We study the statistical complexity of offline Nevertheless, learning good policies from offline data decision-making with function approximation, presents a unique challenge not present in online decisionmaking: establishing (near) minimax-optimal rates for distributional shift. In essence, the policy that stochastic contextual bandits and Markov decision interacts with the environment and collects data differs from processes. The performance limits are captured by the target policy we aim to learn. This challenge becomes the pseudo-dimension of the (value) function class more pronounced in real-world problems with large state and a new characterization of the behavior policy spaces, where it necessitates function approximation to generalize that strictly subsumes all the previous notions of from observed states to unseen ones.

Learning the structure of Bayesian networks from data provides insights into underlying processes and the causal relationships that generate the data, but its usefulness depends on the homogeneity of the data population, a condition often violated in real-world applications. In such cases, using a single network structure for inference can be misleading, as it may not capture sub-population differences. To address this, we propose a novel approach of modelling a mixture of Bayesian networks where component probabilities depend on individual characteristics. Our method identifies both network structures and demographic predictors of sub-population membership, aiding personalised interventions. We evaluate our method through simulations and a youth mental health case study, demonstrating its potential to improve tailored interventions in health, education, and social policy.

Without any assumptions about data generation, multiple causal models may explain our observations equally well. To avoid selecting a single arbitrary model that could result in unsafe decisions if it does not match reality, it is therefore essential to maintain a notion of epistemic uncertainty about our possible candidates. This thesis studies the problem of structure learning from a Bayesian perspective, approximating the posterior distribution over the structure of a causal model, represented as a directed acyclic graph (DAG), given data. It introduces Generative Flow Networks (GFlowNets), a novel class of probabilistic models designed for modeling distributions over discrete and compositional objects such as graphs. They treat generation as a sequential decision making problem, constructing samples of a target distribution defined up to a normalization constant piece by piece. In the first part of this thesis, we present the mathematical foundations of GFlowNets, their connections to existing domains of machine learning and statistics such as variational inference and reinforcement learning, and their extensions beyond discrete problems. In the second part of this thesis, we show how GFlowNets can approximate the posterior distribution over DAG structures of causal Bayesian Networks, along with the parameters of its causal mechanisms, given observational and experimental data.

Score Distillation Sampling (SDS) has made significant strides in distilling image-generative models for 3D generation. However, its maximum-likelihood-seeking behavior often leads to degraded visual quality and diversity, limiting its effectiveness in 3D applications. In this work, we propose Consistent Flow Distillation (CFD), which addresses these limitations. We begin by leveraging the gradient of the diffusion ODE or SDE sampling process to guide the 3D generation. From the gradient-based sampling perspective, we find that the consistency of 2D image flows across different viewpoints is important for high-quality 3D generation. To achieve this, we introduce multi-view consistent Gaussian noise on the 3D object, which can be rendered from various viewpoints to compute the flow gradient. Our experiments demonstrate that CFD, through consistent flows, significantly outperforms previous methods in text-to-3D generation.

Error accumulation is effective for gradient sparsification in distributed settings: initially-unselected gradient entries are eventually selected as their accumulated error exceeds a certain level. The accumulation essentially behaves as a scaling of the learning rate for the selected entries. Although this property prevents the slow-down of lateral movements in distributed gradient descent, it can deteriorate convergence in some settings. This work proposes a novel sparsification scheme that controls the learning rate scaling of error accumulation. The development of this scheme follows two major steps: first, gradient sparsification is formulated as an inverse probability (inference) problem, and the Bayesian optimal sparsification mask is derived as a maximum-a-posteriori estimator. Using the prior distribution inherited from Top-$k$, we derive a new sparsification algorithm which can be interpreted as a regularized form of Top-$k$. We call this algorithm regularized Top-$k$ (RegTop-$k$). It utilizes past aggregated gradients to evaluate posterior statistics of the next aggregation. It then prioritizes the local accumulated gradient entries based on these posterior statistics. We validate our derivation through numerical experiments. In distributed linear regression, it is observed that while Top-$k$ remains at a fixed distance from the global optimum, RegTop-$k$ converges to the global optimum at significantly higher compression ratios. We further demonstrate the generalization of this observation by employing RegTop-$k$ in distributed training of ResNet-18 on CIFAR-10, where it noticeably outperforms Top-$k$.

Assistive mobile robots are a transformative technology that helps persons with disabilities regain the ability to move freely. Although autonomous wheelchairs significantly reduce user effort, they still require human input to allow users to maintain control and adapt to changing environments. Brain Computer Interface (BCI) stands out as a highly user-friendly option that does not require physical movement. Current BCI systems can understand whether users want to accelerate or decelerate, but they implement these changes in discrete speed steps rather than allowing for smooth, continuous velocity adjustments. This limitation prevents the systems from mimicking the natural, fluid speed changes seen in human self-paced motion. The authors aim to address this limitation by redesigning the perception-action cycle in a BCI controlled robotic system: improving how the robotic agent interprets the user's motion intentions (world state) and implementing these actions in a way that better reflects natural physical properties of motion, such as inertia and damping. The scope of this paper focuses on the perception aspect. We asked and answered a normative question "what computation should the robotic agent carry out to optimally perceive incomplete or noisy sensory observations?" Empirical EEG data were collected, and probabilistic representation that served as world state distributions were learned and evaluated in a Generative Adversarial Network framework. The ROS framework was established that connected with a Gazebo environment containing a digital twin of an indoor space and a virtual model of a robotic wheelchair. Signal processing and statistical analyses were implemented to identity the most discriminative features in the spatial-spectral-temporal dimensions, which are then used to construct the world model for the robotic agent to interpret user motion intentions as a Bayesian observer.

Monotone learning refers to learning processes in which expected performance consistently improves as more training data is introduced. Non-monotone behavior of machine learning has been the topic of a series of recent works, with various proposals that ensure monotonicity by applying transformations or wrappers on learning algorithms. In this work, from a different perspective, we tackle the topic of monotone learning within the framework of Probably Approximately Correct (PAC) learning theory. Following the mechanism that estimates sample complexity of a PAC-learnable problem, we derive a performance lower bound for that problem, and prove the monotonicity of that bound as the sample sizes increase. By calculating the lower bound distribution, we are able to prove that given a PAC-learnable problem with a hypothesis space that is either of finite size or of finite VC dimension, any learning algorithm based on Empirical Risk Minimization (ERM) is monotone if training samples are independent and identically distributed (i.i.d.). We further carry out an experiment on two concrete machine learning problems, one of which has a finite hypothesis set, and the other of finite VC dimension, and compared the experimental data for the empirical risk distributions with the estimated theoretical bound. The results of the comparison have confirmed the monotonicity of learning for the two PAC-learnable problems.

The performance of pavement under loading depends on the strength of the subgrade. However, experimental estimation of properties of pavement strengths such as California bearing ratio (CBR), unconfined compressive strength (UCS) and resistance value (R) are often tedious, time-consuming and costly, thereby inspiring a growing interest in machine learning based tools which are simple, cheap and fast alternatives. Thus, the potential application of two boosting techniques; categorical boosting (CatBoost) and extreme gradient boosting (XGBoost) and support vector regression (SVR), is similarly explored in this study for estimation of properties of subgrade soil modified with hydrated lime activated rice husk ash (HARSH). Using 121 experimental data samples of varying proportions of HARSH, plastic limit, liquid limit, plasticity index, clay activity, optimum moisture content, and maximum dry density as input for CBR, UCS and R estimation, four evaluation metrics namely coefficient of determination (R2), root mean squared error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE) are used to evaluate the models' performance. The results indicate that XGBoost outperformed CatBoost and SVR in estimating these properties, yielding R2 of 0.9994, 0.9995 and 0.9999 in estimating the CBR, UCS and R respectively. Also, SVR outperformed CatBoost in estimating the CBR and R with R2 of 0.9997 respectively. On the other hand, CatBoost outperformed SVR in estimating the UCS with R2 of 0.9994. Feature sensitivity analysis shows that the three machine learning techniques are unanimous that increasing HARSH proportion lead to values of the estimated properties respectively. A comparison with previous results also shows superiority of XGBoost in estimating subgrade properties.

An event sequence generated by a temporal point process is often associated with a hidden and structured event branching process that captures the triggering relations between its historical and current events. In this study, we design a new plug-and-play module based on the Bregman ADMM (BADMM) algorithm, which infers event branches associated with event sequences in the maximum likelihood estimation framework of temporal point processes (TPPs). Specifically, we formulate the inference of event branches as an optimization problem for the event transition matrix under sparse and low-rank constraints, which is embedded in existing TPP models or their learning paradigms. We can implement this optimization problem based on subspace clustering and sparse group-lasso, respectively, and solve it using the Bregman ADMM algorithm, whose unrolling leads to the proposed BADMM module. When learning a classic TPP (e.g., Hawkes process) by the expectation-maximization algorithm, the BADMM module helps derive structured responsibility matrices in the E-step. Similarly, the BADMM module helps derive low-rank and sparse attention maps for the neural TPPs with self-attention layers. The structured responsibility matrices and attention maps, which work as learned event transition matrices, indicate event branches, e.g., inferring isolated events and those key events triggering many subsequent events. Experiments on both synthetic and real-world data show that plugging our BADMM module into existing TPP models and learning paradigms can improve model performance and provide us with interpretable structured event branches.

Expanding on neural operators, we propose a novel framework for stochastic process learning across arbitrary domains. In particular, we develop operator flow matching (OFM) for learning stochastic process priors on function spaces. OFM provides the probability density of the values of any collection of points and enables mathematically tractable functional regression at new points with mean and density estimation. Our method outperforms state-of-the-art models in stochastic process learning, functional regression, and prior learning.