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Existing studies have demonstrated significant sex differences in the neural mechanisms of daily life and neuropsychiatric disorders. The hierarchical organization of the functional brain network is a critical feature for assessing these neural mechanisms. But sex differences on the hierarchical organization is not fully investigated. Here, we explore whether hierarchical structure of brain network differs between females and males. At the group level, we measure the hierarchical entropy and the maximum modularity of each individual, and identify a significant negative correlation between the complexity of hierarchy and modularity in brain networks. On average, female brain networks have stronger connectivity within the module, whereas male brain networks demonstrate more complex hierarchy. At the consensus level, we use co-classification matrix to investigate the detailed differences in the hierarchical organization between sexes and observe that females and males exhibit different interaction patterns of brain regions in the dorsal attention network (DAN) and visual network (VIN). Our finding suggests that females and males employ different network topology to achieve brain functions. In addition, the negative correlation between hierarchy and modularity implies a need to balance the complexity in hierarchical organization of the brain network, which shed light on future studies of brain functions., Comment: 12 pages,4 figures

Recent works have demonstrated the effectiveness of retrieval augmentation in the Event Argument Extraction (EAE) task. However, existing retrieval-based EAE methods have two main limitations: (1) input length constraints and (2) the gap between the retriever and the inference model. These issues limit the diversity and quality of the retrieved information. In this paper, we propose a Compressive Memory-based Retrieval (CMR) mechanism for EAE, which addresses the two limitations mentioned above. Our compressive memory, designed as a dynamic matrix that effectively caches retrieved information and supports continuous updates, overcomes the limitations of the input length. Additionally, after pre-loading all candidate demonstrations into the compressive memory, the model further retrieves and filters relevant information from memory based on the input query, bridging the gap between the retriever and the inference model. Extensive experiments show that our method achieves new state-of-the-art performance on three public datasets (RAMS, WikiEvents, ACE05), significantly outperforming existing retrieval-based EAE methods., Comment: 15 pages

Currently, machine learning techniques have seen significant success across various applications. Most of these techniques rely on supervision from human-generated labels or a mixture of noisy and imprecise labels from multiple sources. However, for certain complex tasks, even noisy or inexact labels are unavailable due to the intricacy of the objectives. To tackle this issue, we propose a method that breaks down the complex objective into simpler tasks and generates supervision signals for each one. We then integrate these supervision signals into a manageable form, resulting in a straightforward learning procedure. As a case study, we demonstrate a system used for topic-based summarization. This system leverages rich supervision signals to promote both summarization and topic relevance. Remarkably, we can train the model end-to-end without any labels. Experimental results indicate that our approach performs exceptionally well on the CNN and DailyMail datasets.

Gibbs sampling is one of the most commonly used Markov Chain Monte Carlo (MCMC) algorithms due to its simplicity and efficiency. It cycles through the latent variables, sampling each one from its distribution conditional on the current values of all the other variables. Conventional Gibbs sampling is based on the systematic scan (with a deterministic order of variables). In contrast, in recent years, Gibbs sampling with random scan has shown its advantage in some scenarios. However, almost all the analyses of Gibbs sampling with the random scan are based on uniform selection of variables. In this paper, we focus on a random scan Gibbs sampling method that selects each latent variable non-uniformly. Firstly, we show that this non-uniform scan Gibbs sampling leaves the target posterior distribution invariant. Then we explore how to determine the selection probability for latent variables. In particular, we construct an objective as a function of the selection probability and solve the constrained optimization problem. We further derive an analytic solution of the selection probability, which can be estimated easily. Our algorithm relies on the simple intuition that choosing the variable updates according to their marginal probabilities enhances the mixing time of the Markov chain. Finally, we validate the effectiveness of the proposed Gibbs sampler by conducting a set of experiments on real-world applications.

The single-stage point-based 3D object detectors have attracted widespread research interest due to their advantages of lightweight and fast inference speed. However, they still face challenges such as inadequate learning of low-quality objects (ILQ) and misalignment between localization accuracy and classification confidence (MLC). In this paper, we propose SGCCNet to alleviate these two issues. For ILQ, SGCCNet adopts a Saliency-Guided Data Augmentation (SGDA) strategy to enhance the robustness of the model on low-quality objects by reducing its reliance on salient features. Specifically, We construct a classification task and then approximate the saliency scores of points by moving points towards the point cloud centroid in a differentiable process. During the training process, SGCCNet will be forced to learn from low saliency features through dropping points. Meanwhile, to avoid internal covariate shift and contextual features forgetting caused by dropping points, we add a geometric normalization module and skip connection block in each stage. For MLC, we design a Confidence Correction Mechanism (CCM) specifically for point-based multi-class detectors. This mechanism corrects the confidence of the current proposal by utilizing the predictions of other key points within the local region in the post-processing stage. Extensive experiments on the KITTI dataset demonstrate the generality and effectiveness of our SGCCNet. On the KITTI \textit{test} set, SGCCNet achieves $80.82\%$ for the metric of $AP_{3D}$ on the \textit{Moderate} level, outperforming all other point-based detectors, surpassing IA-SSD and Fast Point R-CNN by $2.35\%$ and $3.42\%$, respectively. Additionally, SGCCNet demonstrates excellent portability for other point-based detectors, Comment: 16 pages, 16 figures

Therapeutic antibodies have been extensively studied in drug discovery and development in the past decades. Antibodies are specialized protective proteins that bind to antigens in a lock-to-key manner. The binding strength/affinity between an antibody and a specific antigen is heavily determined by the complementarity-determining regions (CDRs) on the antibodies. Existing machine learning methods cast in silico development of CDRs as either sequence or 3D graph (with a single chain) generation tasks and have achieved initial success. However, with CDR loops having specific geometry shapes, learning the 3D geometric structures of CDRs remains a challenge. To address this issue, we propose AntibodyFlow, a 3D flow model to design antibody CDR loops. Specifically, AntibodyFlow first constructs the distance matrix, then predicts amino acids conditioned on the distance matrix. Also, AntibodyFlow conducts constraint learning and constrained generation to ensure valid 3D structures. Experimental results indicate that AntibodyFlow outperforms the best baseline consistently with up to 16.0% relative improvement in validity rate and 24.3% relative reduction in geometric graph level error (root mean square deviation, RMSD).

Recent mainstream event argument extraction methods process each event in isolation, resulting in inefficient inference and ignoring the correlations among multiple events. To address these limitations, here we propose a multiple-event argument extraction model DEEIA (Dependency-guided Encoding and Event-specific Information Aggregation), capable of extracting arguments from all events within a document simultaneouslyThe proposed DEEIA model employs a multi-event prompt mechanism, comprising DE and EIA modules. The DE module is designed to improve the correlation between prompts and their corresponding event contexts, whereas the EIA module provides event-specific information to improve contextual understanding. Extensive experiments show that our method achieves new state-of-the-art performance on four public datasets (RAMS, WikiEvents, MLEE, and ACE05), while significantly saving the inference time compared to the baselines. Further analyses demonstrate the effectiveness of the proposed modules., Comment: Accepted to Findings of ACL 2024

Recent studies have highlighted the presence of cultural biases in Large Language Models (LLMs), yet often lack a robust methodology to dissect these phenomena comprehensively. Our work aims to bridge this gap by delving into the Food domain, a universally relevant yet culturally diverse aspect of human life. We introduce FmLAMA, a multilingual dataset centered on food-related cultural facts and variations in food practices. We analyze LLMs across various architectures and configurations, evaluating their performance in both monolingual and multilingual settings. By leveraging templates in six different languages, we investigate how LLMs interact with language-specific and cultural knowledge. Our findings reveal that (1) LLMs demonstrate a pronounced bias towards food knowledge prevalent in the United States; (2) Incorporating relevant cultural context significantly improves LLMs' ability to access cultural knowledge; (3) The efficacy of LLMs in capturing cultural nuances is highly dependent on the interplay between the probing language, the specific model architecture, and the cultural context in question. This research underscores the complexity of integrating cultural understanding into LLMs and emphasizes the importance of culturally diverse datasets to mitigate biases and enhance model performance across different cultural domains., Comment: 20 pages,8 figures

Directed acyclic graphs (DAGs) are commonly used to model causal relationships among random variables. In general, learning the DAG structure is both computationally and statistically challenging. Moreover, without additional information, the direction of edges may not be estimable from observational data. In contrast, given a complete causal ordering of the variables, the problem can be solved efficiently, even in high dimensions. In this paper, we consider the intermediate problem of learning DAGs when a partial causal ordering of variables is available. We propose a general estimation framework for leveraging the partial ordering and present efficient estimation algorithms for low- and high-dimensional problems. The advantages of the proposed framework are illustrated via numerical studies., Comment: 29 pages, 5 figures

The increasing computational demands of modern neural networks present deployment challenges on resource-constrained devices. Network pruning offers a solution to reduce model size and computational cost while maintaining performance. However, most current pruning methods focus primarily on improving sparsity by reducing the number of nonzero parameters, often neglecting other deployment costs such as inference time, which are closely related to the number of floating-point operations (FLOPs). In this paper, we propose FALCON, a novel combinatorial-optimization-based framework for network pruning that jointly takes into account model accuracy (fidelity), FLOPs, and sparsity constraints. A main building block of our approach is an integer linear program (ILP) that simultaneously handles FLOP and sparsity constraints. We present a novel algorithm to approximately solve the ILP. We propose a novel first-order method for our optimization framework which makes use of our ILP solver. Using problem structure (e.g., the low-rank structure of approx. Hessian), we can address instances with millions of parameters. Our experiments demonstrate that FALCON achieves superior accuracy compared to other pruning approaches within a fixed FLOP budget. For instance, for ResNet50 with 20% of the total FLOPs retained, our approach improves the accuracy by 48% relative to state-of-the-art. Furthermore, in gradual pruning settings with re-training between pruning steps, our framework outperforms existing pruning methods, emphasizing the significance of incorporating both FLOP and sparsity constraints for effective network pruning.

With the rapid advancement of hardware and software technologies, research in autonomous driving has seen significant growth. The prevailing framework for multi-sensor autonomous driving encompasses sensor installation, perception, path planning, decision-making, and motion control. At the perception phase, a common approach involves utilizing neural networks to infer 3D bounding box (Bbox) attributes from raw sensor data, including classification, size, and orientation. In this paper, we present a novel attribute and its corresponding algorithm: 3D object visibility. By incorporating multi-task learning, the introduction of this attribute, visibility, negligibly affects the model's effectiveness and efficiency. Our proposal of this attribute and its computational strategy aims to expand the capabilities for downstream tasks, thereby enhancing the safety and reliability of real-time autonomous driving in real-world scenarios.

Graph clustering, an important unsupervised problem, has been shown to be more resistant to advances in Graph Neural Networks (GNNs). In addition, almost all clustering methods focus on homophilic graphs and ignore heterophily. This significantly limits their applicability in practice, since real-world graphs exhibit a structural disparity and cannot simply be classified as homophily and heterophily. Thus, a principled way to handle practical graphs is urgently needed. To fill this gap, we provide a novel solution with theoretical support. Interestingly, we find that most homophilic and heterophilic edges can be correctly identified on the basis of neighbor information. Motivated by this finding, we construct two graphs that are highly homophilic and heterophilic, respectively. They are used to build low-pass and high-pass filters to capture holistic information. Important features are further enhanced by the squeeze-and-excitation block. We validate our approach through extensive experiments on both homophilic and heterophilic graphs. Empirical results demonstrate the superiority of our method compared to state-of-the-art clustering methods., Comment: 12 pages, 5 figures

Graph is a fundamental mathematical structure in characterizing relations between different objects and has been widely used on various learning tasks. Most methods implicitly assume a given graph to be accurate and complete. However, real data is inevitably noisy and sparse, which will lead to inferior results. Despite the remarkable success of recent graph representation learning methods, they inherently presume that the graph is homophilic, and largely overlook heterophily, where most connected nodes are from different classes. In this regard, we propose a novel robust graph structure learning method to achieve a high-quality graph from heterophilic data for downstream tasks. We first apply a high-pass filter to make each node more distinctive from its neighbors by encoding structure information into the node features. Then, we learn a robust graph with an adaptive norm characterizing different levels of noise. Afterwards, we propose a novel regularizer to further refine the graph structure. Clustering and semi-supervised classification experiments on heterophilic graphs verify the effectiveness of our method., Comment: 26 pages, 5 figures

While Transformer-based pre-trained language models and their variants exhibit strong semantic representation capabilities, the question of comprehending the information gain derived from the additional components of PLMs remains an open question in this field. Motivated by recent efforts that prove Multilayer-Perceptrons (MLPs) modules achieving robust structural capture capabilities, even outperforming Graph Neural Networks (GNNs), this paper aims to quantify whether simple MLPs can further enhance the already potent ability of PLMs to capture linguistic information. Specifically, we design a simple yet effective probing framework containing MLPs components based on BERT structure and conduct extensive experiments encompassing 10 probing tasks spanning three distinct linguistic levels. The experimental results demonstrate that MLPs can indeed enhance the comprehension of linguistic structure by PLMs. Our research provides interpretable and valuable insights into crafting variations of PLMs utilizing MLPs for tasks that emphasize diverse linguistic structures., Comment: Accepted by ICASSP 2024

In the field of natural language understanding, the intersection of neural models and graph meaning representations (GMRs) remains a compelling area of research. Despite the growing interest, a critical gap persists in understanding the exact influence of GMRs, particularly concerning relation extraction tasks. Addressing this, we introduce DAGNN-plus, a simple and parameter-efficient neural architecture designed to decouple contextual representation learning from structural information propagation. Coupled with various sequence encoders and GMRs, this architecture provides a foundation for systematic experimentation on two English and two Chinese datasets. Our empirical analysis utilizes four different graph formalisms and nine parsers. The results yield a nuanced understanding of GMRs, showing improvements in three out of the four datasets, particularly favoring English over Chinese due to highly accurate parsers. Interestingly, GMRs appear less effective in literary-domain datasets compared to general-domain datasets. These findings lay the groundwork for better-informed design of GMRs and parsers to improve relation classification, which is expected to tangibly impact the future trajectory of natural language understanding research., Comment: 10 pages

The increasing ubiquity of language technology necessitates a shift towards considering cultural diversity in the machine learning realm, particularly for subjective tasks that rely heavily on cultural nuances, such as Offensive Language Detection (OLD). Current understanding underscores that these tasks are substantially influenced by cultural values, however, a notable gap exists in determining if cultural features can accurately predict the success of cross-cultural transfer learning for such subjective tasks. Addressing this, our study delves into the intersection of cultural features and transfer learning effectiveness. The findings reveal that cultural value surveys indeed possess a predictive power for cross-cultural transfer learning success in OLD tasks and that it can be further improved using offensive word distance. Based on these results, we advocate for the integration of cultural information into datasets. Additionally, we recommend leveraging data sources rich in cultural information, such as surveys, to enhance cultural adaptability. Our research signifies a step forward in the quest for more inclusive, culturally sensitive language technologies., Comment: Findings of EMNLP 2023 (update)

Document-level event argument extraction is a crucial yet challenging task within the field of information extraction. Current mainstream approaches primarily focus on the information interaction between event triggers and their arguments, facing two limitations: insufficient context interaction and the ignorance of event correlations. Here, we introduce a novel framework named CARLG (Contextual Aggregation of clues and Role-based Latent Guidance), comprising two innovative components: the Contextual Clues Aggregation (CCA) and the Role-based Latent Information Guidance (RLIG). The CCA module leverages the attention weights derived from a pre-trained encoder to adaptively assimilates broader contextual information, while the RLIG module aims to capture the semantic correlations among event roles. We then instantiate the CARLG framework into two variants based on two types of current mainstream EAE approaches. Notably, our CARLG framework introduces less than 1% new parameters yet significantly improving the performance. Comprehensive experiments across the RAMS, WikiEvents, and MLEE datasets confirm the superiority of CARLG, showing significant superiority in terms of both performance and inference speed compared to major benchmarks. Further analyses demonstrate the effectiveness of the proposed modules., Comment: pre-submission

Major depressive disorder is a serious and heterogeneous psychiatric disorder that needs accurate diagnosis. Resting-state functional MRI (rsfMRI), which captures multiple perspectives on brain structure, function, and connectivity, is increasingly applied in the diagnosis and pathological research of mental diseases. Different machine learning algorithms are then developed to exploit the rich information in rsfMRI and discriminate MDD patients from normal controls. Despite recent advances reported, the discrimination accuracy has room for further improvement. The generalizability and interpretability of the method are not sufficiently addressed either. Here, we propose a machine learning method (MFMC) for MDD discrimination by concatenating multiple features and stacking multiple classifiers. MFMC is tested on the REST-meta-MDD data set that contains 2428 subjects collected from 25 different sites. MFMC yields 96.9% MDD discrimination accuracy, demonstrating a significant improvement over existing methods. In addition, the generalizability of MFMC is validated by the good performance when the training and testing subjects are from independent sites. The use of XGBoost as the meta classifier allows us to probe the decision process of MFMC. We identify 13 feature values related to 9 brain regions including the posterior cingulate gyrus, superior frontal gyrus orbital part, and angular gyrus, which contribute most to the classification and also demonstrate significant differences at the group level. The use of these 13 feature values alone can reach 87% of MFMC's full performance when taking all feature values. These features may serve as clinically useful diagnostic and prognostic biomarkers for mental disorders in the future.

We consider the problem of learning a sparse graph underlying an undirected Gaussian graphical model, a key problem in statistical machine learning. Given $n$ samples from a multivariate Gaussian distribution with $p$ variables, the goal is to estimate the $p \times p$ inverse covariance matrix (aka precision matrix), assuming it is sparse (i.e., has a few nonzero entries). We propose GraphL0BnB, a new estimator based on an $\ell_0$-penalized version of the pseudolikelihood function, while most earlier approaches are based on the $\ell_1$-relaxation. Our estimator can be formulated as a convex mixed integer program (MIP) which can be difficult to compute at scale using off-the-shelf commercial solvers. To solve the MIP, we propose a custom nonlinear branch-and-bound (BnB) framework that solves node relaxations with tailored first-order methods. As a by-product of our BnB framework, we propose large-scale solvers for obtaining good primal solutions that are of independent interest. We derive novel statistical guarantees (estimation and variable selection) for our estimator and discuss how our approach improves upon existing estimators. Our numerical experiments on real/synthetic datasets suggest that our method can solve, to near-optimality, problem instances with $p = 10^4$ -- corresponding to a symmetric matrix of size $p \times p$ with $p^2/2$ binary variables. We demonstrate the usefulness of GraphL0BnB versus various state-of-the-art approaches on a range of datasets.

The sparse Mixture-of-Experts (Sparse-MoE) framework efficiently scales up model capacity in various domains, such as natural language processing and vision. Sparse-MoEs select a subset of the "experts" (thus, only a portion of the overall network) for each input sample using a sparse, trainable gate. Existing sparse gates are prone to convergence and performance issues when training with first-order optimization methods. In this paper, we introduce two improvements to current MoE approaches. First, we propose a new sparse gate: COMET, which relies on a novel tree-based mechanism. COMET is differentiable, can exploit sparsity to speed up computation, and outperforms state-of-the-art gates. Second, due to the challenging combinatorial nature of sparse expert selection, first-order methods are typically prone to low-quality solutions. To deal with this challenge, we propose a novel, permutation-based local search method that can complement first-order methods in training any sparse gate, e.g., Hash routing, Top-k, DSelect-k, and COMET. We show that local search can help networks escape bad initializations or solutions. We performed large-scale experiments on various domains, including recommender systems, vision, and natural language processing. On standard vision and recommender systems benchmarks, COMET+ (COMET with local search) achieves up to 13% improvement in ROC AUC over popular gates, e.g., Hash routing and Top-k, and up to 9% over prior differentiable gates e.g., DSelect-k. When Top-k and Hash gates are combined with local search, we see up to $100\times$ reduction in the budget needed for hyperparameter tuning. Moreover, for language modeling, our approach improves over the state-of-the-art MoEBERT model for distilling BERT on 5/7 GLUE benchmarks as well as SQuAD dataset., Comment: Accepted in KDD 2023

The sheer size of modern neural networks makes model serving a serious computational challenge. A popular class of compression techniques overcomes this challenge by pruning or sparsifying the weights of pretrained networks. While useful, these techniques often face serious tradeoffs between computational requirements and compression quality. In this work, we propose a novel optimization-based pruning framework that considers the combined effect of pruning (and updating) multiple weights subject to a sparsity constraint. Our approach, CHITA, extends the classical Optimal Brain Surgeon framework and results in significant improvements in speed, memory, and performance over existing optimization-based approaches for network pruning. CHITA's main workhorse performs combinatorial optimization updates on a memory-friendly representation of local quadratic approximation(s) of the loss function. On a standard benchmark of pretrained models and datasets, CHITA leads to significantly better sparsity-accuracy tradeoffs than competing methods. For example, for MLPNet with only 2% of the weights retained, our approach improves the accuracy by 63% relative to the state of the art. Furthermore, when used in conjunction with fine-tuning SGD steps, our method achieves significant accuracy gains over the state-of-the-art approaches.

Reference-based line-art colorization is a challenging task in computer vision. The color, texture, and shading are rendered based on an abstract sketch, which heavily relies on the precise long-range dependency modeling between the sketch and reference. Popular techniques to bridge the cross-modal information and model the long-range dependency employ the attention mechanism. However, in the context of reference-based line-art colorization, several techniques would intensify the existing training difficulty of attention, for instance, self-supervised training protocol and GAN-based losses. To understand the instability in training, we detect the gradient flow of attention and observe gradient conflict among attention branches. This phenomenon motivates us to alleviate the gradient issue by preserving the dominant gradient branch while removing the conflict ones. We propose a novel attention mechanism using this training strategy, Stop-Gradient Attention (SGA), outperforming the attention baseline by a large margin with better training stability. Compared with state-of-the-art modules in line-art colorization, our approach demonstrates significant improvements in Fr\'echet Inception Distance (FID, up to 27.21%) and structural similarity index measure (SSIM, up to 25.67%) on several benchmarks. The code of SGA is available at https://github.com/kunkun0w0/SGA ., Comment: Accepted by ECCV2022

Major depressive disorder (MDD) is one of the most common mental health conditions that has been intensively investigated for its association with brain atrophy and mortality. Recent studies reveal that the deviation between the predicted and the chronological age can be a marker of accelerated brain aging to characterize MDD. However, current conclusions are usually drawn based on structural MRI information collected from Caucasian participants. The universality of this biomarker needs to be further validated by subjects with different ethnic/racial backgrounds and by different types of data. Here we make use of the REST-meta-MDD, a large scale resting-state fMRI dataset collected from multiple cohort participants in China. We develop a stacking machine learning model based on 1101 healthy controls, which estimates a subject's chronological age from fMRI with promising accuracy. The trained model is then applied to 1276 MDD patients from 24 sites. We observe that MDD patients exhibit a $+4.43$ years ($\text{$p$} < 0.0001$, $\text{Cohen's $d$} = 0.35$, $\text{95\% CI}:1.86 - 3.91$) higher brain-predicted age difference (brain-PAD) compared to controls. In the MDD subgroup, we observe a statistically significant $+2.09$ years ($\text{$p$} < 0.05$, $\text{Cohen's $d$} = 0.134483$) brain-PAD in antidepressant users compared to medication-free patients. The statistical relationship observed is further checked by three different machine learning algorithms. The positive brain-PAD observed in participants in China confirms the presence of accelerated brain aging in MDD patients. The utilization of functional brain connectivity for age estimation verifies existing findings from a new dimension., Comment: 32 pages,13 figures

Graph neural networks (GNNs) have drawn increasing attention in recent years and achieved remarkable performance in many graph-based tasks, especially in semi-supervised learning on graphs. However, most existing GNNs are based on the message-passing paradigm to iteratively aggregate neighborhood information in a single topology space. Despite their success, the expressive power of GNNs is limited by some drawbacks, such as inflexibility of message source expansion, negligence of node-level message output discrepancy, and restriction of single message space. To address these drawbacks, we present a novel message-passing paradigm, based on the properties of multi-step message source, node-specific message output, and multi-space message interaction. To verify its validity, we instantiate the new message-passing paradigm as a Dual-Perception Graph Neural Network (DPGNN), which applies a node-to-step attention mechanism to aggregate node-specific multi-step neighborhood information adaptively. Our proposed DPGNN can capture the structural neighborhood information and the feature-related information simultaneously for graph representation learning. Experimental results on six benchmark datasets with different topological structures demonstrate that our method outperforms the latest state-of-the-art models, which proves the superiority and versatility of our method. To our knowledge, we are the first to consider node-specific message passing in the GNNs., Comment: Published in Knowledge-Based Systems

We consider the problem of learning causal structures in sparse high-dimensional settings that may be subject to the presence of (potentially many) unmeasured confounders, as well as selection bias. Based on the structure found in common families of large random networks and examining the representation of local structures in linear structural equation models (SEM), we propose a new local notion of sparsity for consistent structure learning in the presence of latent and selection variables, and develop a new version of the Fast Causal Inference (FCI) algorithm with reduced computational and sample complexity, which we refer to as local FCI (lFCI). The new notion of sparsity allows the presence of highly connected hub nodes, which are common in real-world networks, but problematic for existing methods. Our numerical experiments indicate that the lFCI algorithm achieves state-of-the-art performance across many classes of large random networks, and its performance is superior to that of existing methods for networks containing hub nodes.

In Statistics, log-concave density estimation is a central problem within the field of nonparametric inference under shape constraints. Despite great progress in recent years on the statistical theory of the canonical estimator, namely the log-concave maximum likelihood estimator, adoption of this method has been hampered by the complexities of the non-smooth convex optimization problem that underpins its computation. We provide enhanced understanding of the structural properties of this optimization problem, which motivates the proposal of new algorithms, based on both randomized and Nesterov smoothing, combined with an appropriate integral discretization of increasing accuracy. We prove that these methods enjoy, both with high probability and in expectation, a convergence rate of order $1/T$ up to logarithmic factors on the objective function scale, where $T$ denotes the number of iterations. The benefits of our new computational framework are demonstrated on both synthetic and real data, and our implementation is available in a github repository \texttt{LogConcComp} (Log-Concave Computation).

In causal graphical models based on directed acyclic graphs (DAGs), directed paths represent causal pathways between the corresponding variables. The variable at the beginning of such a path is referred to as an ancestor of the variable at the end of the path. Ancestral relations between variables play an important role in causal modeling. In existing literature on structure learning, these relations are usually deduced from learned structures and used for orienting edges or formulating constraints of the space of possible DAGs. However, they are usually not posed as immediate target of inference. In this work we investigate the graphical characterization of ancestral relations via CPDAGs and d-separation relations. We propose a framework that can learn definite non-ancestral relations without first learning the skeleton. This frame-work yields structural information that can be used in both score- and constraint-based algorithms to learn causal DAGs more efficiently.