NeurIPS 2024 论文列表

Conference on Neural Information Processing Systems

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Semi-Random Matrix Completion via Flow-Based Adaptive Reweighting

Jonathan Kelner, Jerry Li, Allen Liu, Aaron Sidford, Kevin Tian

展开摘要

We consider the well-studied problem of completing a rank-$r$, $\mu$-incoherent matrix $\mathbf{M} \in \mathbb{R}^{d \times d}$ from incomplete observations. We focus on this problem in the semi-random setting where each entry is independently revealed with probability at least $p = \frac{\textup{poly}(r, \mu, \log d)}{d}$. Whereas multiple nearly-linear time algorithms have been established in the more specialized fully-random setting where each entry is revealed with probablity exactly $p$, the only known nearly-linear time algorithm in the semi-random setting is due to [CG18], whose sample complexity has a polynomial dependence on the inverse accuracy and condition number and thus cannot achieve high-accuracy recovery. Our main result is the first high-accuracy nearly-linear time algorithm for solving semi-random matrix completion, and an extension to the noisy observation setting. Our result builds upon the recent short-flat decomposition framework of [KLLST23a, KLLST23b] and leverages fast algorithms for flow problems on graphs to solve adaptive reweighting subproblems efficiently.

Poster
MultiOrg: A Multi-rater Organoid-detection Dataset

Christina Bukas, Harshavardhan Subramanian, Fenja See, Carina Steinchen, Ivan Ezhov, Gowtham Boosarpu, Sara Asgharpour, Gerald Burgstaller, Mareike Lehmann, Florian Kofler, Marie Piraud

展开摘要

High-throughput image analysis in the biomedical domain has gained significant attention in recent years, driving advancements in drug discovery, disease prediction, and personalized medicine. Organoids, specifically, are an active area of research, providing excellent models for human organs and their functions. Automating the quantification of organoids in microscopy images would provide an effective solution to overcome substantial manual quantification bottlenecks, particularly in high-throughput image analysis. However, there is a notable lack of open biomedical datasets, in contrast to other domains, such as autonomous driving, and, notably, only few of them have attempted to quantify annotation uncertainty. In this work, we present MultiOrg a comprehensive organoid dataset tailored for object detection tasks with uncertainty quantification. This dataset comprises over 400 high-resolution 2d microscopy images and curated annotations of more than 60,000 organoids. Most importantly, it includes three label sets for the test data, independently annotated by two experts at distinct time points. We additionally provide a benchmark for organoid detection, and make the best model available through an easily installable, interactive plugin for the popular image visualization tool Napari, to perform organoid quantification.

Poster
Polyhedral Complex Derivation from Piecewise Trilinear Networks

Jin-Hwa Kim

展开摘要

Recent advancements in visualizing deep neural networks provide insights into their structures and mesh extraction from Continuous Piecewise Affine (CPWA) functions. Meanwhile, developments in neural surface representation learning incorporate non-linear positional encoding, addressing issues like spectral bias; however, this poses challenges in applying mesh extraction techniques based on CPWA functions. Focusing on trilinear interpolating methods as positional encoding, we present theoretical insights and an analytical mesh extraction, showing the transformation of hypersurfaces to flat planes within the trilinear region under the eikonal constraint. Moreover, we introduce a method for approximating intersecting points among three hypersurfaces contributing to broader applications. We empirically validate correctness and parsimony through chamfer distance and efficiency, and angular distance, while examining the correlation between the eikonal loss and the planarity of the hypersurfaces.

Poster
No Free Delivery Service: Epistemic limits of passive data collection in complex social systems

Maximilian Nickel

展开摘要

Rapid model validation via the train-test paradigm has been a key driver for the breathtaking progress in machine learning and AI. However, modern AI systems often depend on a combination of tasks and data collection practices that violate all assumptions ensuring test validity. Yet, without rigorous model validation we cannot ensure the intended outcomes of deployed AI systems, including positive social impact, nor continue to advance AI research in a scientifically sound way. In this paper, I will show that for widely considered inference settings in complex social systems the train-test paradigm does not only lack a justification but is indeed invalid for any risk estimator, including counterfactual and causal estimators, with high probability. These formal impossibility results highlight a fundamental epistemic issue, i.e., that for key tasks in modern AI we cannot know whether models are valid under current data collection practices. Importantly, this includes variants of both recommender systems and reasoning via large language models, and neither naïve scaling nor limited benchmarks are suited to address this issue. I am illustrating these results via the widely used MovieLens benchmark and conclude by discussing the implications of these results for AI in social systems, including possible remedies such as participatory data curation and open science.

Poster
How does Gradient Descent Learn Features --- A Local Analysis for Regularized Two-Layer Neural Networks

Mo Zhou, Rong Ge

展开摘要

The ability of learning useful features is one of the major advantages of neural networks. Although recent works show that neural network can operate in a neural tangent kernel (NTK) regime that does not allow feature learning, many works also demonstrate the potential for neural networks to go beyond NTK regime and perform feature learning. Recently, a line of work highlighted the feature learning capabilities of the early stages of gradient-based training. In this paper we consider another mechanism for feature learning via gradient descent through a local convergence analysis. We show that once the loss is below a certain threshold, gradient descent with a carefully regularized objective will capture ground-truth directions. We further strengthen this local convergence analysis by incorporating early-stage feature learning analysis. Our results demonstrate that feature learning not only happens at the initial gradient steps, but can also occur towards the end of training.

Poster
Gradient Rewiring for Editable Graph Neural Network Training

Zhimeng Jiang, Zirui Liu, Xiaotian Han, Qizhang Feng, Hongye Jin, Qiaoyu Tan, Kaixiong Zhou, Na Zou, Xia Hu

展开摘要

Deep neural networks are ubiquitously adopted in many applications, such as computer vision, natural language processing, and graph analytics. However, well-trained neural networks can make prediction errors after deployment as the world changes. \textit{Model editing} involves updating the base model to correct prediction errors with less accessible training data and computational resources. Despite recent advances in model editors in computer vision and natural language processing, editable training in graph neural networks (GNNs) is rarely explored. The challenge with editable GNN training lies in the inherent information aggregation across neighbors, which can lead model editors to affect the predictions of other nodes unintentionally. In this paper, we first observe the gradient of cross-entropy loss for the target node and training nodes with significant inconsistency, which indicates that directly fine-tuning the base model using the loss on the target node deteriorates the performance on training nodes. Motivated by the gradient inconsistency observation, we propose a simple yet effective \underline{G}radient \underline{R}ewiring method for \underline{E}ditable graph neural network training, named \textbf{GRE}. Specifically, we first store the anchor gradient of the loss on training nodes to preserve the locality. Subsequently, we rewire the gradient of the loss on the target node to preserve performance on the training node using anchor gradient. Experiments demonstrate the effectiveness of GRE on various model architectures and graph datasets in terms of multiple editing situations. The source code is available at \url{https://github.com/zhimengj0326/Gradient_rewiring_editing}.

Poster
MedJourney: Benchmark and Evaluation of Large Language Models over Patient Clinical Journey

Xian Wu, Yutian Zhao, Yunyan Zhang, Jiageng Wu, Zhihong Zhu, Yingying Zhang, Yi Ouyang, Ziheng Zhang, Huimin Wang, Zhenxi Lin, Jie Yang, Shuang Zhao, Yefeng Zheng

展开摘要

Large language models (LLMs) have demonstrated remarkable capabilities in language understanding and generation, leading to their widespread adoption across various fields. Among these, the medical field is particularly well-suited for LLM applications, as many medical tasks can be enhanced by LLMs. Despite the existence of benchmarks for evaluating LLMs in medical question-answering and exams, there remains a notable gap in assessing LLMs' performance in supporting patients throughout their entire hospital visit journey in real-world clinical practice. In this paper, we address this gap by dividing a typical patient's clinical journey into four stages: planning, access, delivery and ongoing care. For each stage, we introduce multiple tasks and corresponding datasets, resulting in a comprehensive benchmark comprising 12 datasets, of which five are newly introduced, and seven are constructed from existing datasets. This proposed benchmark facilitates a thorough evaluation of LLMs' effectiveness across the entire patient journey, providing insights into their practical application in clinical settings. Additionally, we evaluate three categories of LLMs against this benchmark: 1) proprietary LLM services such as GPT-4; 2) public LLMs like QWen; and 3) specialized medical LLMs, like HuatuoGPT2. Through this extensive evaluation, we aim to provide a better understanding of LLMs' performance in the medical domain, ultimately contributing to their more effective deployment in healthcare settings.

Poster
Training-Free Open-Ended Object Detection and Segmentation via Attention as Prompts

Zhiwei Lin, Yongtao Wang, Zhi Tang

展开摘要

Existing perception models achieve great success by learning from large amounts of labeled data, but they still struggle with open-world scenarios. To alleviate this issue, researchers introduce open-set perception tasks to detect or segment unseen objects in the training set. However, these models require predefined object categories as inputs during inference, which are not available in real-world scenarios. Recently, researchers pose a new and more practical problem, i.e., open-ended object detection, which discovers unseen objects without any object categories as inputs. In this paper, we present VL-SAM, a training-free framework that combines the generalized object recognition model (i.e., Vision-Language Model) with the generalized object localization model (i.e., Segment-Anything Model), to address the open-ended object detection and segmentation task. Without additional training, we connect these two generalized models with attention maps as the prompts. Specifically, we design an attention map generation module by employing head aggregation and a regularized attention flow to aggregate and propagate attention maps across all heads and layers in VLM, yielding high-quality attention maps. Then, we iteratively sample positive and negative points from the attention maps with a prompt generation module and send the sampled points to SAM to segment corresponding objects. Experimental results on the long-tail instance segmentation dataset (LVIS) show that our method surpasses the previous open-ended method on the object detection task and can provide additional instance segmentation masks. Besides, VL-SAM achieves favorable performance on the corner case object detection dataset (CODA), demonstrating the effectiveness of VL-SAM in real-world applications. Moreover, VL-SAM exhibits good model generalization that can incorporate various VLMs and SAMs.

Poster
Optimus-1: Hybrid Multimodal Memory Empowered Agents Excel in Long-Horizon Tasks

Zaijing Li, Yuquan Xie, Rui Shao, Gongwei Chen, Dongmei Jiang, Liqiang Nie

展开摘要

Building a general-purpose agent is a long-standing vision in the field of artificial intelligence. Existing agents have made remarkable progress in many domains, yet they still struggle to complete long-horizon tasks in an open world. We attribute this to the lack of necessary world knowledge and multimodal experience that can guide agents through a variety of long-horizon tasks. In this paper, we propose a Hybrid Multimodal Memory module to address the above challenges. It 1) transforms knowledge into Hierarchical Directed Knowledge Graph that allows agents to explicitly represent and learn world knowledge, and 2) summarises historical information into Abstracted Multimodal Experience Pool that provide agents with rich references for in-context learning. On top of the Hybrid Multimodal Memory module, a multimodal agent, Optimus-1, is constructed with dedicated Knowledge-guided Planner and Experience-Driven Reflector, contributing to a better planning and reflection in the face of long-horizon tasks in Minecraft. Extensive experimental results show that Optimus-1 significantly outperforms all existing agents on challenging long-horizon task benchmarks, and exhibits near human-level performance on many tasks. In addition, we introduce various Multimodal Large Language Models (MLLMs) as the backbone of Optimus-1. Experimental results show that Optimus-1 exhibits strong generalization with the help of the Hybrid Multimodal Memory module, outperforming the GPT-4V baseline on many tasks.

Poster
MoLE: Enhancing Human-centric Text-to-image Diffusion via Mixture of Low-rank Experts

Jie Zhu, Yixiong Chen, Mingyu Ding, Ping Luo, Leye Wang, Jingdong Wang

展开摘要

Text-to-image diffusion has attracted vast attention due to its impressive image-generation capabilities. However, when it comes to human-centric text-to-image generation, particularly in the context of faces and hands, the results often fall short of naturalness due to insufficient training priors. We alleviate the issue in this work from two perspectives. 1) From the data aspect, we carefully collect a human-centric dataset comprising over one million high-quality human-in-the-scene images and two specific sets of close-up images of faces and hands. These datasets collectively provide a rich prior knowledge base to enhance the human-centric image generation capabilities of the diffusion model. 2) On the methodological front, we propose a simple yet effective method called Mixture of Low-rank Experts (MoLE) by considering low-rank modules trained on close-up hand and face images respectively as experts. This concept draws inspiration from our observation of low-rank refinement, where a low-rank module trained by a customized close-up dataset has the potential to enhance the corresponding image part when applied at an appropriate scale. To validate the superiority of MoLE in the context of human-centric image generation compared to state-of-the-art, we construct two benchmarks and perform evaluations with diverse metrics and human studies. Datasets, model, and code are released at https://sites.google.com/view/mole4diffuser/.

Poster
Maia-2: A Unified Model for Human-AI Alignment in Chess

Zhenwei Tang, Difan Jiao, Reid McIlroy-Young, Jon Kleinberg, Siddhartha Sen, Ashton Anderson

展开摘要

There are an increasing number of domains in which artificial intelligence (AI) systems both surpass human ability and accurately model human behavior. This introduces the possibility of algorithmically-informed teaching in these domains through more relatable AI partners and deeper insights into human decision-making. Critical to achieving this goal, however, is coherently modeling human behavior at various skill levels. Chess is an ideal model system for conducting research into this kind of human-AI alignment, with its rich history as a pivotal testbed for AI research, mature superhuman AI systems like AlphaZero, and precise measurements of skill via chess rating systems. Previous work in modeling human decision-making in chess uses completely independent models to capture human style at different skill levels, meaning they lack coherence in their ability to adapt to the full spectrum of human improvement and are ultimately limited in their effectiveness as AI partners and teaching tools. In this work, we propose a unified modeling approach for human-AI alignment in chess that coherently captures human style across different skill levels and directly captures how people improve. Recognizing the complex, non-linear nature of human learning, we introduce a skill-aware attention mechanism to dynamically integrate players’ strengths with encoded chess positions, enabling our model to be sensitive to evolving player skill. Our experimental results demonstrate that this unified framework significantly enhances the alignment between AI and human players across a diverse range of expertise levels, paving the way for deeper insights into human decision-making and AI-guided teaching tools.

Poster
Optimistic Critic Reconstruction and Constrained Fine-Tuning for General Offline-to-Online RL

Qin-Wen Luo, Ming-Kun Xie, Ye-Wen Wang, Sheng-Jun Huang

展开摘要

Offline-to-online (O2O) reinforcement learning (RL) provides an effective means of leveraging an offline pre-trained policy as initialization to improve performance rapidly with limited online interactions. Recent studies often design fine-tuning strategies for a specific offline RL method and cannot perform general O2O learning from any offline method. To deal with this problem, we disclose that there are evaluation and improvement mismatches between the offline dataset and the online environment, which hinders the direct application of pre-trained policies to online fine-tuning. In this paper, we propose to handle these two mismatches simultaneously, which aims to achieve general O2O learning from any offline method to any online method. Before online fine-tuning, we re-evaluate the pessimistic critic trained on the offline dataset in an optimistic way and then calibrate the misaligned critic with the reliable offline actor to avoid erroneous update. After obtaining an optimistic and and aligned critic, we perform constrained fine-tuning to combat distribution shift during online learning. We show empirically that the proposed method can achieve stable and efficient performance improvement on multiple simulated tasks when compared to the state-of-the-art methods.

Poster
Continuous Product Graph Neural Networks

Aref Einizade, Fragkiskos D. Malliaros, Jhony H. Giraldo

展开摘要

Processing multidomain data defined on multiple graphs holds significant potential in various practical applications in computer science. However, current methods are mostly limited to discrete graph filtering operations. Tensorial partial differential equations on graphs (TPDEGs) provide a principled framework for modeling structured data across multiple interacting graphs, addressing the limitations of the existing discrete methodologies. In this paper, we introduce Continuous Product Graph Neural Networks (CITRUS) that emerge as a natural solution to the TPDEG. CITRUS leverages the separability of continuous heat kernels from Cartesian graph products to efficiently implement graph spectral decomposition. We conduct thorough theoretical analyses of the stability and over-smoothing properties of CITRUS in response to domain-specific graph perturbations and graph spectra effects on the performance. We evaluate CITRUS on well-known traffic and weather spatiotemporal forecasting datasets, demonstrating superior performance over existing approaches. The implementation codes are available at https://github.com/ArefEinizade2/CITRUS.

Poster
Fine-Tuning is Fine, if Calibrated

Zheda Mai, Arpita Chowdhury, Ping Zhang, Cheng-Hao Tu, Hong-You Chen, Vardaan Pahuja, Tanya Berger-Wolf, Song Gao, Charles Stewart, Yu Su, Wei-Lun Chao

展开摘要

Fine-tuning is arguably the most straightforward way to tailor a pre-trained model (e.g., a foundation model) to downstream applications, but it also comes with the risk of losing valuable knowledge the model had learned in pre-training. For example, fine-tuning a pre-trained classifier capable of recognizing a large number of classes to master a subset of classes at hand is shown to drastically degrade the model's accuracy in the other classes it had previously learned. As such, it is hard to further use the fine-tuned model when it encounters classes beyond the fine-tuning data. In this paper, we systematically dissect the issue, aiming to answer the fundamental question, "What has been damaged in the fine-tuned model?" To our surprise, we find that the fine-tuned model neither forgets the relationship among the other classes nor degrades the features to recognize these classes. Instead, the fine-tuned model often produces more discriminative features for these other classes, even if they were missing during fine-tuning! What really hurts the accuracy is the discrepant logit scales between the fine-tuning classes and the other classes, implying that a simple post-processing calibration would bring back the pre-trained model's capability and at the same time unveil the feature improvement over all classes. We conduct an extensive empirical study to demonstrate the robustness of our findings and provide preliminary explanations underlying them, suggesting new directions for future theoretical analysis.

Poster
Probabilistic Decomposed Linear Dynamical Systems for Robust Discovery of Latent Neural Dynamics

Yenho Chen, Noga Mudrik, Kyle A. Johnsen, Sankaraleengam Alagapan, Adam Shabti Charles, Christopher John Rozell

展开摘要

Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve according to simple locally linear dynamics. However, existing methods for latent variable estimation are not robust to dynamical noise and system nonlinearity due to noise-sensitive inference procedures and limited model formulations. This can lead to inconsistent results on signals with similar dynamics, limiting the model's ability to provide scientific insight. In this work, we address these limitations and propose a probabilistic approach to latent variable estimation in decomposed models that improves robustness against dynamical noise. Additionally, we introduce an extended latent dynamics model to improve robustness against system nonlinearities. We evaluate our approach on several synthetic dynamical systems, including an empirically-derived brain-computer interface experiment, and demonstrate more accurate latent variable inference in nonlinear systems with diverse noise conditions. Furthermore, we apply our method to a real-world clinical neurophysiology dataset, illustrating the ability to identify interpretable and coherent structure where previous models cannot.

Poster
Linear Uncertainty Quantification of Graphical Model Inference

Chenghua Guo, Han Yu, Jiaxin Liu, Chao Chen, Qi Li, Sihong Xie, Xi Zhang

展开摘要

Uncertainty Quantification (UQ) is vital for decision makers as it offers insights into the potential reliability of data and model, enabling more informed and risk-aware decision-making. Graphical models, capable of representing data with complex dependencies, are widely used across domains. Existing sampling-based UQ methods are unbiased but cannot guarantee convergence and are time-consuming on large-scale graphs. There are fast UQ methods for graphical models with closed-form solutions and convergence guarantee but with uncertainty underestimation. We propose *LinUProp*, a UQ method that utilizes a novel linear propagation of uncertainty to model uncertainty among related nodes additively instead of multiplicatively, to offer linear scalability, guaranteed convergence, and closed-form solutions without underestimating uncertainty. Theoretically, we decompose the expected prediction error of the graphical model and prove that the uncertainty computed by *LinUProp* is the *generalized variance component* of the decomposition. Experimentally, we demonstrate that *LinUProp* is consistent with the sampling-based method but with linear scalability and fast convergence. Moreover, *LinUProp* outperforms competitors in uncertainty-based active learning on four real-world graph datasets, achieving higher accuracy with a lower labeling budget.

Poster
dopanim: A Dataset of Doppelganger Animals with Noisy Annotations from Multiple Humans

Marek Herde, Denis Huseljic, Lukas Rauch, Bernhard Sick

展开摘要

Human annotators typically provide annotated data for training machine learning models, such as neural networks. Yet, human annotations are subject to noise, impairing generalization performances. Methodological research on approaches counteracting noisy annotations requires corresponding datasets for a meaningful empirical evaluation. Consequently, we introduce a novel benchmark dataset, dopanim, consisting of about 15,750 animal images of 15 classes with ground truth labels. For approximately 10,500 of these images, 20 humans provided over 52,000 annotations with an accuracy of circa 67%. Its key attributes include (1) the challenging task of classifying doppelganger animals, (2) human-estimated likelihoods as annotations, and (3) annotator metadata. We benchmark well-known multi-annotator learning approaches using seven variants of this dataset and outline further evaluation use cases such as learning beyond hard class labels and active learning. Our dataset and a comprehensive codebase are publicly available to emulate the data collection process and to reproduce all empirical results.

Poster
Visual Data Diagnosis and Debiasing with Concept Graphs

Rwiddhi Chakraborty, Yinong Oliver Wang, Jialu Gao, Runkai Zheng, Cheng Zhang, Fernando De la Torre

展开摘要

The widespread success of deep learning models today is owed to the curation of extensive datasets significant in size and complexity. However, such models frequently pick up inherent biases in the data during the training process, leading to unreliable predictions. Diagnosing and debiasing datasets is thus a necessity to ensure reliable model performance. In this paper, we present ConBias, a novel framework for diagnosing and mitigating Concept co-occurrence Biases in visual datasets. ConBias represents visual datasets as knowledge graphs of concepts, enabling meticulous analysis of spurious concept co-occurrences to uncover concept imbalances across the whole dataset. Moreover, we show that by employing a novel clique-based concept balancing strategy, we can mitigate these imbalances, leading to enhanced performance on downstream tasks. Extensive experiments show that data augmentation based on a balanced concept distribution augmented by ConBias improves generalization performance across multiple datasets compared to state-of-the-art methods.

Poster
High-probability complexity bounds for stochastic non-convex minimax optimization

Yassine Laguel, Yasa Syed, Necdet Aybat, Mert Gurbuzbalaban

展开摘要

Stochastic smooth nonconvex minimax problems are prevalent in machine learning, e.g., GAN training, fair classification, and distributionally robust learning. Stochastic gradient descent ascent (GDA)-type methods are popular in practice due to their simplicity and single-loop nature. However, there is a significant gap between the theory and practice regarding high-probability complexity guarantees for these methods on stochastic nonconvex minimax problems. Existing high-probability bounds for GDA-type single-loop methods only apply to convex/concave minimax problems and to particular non-monotone variational inequality problems under some restrictive assumptions. In this work, we address this gap by providing the first high-probability complexity guarantees for nonconvex/PL minimax problems corresponding to a smooth function that satisfies the PL-condition in the dual variable. Specifically, we show that when the stochastic gradients are light-tailed, the smoothed alternating GDA method can compute an $\varepsilon$-stationary point within $\mathcal{O}(\frac{\ell \kappa^2 \delta^2}{\varepsilon^4} + \frac{\kappa}{\varepsilon^2}(\ell+\delta^2\log({1}/{\bar{q}})))$ stochastic gradient calls with probability at least $1-\bar{q}$ for any $\bar{q}\in(0,1)$, where $\mu$ is the PL constant, $\ell$ is the Lipschitz constant of the gradient, $\kappa=\ell/\mu$ is the condition number, and $\delta^2$ denotes a bound on the variance of stochastic gradients. We also present numerical results on a nonconvex/PL problem with synthetic data and on distributionally robust optimization problems with real data, illustrating our theoretical findings.

Poster
Sample Complexity of Interventional Causal Representation Learning

Emre Acartürk, Burak Varıcı, Karthikeyan Shanmugam, Ali Tajer

展开摘要

Consider a data-generation process that transforms low-dimensional _latent_ causally-related variables to high-dimensional _observed_ variables. Causal representation learning (CRL) is the process of using the observed data to recover the latent causal variables and the causal structure among them. Despite the multitude of identifiability results under various interventional CRL settings, the existing guarantees apply exclusively to the _infinite-sample_ regime (i.e., infinite observed samples). This paper establishes the first sample-complexity analysis for the finite-sample regime, in which the interactions between the number of observed samples and probabilistic guarantees on recovering the latent variables and structure are established. This paper focuses on _general_ latent causal models, stochastic _soft_ interventions, and a linear transformation from the latent to the observation space. The identifiability results ensure graph recovery up to ancestors and latent variables recovery up to mixing with parent variables. Specifically, ${\cal O}((\log \frac{1}{\delta})^{4})$ samples suffice for latent graph recovery up to ancestors with probability $1 - \delta$, and ${\cal O}((\frac{1}{\epsilon}\log \frac{1}{\delta})^{4})$ samples suffice for latent causal variables recovery that is $\epsilon$ close to the identifiability class with probability $1 - \delta$.

Poster