Machine learning models have exhibited exceptional results in various domains. The most prevalent approach for learning is the empirical risk minimizer (ERM), which adapts the model's weights to reduce the loss on a training set and subsequently leverages these weights to predict the label for new test data. Nonetheless, ERM makes the assumption that the test distribution is similar to the training distribution, which may not always hold in real-world situations. In contrast, the predictive normalized maximum likelihood (pNML) was proposed as a min-max solution for the individual setting where no assumptions are made on the distribution of the tested input. This study investigates pNML's learnability for linear regression and neural networks, and demonstrates that pNML can improve the performance and robustness of these models on various tasks. Moreover, the pNML provides an accurate confidence measure for its output, showcasing state-of-the-art results for out-of-distribution detection, resistance to adversarial attacks, and active learning.

Disease progression prediction based on patients' evolving health information is challenging when true disease states are unknown due to diagnostic capabilities or high costs. For example, the absence of gold-standard neurological diagnoses hinders distinguishing Alzheimer's disease (AD) from related conditions such as AD-related dementias (ADRDs), including Lewy body dementia (LBD). Combining temporally dependent surrogate labels and health markers may improve disease prediction. However, existing literature models informative surrogate labels and observed variables that reflect the underlying states using purely generative approaches, limiting the ability to predict future states. We propose integrating the conventional hidden Markov model as a generative model with a time-varying discriminative classification model to simultaneously handle potentially misspecified surrogate labels and incorporate important markers of disease progression. We develop an adaptive forward-backward algorithm with subjective labels for estimation, and utilize the modified posterior and Viterbi algorithms to predict the progression of future states or new patients based on objective markers only. Importantly, the adaptation eliminates the need to model the marginal distribution of longitudinal markers, a requirement in traditional algorithms. Asymptotic properties are established, and significant improvement with finite samples is demonstrated via simulation studies. Analysis of the neuropathological dataset of the National Alzheimer's Coordinating Center (NACC) shows much improved accuracy in distinguishing LBD from AD.

Although the Cox proportional hazards model is well established and extensively used in the analysis of survival data, the proportional hazards (PH) assumption may not always hold in practical scenarios. The semiparametric transformation model extends the conventional Cox model and also includes many other survival models as special cases. This paper introduces a deep partially linear transformation model (DPLTM) as a general and flexible framework for estimation, inference and prediction. The proposed method is capable of avoiding the curse of dimensionality while still retaining the interpretability of some covariates of interest. We derive the overall convergence rate of the maximum likelihood estimators, the minimax lower bound of the nonparametric deep neural network (DNN) estimator, the asymptotic normality and the semiparametric efficiency of the parametric estimator. Comprehensive simulation studies demonstrate the impressive performance of the proposed estimation procedure in terms of both estimation accuracy and prediction power, which is further validated by an application to a real-world dataset.

Causal discovery is a crucial initial step in establishing causality from empirical data and background knowledge. Numerous algorithms have been developed for this purpose. Among them, the score-matching method has demonstrated superior performance across various evaluation metrics, particularly for the commonly encountered Additive Nonlinear Causal Models. However, current score-matching-based algorithms are primarily designed to analyze independent and identically distributed (i.i.d.) data. More importantly, they suffer from high computational complexity due to the pruning step required for handling dense Directed Acyclic Graphs (DAGs). To enhance the scalability of score matching, we have developed a new parent-finding subroutine for leaf nodes in DAGs, significantly accelerating the most time-consuming part of the process: the pruning step. This improvement results in an efficiency-lifted score matching algorithm, termed Parent Identification-based Causal structure learning for both i.i.d. and temporal data on networKs, or PICK. The new score-matching algorithm extends the scope of existing algorithms and can handle static and temporal data on networks with weak network interference. Our proposed algorithm can efficiently cope with increasingly complex datasets that exhibit spatial and temporal dependencies, commonly encountered in academia and industry. The proposed algorithm can accelerate score-matching-based methods while maintaining high accuracy in real-world applications.

Are generative pre-trained transformer (GPT) models only trained to predict the next token, or do they implicitly learn a world model from which a sequence is generated one token at a time? We examine this question by deriving a causal interpretation of the attention mechanism in GPT, and suggesting a causal world model that arises from this interpretation. Furthermore, we propose that GPT-models, at inference time, can be utilized for zero-shot causal structure learning for in-distribution sequences. Empirical evaluation is conducted in a controlled synthetic environment using the setup and rules of the Othello board game. A GPT, pre-trained on real-world games played with the intention of winning, is tested on synthetic data that only adheres to the game rules. We find that the GPT model tends to generate next moves that adhere to the game rules for sequences for which the attention mechanism encodes a causal structure with high confidence. In general, in cases for which the GPT model generates moves that do not adhere to the game rules, it also fails to capture any causal structure.

Accurately reproducing real-world dynamics often requires stochastic simulators, particularly in fields like epidemiology, operations research, and hyperparameter tuning. In these contexts it becomes important to distinguish between aleatoric uncertainty - arising from noise in observations, from epistemic uncertainty - stemming from uncertainty in the model. The former is sometimes called intrinsic uncertainty while the latter is referred to as extrinsic uncertainty, see e.g., Ankenman et al. (2010). Gaussian process (GP) based surrogate methods (see, e.g., Rasmussen and Williams (2006); Gramacy (2020)) can be easily adapted from deterministic to noisy settings while maintaining strong predictive power, computational efficiency, and analytical tractability. Even in the deterministic setup, it is common to add a small diagonal nugget (also known as a jitter) term to the covariance matrix of the GP equations to ease its numerical inversion. It is also interpreted as a regularization term, especially in the reproducing kernel Hilbert space (RKHS) context, see, e.g., Kanagawa et al. (2018). This can be contrasted to the use of pseudo-inverses, which reverts to interpolation, see for instance the discussion by Mohammadi et al. (2016). Here we will prefer the term noise variance to relate it to intrinsic uncertainty, and also because the nugget effect has a different meaning in the kriging literature (see e.g., Roustant et al. (2012)).

To ensure and monitor large language models (LLMs) reliably, various evaluation metrics have been proposed in the literature. However, there is little research on prescribing a methodology to identify a robust threshold on these metrics even though there are many serious implications of an incorrect choice of the thresholds during deployment of the LLMs. Translating the traditional model risk management (MRM) guidelines within regulated industries such as the financial industry, we propose a step-by-step recipe for picking a threshold for a given LLM evaluation metric. We emphasize that such a methodology should start with identifying the risks of the LLM application under consideration and risk tolerance of the stakeholders. We then propose concrete and statistically rigorous procedures to determine a threshold for the given LLM evaluation metric using available ground-truth data. As a concrete example to demonstrate the proposed methodology at work, we employ it on the Faithfulness metric, as implemented in various publicly available libraries, using the publicly available HaluBench dataset. We also lay a foundation for creating systematic approaches to select thresholds, not only for LLMs but for any GenAI applications.

Flow Matching (FM) is a recent framework for generative modeling that has achieved state-of-the-art performance across various domains, including image, video, audio, speech, and biological structures. This guide offers a comprehensive and self-contained review of FM, covering its mathematical foundations, design choices, and extensions. By also providing a PyTorch package featuring relevant examples (e.g., image and text generation), this work aims to serve as a resource for both novice and experienced researchers interested in understanding, applying and further developing FM.

The capability of UAVs for efficient autonomous navigation and obstacle avoidance in complex and unknown environments is critical for applications in agricultural irrigation, disaster relief and logistics. In this paper, we propose the DPRL (Distributed Privileged Reinforcement Learning) navigation algorithm, an end-to-end policy designed to address the challenge of high-speed autonomous UAV navigation under partially observable environmental conditions. Our approach combines deep reinforcement learning with privileged learning to overcome the impact of observation data corruption caused by partial observability. We leverage an asymmetric Actor-Critic architecture to provide the agent with privileged information during training, which enhances the model's perceptual capabilities. Additionally, we present a multi-agent exploration strategy across diverse environments to accelerate experience collection, which in turn expedites model convergence. We conducted extensive simulations across various scenarios, benchmarking our DPRL algorithm against the state-of-the-art navigation algorithms. The results consistently demonstrate the superior performance of our algorithm in terms of flight efficiency, robustness and overall success rate.

In the last decade, Deep Reinforcement Learning has evolved into a powerful tool for complex sequential decision-making problems. It combines deep learning's proficiency in processing rich input signals with reinforcement learning's adaptability across diverse control tasks. At its core, an RL agent seeks to maximize its cumulative reward, enabling AI algorithms to uncover novel solutions previously unknown to experts. However, this focus on reward maximization also introduces a significant difficulty: improper reward specification can result in unexpected, misaligned agent behavior and inefficient learning. The complexity of accurately specifying the reward function is further amplified by the sequential nature of the task, the sparsity of learning signals, and the multifaceted aspects of the desired behavior. In this thesis, we survey the literature on effective reward specification strategies, identify core challenges relating to each of these approaches, and propose original contributions addressing the issue of sample efficiency and alignment in deep reinforcement learning. Reward specification represents one of the most challenging aspects of applying reinforcement learning in real-world domains. Our work underscores the absence of a universal solution to this complex and nuanced challenge; solving it requires selecting the most appropriate tools for the specific requirements of each unique application.