A Gaussian Cox process is a popular model for point process data, in which the intensity function is a transformation of a Gaussian process. Posterior inference of this intensity function involves an intractable integral (i.e., the cumulative intensity function) in the likelihood resulting in doubly intractable posterior distribution. Here, we propose a nonparametric Bayesian approach for estimating the intensity function of an inhomogeneous Poisson process without reliance on large data augmentation or approximations of the likelihood function. We propose to jointly model the intensity and the cumulative intensity function as a transformed Gaussian process, allowing us to directly bypass the need of approximating the cumulative intensity function in the likelihood. We propose an exact MCMC sampler for posterior inference and evaluate its performance on simulated data. We demonstrate the utility of our method in three real-world scenarios including temporal and spatial event data, as well as aggregated time count data collected at multiple resolutions. Finally, we discuss extensions of our proposed method to other point processes.

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.

Learning faithful representations of quantum states is crucial to fully characterizing the variety of many-body states created on quantum processors. While various tomographic methods such as classical shadow and MPS tomography have shown promise in characterizing a wide class of quantum states, they face unique limitations in detecting topologically ordered two-dimensional states. To address this problem, we implement and study a heuristic tomographic method that combines variational optimization on tensor networks with randomized measurement techniques. Using this approach, we demonstrate its ability to learn the ground state of the surface code Hamiltonian as well as an experimentally realizable quantum spin liquid state. In particular, we perform numerical experiments using MPS ans\"atze and systematically investigate the sample complexity required to achieve high fidelities for systems of sizes up to $48$ qubits. In addition, we provide theoretical insights into the scaling of our learning algorithm by analyzing the statistical properties of maximum likelihood estimation. Notably, our method is sample-efficient and experimentally friendly, only requiring snapshots of the quantum state measured randomly in the $X$ or $Z$ bases. Using this subset of measurements, our approach can effectively learn any real pure states represented by tensor networks, and we rigorously prove that random-$XZ$ measurements are tomographically complete for such states.

A method for solving concept-based learning (CBL) problem is proposed. The main idea behind the method is to divide each concept-annotated image into patches, to transform the patches into embeddings by using an autoencoder, and to cluster the embeddings assuming that each cluster will mainly contain embeddings of patches with certain concepts. To find concepts of a new image, the method implements the frequentist inference by computing prior and posterior probabilities of concepts based on rates of patches from images with certain values of the concepts. Therefore, the proposed method is called the Frequentist Inference CBL (FI-CBL). FI-CBL allows us to incorporate the expert rules in the form of logic functions into the inference procedure. An idea behind the incorporation is to update prior and conditional probabilities of concepts to satisfy the rules. The method is transparent because it has an explicit sequence of probabilistic calculations and a clear frequency interpretation. Numerical experiments show that FI-CBL outperforms the concept bottleneck model in cases when the number of training data is small. The code of proposed algorithms is publicly available.

We study the problem of online learning in contextual bandit problems where the loss function is assumed to belong to a known parametric function class. We propose a new analytic framework for this setting that bridges the Bayesian theory of information-directed sampling due to Russo and Van Roy (2018) and the worst-case theory of Foster, Kakade, Qian, and Rakhlin (2021) based on the decision-estimation coefficient. Drawing from both lines of work, we propose a algorithmic template called Optimistic Information-Directed Sampling and show that it can achieve instance-dependent regret guarantees similar to the ones achievable by the classic Bayesian IDS method, but with the major advantage of not requiring any Bayesian assumptions. The key technical innovation of our analysis is introducing an optimistic surrogate model for the regret and using it to define a frequentist version of the Information Ratio of Russo and Van Roy (2018), and a less conservative version of the Decision Estimation Coefficient of Foster et al. (2021). Keywords: Contextual bandits, information-directed sampling, decision estimation coefficient, first-order regret bounds.

The model editing problem concerns how language models should learn new facts about the world over time. While empirical research on model editing has drawn widespread attention, the conceptual foundations of model editing remain shaky -- perhaps unsurprisingly, since model editing is essentially belief revision, a storied problem in philosophy that has eluded succinct solutions for decades. Model editing nonetheless demands a solution, since we need to be able to control the knowledge within language models. With this goal in mind, this paper critiques the standard formulation of the model editing problem and proposes a formal testbed for model editing research. We first describe 12 open problems with model editing, based on challenges with (1) defining the problem, (2) developing benchmarks, and (3) assuming LLMs have editable beliefs in the first place. Many of these challenges are extremely difficult to address, e.g. determining far-reaching consequences of edits, labeling probabilistic entailments between facts, and updating beliefs of agent simulators. Next, we introduce a semi-synthetic dataset for model editing based on Wikidata, where we can evaluate edits against labels given by an idealized Bayesian agent. This enables us to say exactly how belief revision in language models falls short of a desirable epistemic standard. We encourage further research exploring settings where such a gold standard can be compared against. Our code is publicly available at: https://github.com/peterbhase/LLM-belief-revision

Group decision-making (GDM) characterized by complexity and uncertainty is an essential part of various life scenarios. Most existing researches lack tools to fuse information quickly and interpret decision results for partially formed decisions. This limitation is particularly noticeable when there is a need to improve the efficiency of GDM. To address this issue, a novel multi-level sequential three-way decision for group decision-making (S3W-GDM) method is constructed from the perspective of granular computing. This method simultaneously considers the vagueness, hesitation, and variation of GDM problems under double hierarchy hesitant fuzzy linguistic term sets (DHHFLTS) environment. First, for fusing information efficiently, a novel multi-level expert information fusion method is proposed, and the concepts of expert decision table and the extraction/aggregation of decision-leveled information based on the multi-level granularity are defined. Second, the neighborhood theory, outranking relation and regret theory (RT) are utilized to redesign the calculations of conditional probability and relative loss function. Then, the granular structure of DHHFLTS based on the sequential three-way decision (S3WD) is defined to improve the decision-making efficiency, and the decision-making strategy and interpretation of each decision-level are proposed. Furthermore, the algorithm of S3W-GDM is given. Finally, an illustrative example of diagnosis is presented, and the comparative and sensitivity analysis with other methods are performed to verify the efficiency and rationality of the proposed method.

Speaker diarization is usually referred to as the task that determines ``who spoke when'' in a recording. Until a few years ago, all competitive approaches were modular. Systems based on this framework reached state-of-the-art performance in most scenarios but had major difficulties dealing with overlapped speech. More recently, the advent of end-to-end models, capable of dealing with all aspects of speaker diarization with a single model and better performing regarding overlapped speech, has brought high levels of attention. This thesis is framed during a period of co-existence of these two trends. We describe a system based on a Bayesian hidden Markov model used to cluster x-vectors (speaker embeddings obtained with a neural network), known as VBx, which has shown remarkable performance on different datasets and challenges. We comment on its advantages and limitations and evaluate results on different relevant corpora. Then, we move towards end-to-end neural diarization (EEND) methods. Due to the need for large training sets for training these models and the lack of manually annotated diarization data in sufficient quantities, the compromise solution consists in generating training data artificially. We describe an approach for generating synthetic data which resembles real conversations in terms of speaker turns and overlaps. We show how this method generating ``simulated conversations'' allows for better performance than using a previously proposed method for creating ``simulated mixtures'' when training the popular EEND with encoder-decoder attractors (EEND-EDA). We also propose a new EEND-based model, which we call DiaPer, and show that it can perform better than EEND-EDA, especially when dealing with many speakers and handling overlapped speech. Finally, we compare both VBx-based and DiaPer systems on a wide variety of corpora and comment on the advantages of each technique.

In a multi-agent system, agents share their local observations to gain global situational awareness for decision making and collaboration using a message passing system. When to send a message, how to encode a message, and how to leverage the received messages directly affect the effectiveness of the collaboration among agents. When training a multi-agent cooperative game using reinforcement learning (RL), the message passing system needs to be optimized together with the agent policies. This consequently increases the model's complexity and poses significant challenges to the convergence and performance of learning. To address this issue, we propose the Belief-map Assisted Multi-agent System (BAMS), which leverages a neuro-symbolic belief map to enhance training. The belief map decodes the agent's hidden state to provide a symbolic representation of the agent's understanding of the environment and other agent's status. The simplicity of symbolic representation allows the gathering and comparison of the ground truth information with the belief, which provides an additional channel of feedback for the learning. Compared to the sporadic and delayed feedback coming from the reward in RL, the feedback from the belief map is more consistent and reliable. Agents using BAMS can learn a more effective message passing network to better understand each other, resulting in better performance in a cooperative predator and prey game with varying levels of map complexity and compare it to previous multi-agent message passing models. The simulation results showed that BAMS reduced training epochs by 66\%, and agents who apply the BAMS model completed the game with 34.62\% fewer steps on average.

In this chapter, we are interested in formalizing the reasoning of a single agent who can make observations on a dynamic system and considers actions to perform on it. Reasoning about action and change is among the first issues addressed within Artificial Intelligence (AI); especially, it was the subject of the seminal article by McCarthy and Hayes [1969]. Research in this area has been very productive until the late 1990s. Among other things, solutions to the various problems to be faced when dealing with action representation were put forward and a classification of action languages according to their expressive power was undertaken. Moreover, much progress towards the automatization of reasoning about action and change was made, for example through the design and the evaluation of algorithms implementing the reasoning processes of the main action languages and the investigation of the computational complexity of such processes. The reasons why an agent may wish to act in order to modify the current state of a dynamic system or to learn more about it are numerous.