Ordering-based approaches to causal discovery identify topological orders of causal graphs, providing scalable alternatives to combinatorial search methods. Under the Additive Noise Models (ANMs) assumption, recent causal ordering methods based on score matching require an accurate estimation of the Hessian diagonal of the log-densities. However, previous approaches mainly use Stein gradient estimators, which are computationally expensive and memory-intensive. Although DiffAN addresses these limitations by substituting kernel-based estimates with diffusion models, it remains numerically unstable due to the second-order derivatives of score models. To alleviate these problems, we propose Score-informed Neural Operator (SciNO), a probabilistic generative model in smooth function spaces designed to stably approximate the Hessian diagonal and to preserve structural information during the score modeling. Empirical results show that SciNO reduces order divergence by 42.7% on synthetic graphs and by 31.5% in real-world datasets on average compared to DiffAN, while maintaining memory efficiency and scalability. Furthermore, we propose a probabilistic control algorithm for causal reasoning with autoregressive models that integrates SciNO's probability estimates with autoregressive model priors, enabling reliable data-driven causal ordering informed by semantic information. Consequently, the proposed method enhances causal reasoning abilities of LLMs without additional fine-tuning or prompt engineering.

This paper addresses the problem of multi-risk measure agnostic multi-armed bandits in heavy-tailed reward settings. We propose a framework that leverages novel deviation inequalities for the $1$-Wasserstein distance to construct confidence intervals for Lipschitz risk measures. The distributional LCB (DistLCB) algorithm is introduced, which achieves asymptotic optimality by deriving the first lower bounds for risk measure aware bandits with explicit sub-optimality gap dependencies. The DistLCB is further extended to multi-risk objectives, which enables Pareto-optimal solutions that consider multiple aspects of reward distributions. Additionally, we provide a regret analysis that includes both gap-dependent and gap-independent bounds for multi-risk settings. Experiments validate the effectiveness of the proposed methods in synthetic and real-world applications.

Recent advancements in diffusion models and diffusion bridges primarily focus on finite-dimensional spaces, yet many real-world problems necessitate operations in infinite-dimensional function spaces for more natural and interpretable formulations. In this paper, we present a theory of stochastic optimal control (SOC) tailored to infinite-dimensional spaces, aiming to extend diffusion-based algorithms to function spaces. Specifically, we demonstrate how Doob’s $h$-transform, the fundamental tool for constructing diffusion bridges, can be derived from the SOC perspective and expanded to infinite dimensions. This expansion presents a challenge, as infinite-dimensional spaces typically lack closed-form densities. Leveraging our theory, we establish that solving the optimal control problem with a specific objective function choice is equivalent to learning diffusion-based generative models. We propose two applications: 1) learning bridges between two infinite-dimensional distributions and 2) generative models for sampling from an infinite-dimensional distribution. Our approach proves effective for diverse problems involving continuous function space representations, such as resolution-free images, time-series data, and probability density functions.

Interactive segmentation methods have been investigated to address the potential need for additional refinement in automatic segmentation via human-in-the-loop techniques. For accurate segmentation of 3D images, we propose Slice-and-Conquer, a novel planar-to-3D pipeline formulating volumetric mask construction into two stages: 1) 2D interactive segmentation and 2) guided 3D segmentation. Specifically, the first stage enables users to focus on a single 2D slice and provides the corresponding 2D prediction results as strong shape priors. Taking the planar guidance, an accurate 3D mask can be constructed with minimal interactions. To support a flexible iterative refinement, our system recommends a next slice to annotate at the end of the second stage. Since volumetric segmentation can be completed by consecutively annotating a few recommended 2D slices, our method significantly reduces the cognitive burden of exploring volumetric space for users. Through extensive experiments on various datasets of 3D biomedical images, we demonstrate the effectiveness of the proposed pipeline.

Stochastic multiarmed bandits (stochastic MABs) are a problem of sequential decision-making with noisy rewards, where an agent sequentially chooses actions under unknown reward distributions to minimize cumulative regret. The majority of prior works on stochastic MABs assume that the reward distribution of each action has bounded supports or follows light-tailed distribution, i.e., sub-Gaussian distribution. However, in a variety of decision-making problems, the reward distributions follow a heavy-tailed distribution. In this regard, we consider stochastic MABs with heavy-tailed rewards, whose$p$th moment is bounded by a constant$\nu_{p}$for$1

Continuous-time score-based generative models consist of a pair of stochastic differential equations (SDEs)—a forward SDE that smoothly transitions data into a noise space and a reverse SDE that incrementally eliminates noise from a Gaussian prior distribution to generate data distribution samples—are intrinsically connected by the time-reversal theory on diffusion processes. In this paper, we investigate the use of stochastic evolution equations in Hilbert spaces, which expand the applicability of SDEs in two aspects: sample space and evolution operator, so they enable encompassing recent variations of diffusion models, such as generating functional data or replacing drift coefficients with image transformation. To this end, we derive a generalized time-reversal formula to build a bridge between probabilistic diffusion models and stochastic evolution equations and propose a score-based generative model called Hilbert Diffusion Model (HDM). Combining with Fourier neural operator, we verify the superiority of HDM for sampling functions from functional datasets with a power of kernel two-sample test of 4.2 on Quadratic, 0.2 on Melbourne, and 3.6 on Gridwatch, which outperforms existing diffusion models formulated in function spaces. Furthermore, the proposed method shows its strength in motion synthesis tasks by utilizing the Wiener process with values in Hilbert space. Finally, our empirical results on image datasets also validate a connection between HDM and diffusion models using heat dissipation, revealing the potential for exploring evolution operators and sample spaces.

Investigating the optimal stochastic process beyond Gaussian for noise injection in a score-based generative model remains an open question. Brownian motion is a light-tailed process with continuous paths, which leads to a slow convergence rate for the Number of Function Evaluation (NFE). Recent studies have shown that diffusion models suffer from mode-collapse issues on imbalanced data. In order to overcome the limitations of Brownian motion, we introduce a novel score-based generative model referred to as Lévy-Itō Model (LIM). This model utilizes isotropic $\alpha$-stable Lévy processes. We first derive an exact reverse-time stochastic differential equation driven by the Lévy process and develop the corresponding fractional denoising score matching. The proposed generative model takes advantage of the heavy-tailed properties of the Lévy process. Our experimental results show LIM allows for faster and more diverse sampling while maintaining high fidelity compared to existing diffusion models across various image datasets such as CIFAR10, CelebA, and imbalanced dataset CIFAR10LT. Comparing our results to those of DDPM with 3.21 Fréchet Inception Distance (FID) and 0.6437 Recall on the CelebA dataset, we achieve 1.58 FID and 0.7006 Recall using the same architecture. LIM shows the best performance in NFE 500 with $2\times$ faster total wall-clock time than the baseline.

Bootstrapping has been a primary tool for ensemble and uncertainty quantification in machine learning and statistics. However, due to its nature of multiple training and resampling, bootstrapping deep neural networks is computationally burdensome; hence it has difficulties in practical application to the uncertainty estimation and related tasks. To overcome this computational bottleneck, we propose a novel approach called Neural Bootstrapper (NeuBoots), which learns to generate bootstrapped neural networks through single model training. NeuBoots injects the bootstrap weights into the high-level feature layers of the backbone network and outputs the bootstrapped predictions of the target, without additional parameters and the repetitive computations from scratch. We apply NeuBoots to various machine learning tasks related to uncertainty quantification, including prediction calibrations in image classification and semantic segmentation, active learning, and detection of out-of-distribution samples. Our empirical results show that NeuBoots outperforms other bagging based methods under a much lower computational cost without losing the validity of bootstrapping.

Many important applications, including robotics, data-center management, and process control, require planning action sequences in domains with continuous state and action spaces and discontinuous objective functions. Monte Carlo tree search (MCTS) is an effective strategy for planning in discrete action spaces. We provide a novel MCTS algorithm (voot) for deterministic environments with continuous action spaces, which, in turn, is based on a novel black-box function-optimization algorithm (voo) to efficiently sample actions. The voo algorithm uses Voronoi partitioning to guide sampling, and is particularly efficient in high-dimensional spaces. The voot algorithm has an instance of voo at each node in the tree. We provide regret bounds for both algorithms and demonstrate their empirical effectiveness in several high-dimensional problems including two difficult robotics planning problems.

In this paper, we focus on weakly supervised learning with noisy training data for both classification and regression problems. We assume that the training outputs are collected from a mixture of a target and correlated noise distributions. Our proposed method simultaneously estimates the target distribution and the quality of each data which is defined as the correlation between the target and data generating distributions. The cornerstone of the proposed method is a Cholesky Block that enables modeling dependencies among mixture distributions in a differentiable manner where we maintain the distribution over the network weights. We first provide illustrative examples in both regression and classification tasks to show the effectiveness of the proposed method. Then, the proposed method is extensively evaluated in a number of experiments where we show that it constantly shows comparable or superior performances compared to existing baseline methods in the handling of noisy data.

In this paper, we consider stochastic multi-armed bandits (MABs) with heavy-tailed rewards, whose p-th moment is bounded by a constant nu_p for 1

Data augmentation is an essential technique for improving generalization ability of deep learning models. Recently, AutoAugment \cite{cubuk2018autoaugment} has been proposed as an algorithm to automatically search for augmentation policies from a dataset and has significantly enhanced performances on many image recognition tasks. However, its search method requires thousands of GPU hours even for a relatively small dataset. In this paper, we propose an algorithm called Fast AutoAugment that finds effective augmentation policies via a more efficient search strategy based on density matching. In comparison to AutoAugment, the proposed algorithm speeds up the search time by orders of magnitude while achieves comparable performances on image recognition tasks with various models and datasets including CIFAR-10, CIFAR-100, SVHN, and ImageNet. Our code is open to the public by the official GitHub\footnote{\url{https://github.com/kakaobrain/fast-autoaugment}} of Kakao Brain.

In this paper, we propose an uncertainty-aware learning from demonstration method by presenting a novel uncertainty estimation method utilizing a mixture density network appropriate for modeling complex and noisy human behaviors. The proposed uncertainty acquisition can be done with a single forward path without Monte Carlo sampling and is suitable for real-time robotics applications. Then, we show that it can be decomposed into explained variance and unexplained variance where the connections between aleatoric and epistemic uncertainties are addressed. The properties of the proposed uncertainty measure are analyzed through three different synthetic examples, absence of data, heavy measurement noise, and composition of functions scenarios. We show that each case can be distinguished using the proposed uncertainty measure and presented an uncertainty-aware learning from demonstration method for autonomous driving using this property. The proposed uncertainty-aware learning from demonstration method outperforms other compared methods in terms of safety using a complex real-world driving dataset.