However, differential privacy's worst-case nature entails scaling such noise to the range of the queries even for

Topological methods have the potential of exploring data clouds without making assumptions on their the structure. Here we propose a hierarchical topological clustering algorithm that can be implemented with any distance choice. The persistence of outliers and clusters of arbitrary shape is inferred from the resulting hierarchy. We demonstrate the potential of the algorithm on selected datasets in which outliers play relevant roles, consisting of images, medical and economic data. These methods can provide meaningful clusters in situations in which other techniques fail to do so.

Nanopore sequencing is the third-generation sequencing technology with capabilities of generating long-read sequences and directly measuring modifications on DNA/RNA molecules, which makes it ideal for biological applications such as human Telomere-to-Telomere (T2T) genome assembly, Ebola virus surveillance and COVID-19 mRNA vaccine development. However, accuracies of computational methods in various tasks of Nanopore sequencing data analysis are far from satisfactory. For instance, the base calling accuracy of Nanopore RNA sequencing is $\sim$90\%, while the aim is $\sim$99.9\%. This highlights an urgent need of contributions from the machine learning community. A bottleneck that prevents machine learning researchers from entering this field is the lack of a large integrated benchmark dataset.

Computing expected predictions of discriminative models is a fundamental task in machine learning that appears in many interesting applications such as fairness, handling missing values, and data analysis. Unfortunately, computing expectations of a discriminative model with respect to a probability distribution defined by an arbitrary generative model has been proven to be hard in general. In fact, the task is intractable even for simple models such as logistic regression and a naive Bayes distribution. In this paper, we identify a pair of generative and discriminative models that enables tractable computation of expectations, as well as moments of any order, of the latter with respect to the former in case of regression. Specifically, we consider expressive probabilistic circuits with certain structural constraints that support tractable probabilistic inference. Moreover, we exploit the tractable computation of high-order moments to derive an algorithm to approximate the expectations for classification scenarios in which exact computations are intractable. Our framework to compute expected predictions allows for handling of missing data during prediction time in a principled and accurate way and enables reasoning about the behavior of discriminative models. We empirically show our algorithm to consistently outperform standard imputation techniques on a variety of datasets. Finally, we illustrate how our framework can be used for exploratory data analysis.

While synthetic data hold great promise for privacy protection, their statistical analysis poses significant challenges that necessitate innovative solutions. The use of deep generative models (DGMs) for synthetic data generation is known to induce considerable bias and imprecision into synthetic data analyses, compromising their inferential utility as opposed to original data analyses. This bias and uncertainty can be substantial enough to impede statistical convergence rates, even in seemingly straightforward analyses like mean calculation.

Estimating the probabilities of connections between vertices in a random network using an observed adjacency matrix is an important task for network data analysis. Many existing estimation methods are based on certain assumptions on network structure, which limit their applicability in practice. Without making strong assumptions, we develop an iterative connecting probability estimation method based on neighborhood averaging. Starting at a random initial point or an existing estimate, our method iteratively updates the pairwise vertex distances, the sets of similar vertices, and connecting probabilities to improve the precision of the estimate. We propose a two-stage neighborhood selection procedure to achieve the trade-off between smoothness of the estimate and the ability to discover local structure. The tuning parameters can be selected by cross-validation. We establish desirable theoretical properties for our method, and further justify its superior performance by comparing with existing methods in simulation and real data analysis.

Identifying and comparing topological features, particularly cycles, across different topological objects remains a fundamental challenge in persistent homology and topological data analysis. This work introduces a novel framework for constructing cycle communities through two complementary approaches. First, a dendrogram-based methodology leverages merge-tree algorithms to construct hierarchical representations of homology classes from persistence intervals. The Wasserstein distance on merge trees is introduced as a metric for comparing dendrograms, establishing connections to hierarchical clustering frameworks. Through simulation studies, the discriminative power of dendrogram representations for identifying cycle communities is demonstrated. Second, an extension of Stratified Gradient Sampling simultaneously learns multiple filter functions that yield cycle barycenter functions capable of faithfully reconstructing distinct sets of cycles. The set of cycles each filter function can reconstruct constitutes cycle communities that are non-overlapping and partition the space of all cycles. Together, these approaches transform the problem of cycle matching into both a hierarchical clustering and topological optimization framework, providing principled methods to identify similar topological structures both within and across groups of topological objects.

Classification of functional data where observations are curves or trajectories poses unique challenges, particularly under severe class imbalance. Traditional Random Forest algorithms, while robust for tabular data, often fail to capture the intrinsic structure of functional observations and struggle with minority class detection. This paper introduces Functional Random Forest with Adaptive Cost-Sensitive Splitting (FRF-ACS), a novel ensemble framework designed for imbalanced functional data classification. The proposed method leverages basis expansions and Functional Principal Component Analysis (FPCA) to represent curves efficiently, enabling trees to operate on low dimensional functional features. To address imbalance, we incorporate a dynamic cost sensitive splitting criterion that adjusts class weights locally at each node, combined with a hybrid sampling strategy integrating functional SMOTE and weighted bootstrapping. Additionally, curve specific similarity metrics replace traditional Euclidean measures to preserve functional characteristics during leaf assignment. Extensive experiments on synthetic and real world datasets including biomedical signals and sensor trajectories demonstrate that FRF-ACS significantly improves minority class recall and overall predictive performance compared to existing functional classifiers and imbalance handling techniques. This work provides a scalable, interpretable solution for high dimensional functional data analysis in domains where minority class detection is critical.

We present a proof-of-principle study demonstrating the use of large language model (LLM) agents to automate a representative high energy physics (HEP) analysis. Using the Higgs boson diphoton cross-section measurement as a case study with ATLAS Open Data, we design a hybrid system that combines an LLM-based supervisor-coder agent with the Snakemake workflow manager. In this architecture, the workflow manager enforces reproducibility and determinism, while the agent autonomously generates, executes, and iteratively corrects analysis code in response to user instructions. We define quantitative evaluation metrics including success rate, error distribution, costs per specific task, and average number of API calls, to assess agent performance across multi-stage workflows. To characterize variability across architectures, we benchmark a representative selection of state-of-the-art LLMs spanning the Gemini and GPT-5 series, the Claude family, and leading open-weight models. While the workflow manager ensures deterministic execution of all analysis steps, the final outputs still show stochastic variation. Although we set the temperature to zero, other sampling parameters (e.g., top-p, top-k) remained at their defaults, and some reasoning-oriented models internally adjust these settings. Consequently, the models do not produce fully deterministic results. This study establishes the first LLM-agent-driven automated data-analysis framework in HEP, enabling systematic benchmarking of model capabilities, stability, and limitations in real-world scientific computing environments. The baseline code used in this work is available at https://huggingface.co/HWresearch/LLM4HEP. This work was accepted as a poster at the Machine Learning and the Physical Sciences (ML4PS) workshop at NeurIPS 2025. The initial submission was made on August 30, 2025.

In this work, we present JT-DA-8B (JiuTian Data Analyst 8B), a specialized large language model designed for complex table reasoning tasks across diverse real-world scenarios. To address the lack of high-quality supervision in tabular reasoning scenarios, we construct a comprehensive and diverse training corpus with 34 well-defined table reasoning tasks, by aggregating 29 public table QA datasets and 3 million tables. An automatic pipeline is proposed to generate realistic multi-step analytical tasks involving reasoning patterns. The model is trained upon open-source JT-Coder-8B model, an 8B-parameter decoder-only foundation model trained from scratch. In the training stage, we leverage LLM-based scoring and workflow-aligned filtering to distill high-quality, table-centric data. Both supervised fine-tuning (SFT) and Reinforcement learning (RL) are adopted to optimize our model. Afterwards, a four-stage table reasoning workflow is proposed, including table preprocessing, table sensing, tool-integrated reasoning, and prompt engineering, to improve model interpretability and execution accuracy. Experimental results show that JT-DA-8B achieves strong performance in various table reasoning tasks, demonstrating the effectiveness of data-centric generation and workflow-driven optimization.