression method that reduces the bias in two-stage IV regressions and effectively learns high-performing policies. We derive a novel learning objective to reduce bias and design the DML-IV algorithm following the double/debiased machine learning (DML) framework. The learnt DML-IV estimator has strong convergence rate and $O(N^{-1/2})$ suboptimality guarantees that match those when the dataset is unconfounded. DML-IV outperforms state-of-the-art IV regression methods on IV regression benchmarks and learns high-performing policies in the presence of instruments.