The goal of this thesis is to study the use of the Kantorovich-Rubinstein distance as to build a descriptor of sample complexity in classification problems. The idea is to use the fact that the Kantorovich-Rubinstein distance is a metric in the space of measures that also takes into account the geometry and topology of the underlying metric space. We associate to each class of points a measure and thus study the geometrical information that we can obtain from the Kantorovich-Rubinstein distance between those measures. We show that a large Kantorovich-Rubinstein distance between those measures allows to conclude that there exists a 1-Lipschitz classifier that classifies well the classes of points. We also discuss the limitation of the Kantorovich-Rubinstein distance as a descriptor.

Design of process control scheme is critical for quality assurance to reduce variations in manufacturing systems. Taking semiconductor manufacturing as an example, extensive literature focuses on control optimization based on certain process models (usually linear models), which are obtained by experiments before a manufacturing process starts. However, in real applications, pre-defined models may not be accurate, especially for a complex manufacturing system. To tackle model inaccuracy, we propose a model-free reinforcement learning (MFRL) approach to conduct experiments and optimize control simultaneously according to real-time data. Specifically, we design a novel MFRL control scheme by updating the distribution of disturbances using Bayesian inference to reduce their large variations during manufacturing processes. As a result, the proposed MFRL controller is demonstrated to perform well in a nonlinear chemical mechanical planarization (CMP) process when the process model is unknown. Theoretical properties are also guaranteed when disturbances are additive. The numerical studies also demonstrate the effectiveness and efficiency of our methodology.

Machine learning and data science heavily rely on probability distributions that are widely used to capture dependencies among large number of variables. Such high-dimensional distributions naturally appear in various domains including neuroscience [ROL02, CTY06], bioinformatics [BB01], text and image processing [Mur22], and causal inference [Pea09]. Substantial research has been devoted to developing models that represent high-dimensional probability distributions succinctly. One prevalent approach is through graphical models. In a graphical model, a graph describes the conditional dependencies among variables and the probability distribution is factorized according to the adjacency relationships in the graph [KF09]. When the underlying graph is a directed graph, the model is known as a Bayesian network or Bayes net. Two fundamental computational tasks on distributions are distance computation and probabilistic inference. In this work, we establish a novel connection between these two seemingly different computational tasks.

In combinatorial causal bandits (CCB), the learning agent chooses a subset of variables in each round to intervene and collects feedback from the observed variables to minimize expected regret or sample complexity. Previous works study this problem in both general causal models and binary generalized linear models (BGLMs). However, all of them require prior knowledge of causal graph structure. This paper studies the CCB problem without the graph structure on binary general causal models and BGLMs. We first provide an exponential lower bound of cumulative regrets for the CCB problem on general causal models. To overcome the exponentially large space of parameters, we then consider the CCB problem on BGLMs. We design a regret minimization algorithm for BGLMs even without the graph skeleton and show that it still achieves $O(\sqrt{T}\ln T)$ expected regret. This asymptotic regret is the same as the state-of-art algorithms relying on the graph structure. Moreover, we sacrifice the regret to $O(T^{\frac{2}{3}}\ln T)$ to remove the weight gap covered by the asymptotic notation. At last, we give some discussions and algorithms for pure exploration of the CCB problem without the graph structure.

We present TabPFN, a trained Transformer that can do supervised classification for small tabular datasets in less than a second, needs no hyperparameter tuning and is competitive with state-of-the-art classification methods. TabPFN performs in-context learning (ICL), it learns to make predictions using sequences of labeled examples (x, f(x)) given in the input, without requiring further parameter updates. TabPFN is fully entailed in the weights of our network, which accepts training and test samples as a set-valued input and yields predictions for the entire test set in a single forward pass. TabPFN is a Prior-Data Fitted Network (PFN) and is trained offline once, to approximate Bayesian inference on synthetic datasets drawn from our prior. This prior incorporates ideas from causal reasoning: It entails a large space of structural causal models with a preference for simple structures. On the 18 datasets in the OpenML-CC18 suite that contain up to 1 000 training data points, up to 100 purely numerical features without missing values, and up to 10 classes, we show that our method clearly outperforms boosted trees and performs on par with complex state-of-the-art AutoML systems with up to 230$\times$ speedup. This increases to a 5 700$\times$ speedup when using a GPU. We also validate these results on an additional 67 small numerical datasets from OpenML. We provide all our code, the trained TabPFN, an interactive browser demo and a Colab notebook at https://github.com/automl/TabPFN.

Diffusion models have recently emerged as the de facto standard for generating complex, high-dimensional outputs. You may know them for their ability to produce stunning AI art and hyper-realistic synthetic images, but they have also found success in other applications such as drug design and continuous control. The key idea behind diffusion models is to iteratively transform random noise into a sample, such as an image or protein structure. This is typically motivated as a maximum likelihood estimation problem, where the model is trained to generate samples that match the training data as closely as possible. However, most use cases of diffusion models are not directly concerned with matching the training data, but instead with a downstream objective.

With the development of aerospace technology, the increasing population of space debris has posed a great threat to the safety of spacecraft. However, the low intensity of reflected light and high angular velocity of space debris impede the extraction. Besides, due to the limitations of the ground observation methods, small space debris can hardly be detected, making it necessary to enhance the spacecraft's capacity for space situational awareness (SSA). Considering that traditional methods have some defects in low-SNR target detection, such as low effectiveness and large time consumption, this paper proposes a method for low-SNR streak extraction based on local contrast and maximum likelihood estimation (MLE), which can detect space objects with SNR 2.0 efficiently. In the proposed algorithm, local contrast will be applied for crude classifications, which will return connected components as preliminary results, and then MLE will be performed to reconstruct the connected components of targets via orientated growth, further improving the precision. The algorithm has been verified with both simulated streaks and real star tracker images, and the average centroid error of the proposed algorithm is close to the state-of-the-art method like ODCC. At the same time, the algorithm in this paper has significant advantages in efficiency compared with ODCC. In conclusion, the algorithm in this paper is of high speed and precision, which guarantees its promising applications in the extraction of high dynamic targets.

Inverse reinforcement learning (IRL) is the problem of extracting the reward function and policy of a value-maximizing agent from its behavior [1, 2]. IRL is an important tool in domains where manually specifying reward functions or policies is difficult, such as in autonomous driving [3], or when the extracted reward function can reveal novel insights about a target population and be used to device interventions, such as in biology, economics, and human-robot interaction studies [4, 5, 6]. However, wider applications of IRL face two interrelated algorithmic challenges: 1) having access to the target deployment environment or an accurate simulator thereof and 2) robustness of the learned policy and reward function due to the covariate shift between the training and deployment environments or datasets [7, 8, 9]. In this paper, we focus on model-based offline IRL to address challenge 1). A notable class of model-based offline IRL methods estimate the dynamics and reward in a two-stage fashion (see Figure 1) [10, 11, 12, 13]. In the first stage, a Figure 1: Objectives of the traditional two-stage dynamics model is estimated from the offline IRL and the proposed simultaneous estimation approach of Bayesian model-based IRL.

Counterfactual analysis is intuitively performed by humans on a daily basis eg. "What should I have done differently to get the loan approved?". Such counterfactual questions also steer the formulation of scientific hypotheses. More formally it provides insights about potential improvements of a system by inferring the effects of hypothetical interventions into a past observation of the system's behaviour which plays a prominent role in a variety of industrial applications. Due to the hypothetical nature of such analysis, counterfactual distributions are inherently ambiguous. This ambiguity is particularly challenging in continuous settings in which a continuum of explanations exist for the same observation. In this paper, we address this problem by following a hierarchical Bayesian approach which explicitly models such uncertainty. In particular, we derive counterfactual distributions for a Bayesian Warped Gaussian Process thereby allowing for non-Gaussian distributions and non-additive noise. We illustrate the properties our approach on a synthetic and on a semi-synthetic example and show its performance when used within an algorithmic recourse downstream task.

A key challenge in eXplainable Artificial Intelligence is the well-known tradeoff between the transparency of an algorithm (i.e., how easily a human can directly understand the algorithm, as opposed to receiving a post-hoc explanation), and its accuracy. We report on the design of a new deep network that achieves improved transparency without sacrificing accuracy. We design a deep convolutional neuro-fuzzy inference system (DCNFIS) by hybridizing fuzzy logic and deep learning models and show that DCNFIS performs as accurately as three existing convolutional neural networks on four well-known datasets. We furthermore that DCNFIS outperforms state-of-the-art deep fuzzy systems. We then exploit the transparency of fuzzy logic by deriving explanations, in the form of saliency maps, from the fuzzy rules encoded in DCNFIS. We investigate the properties of these explanations in greater depth using the Fashion-MNIST dataset.