By using an parametric value function to replace the Monte-Carlo rollouts for value estimation, the actor-critic (AC) algorithms can reduce the variance of stochastic policy gradient so that to improve the convergence rate. While existing works mainly focus on analyzing convergence rate of AC algorithms under Markovian noise, the impacts of momentum on AC algorithms remain largely unexplored. In this work, we first propose a heavy-ball momentum based advantage actor-critic (\mbox{HB-A2C}) algorithm by integrating the heavy-ball momentum into the critic recursion that is parameterized by a linear function. When the sample trajectory follows a Markov decision process, we quantitatively certify the acceleration capability of the proposed HB-A2C algorithm. Our theoretical results demonstrate that the proposed HB-A2C finds an $\epsilon$-approximate stationary point with $\oo{\epsilon^{-2}}$ iterations for reinforcement learning tasks with Markovian noise. Moreover, we also reveal the dependence of learning rates on the length of the sample trajectory. By carefully selecting the momentum factor of the critic recursion, the proposed HB-A2C can balance the errors introduced by the initialization and the stoschastic approximation.

A text stream is an ordered sequence of text documents generated over time. A massive amount of such text data is generated by online social platforms every day. Designing an algorithm for such text streams to extract useful information is a challenging task due to unique properties of the stream such as infinite length, data sparsity, and evolution. Thereby, learning useful information from such streaming data under the constraint of limited time and memory has gained increasing attention. During the past decade, although many text stream mining algorithms have proposed, there still exists some potential issues. First, high-dimensional text data heavily degrades the learning performance until the model either works on subspace or reduces the global feature space. The second issue is to extract semantic text representation of documents and capture evolving topics over time. Moreover, the problem of label scarcity exists, whereas existing approaches work on the full availability of labeled data. To deal with these issues, in this thesis, new learning models are proposed for clustering and multi-label learning on text streams.

Estimation of cardiovascular model parameters from electronic health records (EHR) poses a significant challenge primarily due to lack of identifiability. Structural non-identifiability arises when a manifold in the space of parameters is mapped to a common output, while practical non-identifiability can result due to limited data, model misspecification, or noise corruption. To address the resulting ill-posed inverse problem, optimization-based or Bayesian inference approaches typically use regularization, thereby limiting the possibility of discovering multiple solutions. In this study, we use inVAErt networks, a neural network-based, data-driven framework for enhanced digital twin analysis of stiff dynamical systems. We demonstrate the flexibility and effectiveness of inVAErt networks in the context of physiological inversion of a six-compartment lumped parameter hemodynamic model from synthetic data to real data with missing components.

Data-driven discovery of partial differential equations (PDEs) has emerged as a promising approach for deriving governing physics when domain knowledge about observed data is limited. Despite recent progress, the identification of governing equations and their parametric dependencies using conventional information criteria remains challenging in noisy situations, as the criteria tend to select overly complex PDEs. In this paper, we introduce an extension of the uncertainty-penalized Bayesian information criterion (UBIC), which is adapted to solve parametric PDE discovery problems efficiently without requiring computationally expensive PDE simulations. This extended UBIC uses quantified PDE uncertainty over different temporal or spatial points to prevent overfitting in model selection. The UBIC is computed with data transformation based on power spectral densities to discover the governing parametric PDE that truly captures qualitative features in frequency space with a few significant terms and their parametric dependencies (i.e., the varying PDE coefficients), evaluated with confidence intervals. Numerical experiments on canonical PDEs demonstrate that our extended UBIC can identify the true number of terms and their varying coefficients accurately, even in the presence of noise. The code is available at \url{https://github.com/Pongpisit-Thanasutives/parametric-discovery}.

When we merge information in Dempster-Shafer Theory (DST), we are faced with anomalous behavior: agents with equal expertise and credibility can have their opinion disregarded after resorting to the belief combination rule of this theory. This problem is interesting because belief fusion is an inherent part of dealing with situations where available information is imprecise, as often occurs in Artificial Intelligence. We managed to identify an isomorphism betwin the DST formal apparatus into that of a Probabilistic Logic. Thus, we solved the problematic inputs affair by replacing the DST combination rule with a new fusion process aiming at eliminating anomalies proposed by that rule. We apply the new fusion method to the DST paradox Problem.

Neural probabilistic logic systems follow the neuro-symbolic (NeSy) paradigm by combining the perceptive and learning capabilities of neural networks with the robustness of probabilistic logic. Learning corresponds to likelihood optimization of the neural networks. However, to obtain the likelihood exactly, expensive probabilistic logic inference is required. To scale learning to more complex systems, we therefore propose to instead optimize a sampling based objective. We prove that the objective has a bounded error with respect to the likelihood, which vanishes when increasing the sample count. Furthermore, the error vanishes faster by exploiting a new concept of sample diversity. We then develop the EXPLAIN, AGREE, LEARN (EXAL) method that uses this objective. EXPLAIN samples explanations for the data. AGREE reweighs each explanation in concordance with the neural component. LEARN uses the reweighed explanations as a signal for learning. In contrast to previous NeSy methods, EXAL can scale to larger problem sizes while retaining theoretical guarantees on the error. Experimentally, our theoretical claims are verified and EXAL outperforms recent NeSy methods when scaling up the MNIST addition and Warcraft pathfinding problems.

Model parsimony is an important \emph{cognitive bias} in data-driven modelling that aids interpretability and helps to prevent over-fitting. Sparse identification of nonlinear dynamics (SINDy) methods are able to learn sparse representations of complex dynamics directly from data, given a basis of library functions. In this work, a novel Bayesian treatment of dictionary learning system identification, as an alternative to SINDy, is envisaged. The proposed method -- Bayesian identification of nonlinear dynamics (BINDy) -- is distinct from previous approaches in that it targets the full joint posterior distribution over both the terms in the library and their parameterisation in the model. This formulation confers the advantage that an arbitrary prior may be placed over the model structure to produce models that are sparse in the model space rather than in parameter space. Because this posterior is defined over parameter vectors that can change in dimension, the inference cannot be performed by standard techniques. Instead, a Gibbs sampler based on reversible-jump Markov-chain Monte-Carlo is proposed. BINDy is shown to compare favourably to ensemble SINDy in three benchmark case-studies. In particular, it is seen that the proposed method is better able to assign high probability to correct model terms.

Mean field games (MFGs) model the interactions within a large-population multi-agent system using the population distribution. Traditional learning methods for MFGs are based on fixed-point iteration (FPI), which calculates best responses and induced population distribution separately and sequentially. However, FPI-type methods suffer from inefficiency and instability, due to oscillations caused by the forward-backward procedure. This paper considers an online learning method for MFGs, where an agent updates its policy and population estimates simultaneously and fully asynchronously, resulting in a simple stochastic gradient descent (SGD) type method called SemiSGD. Not only does SemiSGD exhibit numerical stability and efficiency, but it also provides a novel perspective by treating the value function and population distribution as a unified parameter. We theoretically show that SemiSGD directs this unified parameter along a descent direction to the mean field equilibrium. Motivated by this perspective, we develop a linear function approximation (LFA) for both the value function and the population distribution, resulting in the first population-aware LFA for MFGs on continuous state-action space. Finite-time convergence and approximation error analysis are provided for SemiSGD equipped with population-aware LFA.

Large language models (LLMs) have emerged as powerful tools in various domains. Recent studies have shown that LLMs can surpass humans in certain tasks, such as predicting the outcomes of neuroscience studies. What role does this leave for humans in the overall decision process? One possibility is that humans, despite performing worse than LLMs, can still add value when teamed with them. A human and machine team can surpass each individual teammate when team members' confidence is well-calibrated and team members diverge in which tasks they find difficult (i.e., calibration and diversity are needed). We simplified and extended a Bayesian approach to combining judgments using a logistic regression framework that integrates confidence-weighted judgments for any number of team members. Using this straightforward method, we demonstrated in a neuroscience forecasting task that, even when humans were inferior to LLMs, their combination with one or more LLMs consistently improved team performance. Our hope is that this simple and effective strategy for integrating the judgments of humans and machines will lead to productive collaborations.

This paper presents an unsupervised method for single-channel blind dereverberation and room impulse response (RIR) estimation, called BUDDy. The algorithm is rooted in Bayesian posterior sampling: it combines a likelihood model enforcing fidelity to the reverberant measurement, and an anechoic speech prior implemented by an unconditional diffusion model. We design a parametric filter representing the RIR, with exponential decay for each frequency subband. Room acoustics estimation and speech dereverberation are jointly carried out, as the filter parameters are iteratively estimated and the speech utterance refined along the reverse diffusion trajectory. In a blind scenario where the room impulse response is unknown, BUDDy successfully performs speech dereverberation in various acoustic scenarios, significantly outperforming other blind unsupervised baselines. Unlike supervised methods, which often struggle to generalize, BUDDy seamlessly adapts to different acoustic conditions. This paper extends our previous work by offering new experimental results and insights into the algorithm's performance and versatility. We first investigate the robustness of informed dereverberation methods to RIR estimation errors, to motivate the joint acoustic estimation and dereverberation paradigm. Then, we demonstrate the adaptability of our method to high-resolution singing voice dereverberation, study its performance in RIR estimation, and conduct subjective evaluation experiments to validate the perceptual quality of the results, among other contributions. Audio samples and code can be found online.