Sparse Autoencoders (SAEs) are a prominent tool in mechanistic interpretability (MI) for decomposing neural network activations into interpretable features. However, the aspiration to identify a canonical set of features is challenged by the observed inconsistency of learned SAE features across different training runs, undermining reproducibility and complicating model comparison. We study run-to-run feature consistency in SAEs and argue that it should be reported as a standard evaluation axis alongside reconstruction and sparsity. We propose the Pairwise Dictionary Mean Correlation Coefficient (PW-MCC) as an assignment-based metric to quantify consistency and demonstrate that high levels are achievable (PW-MCC ≈ 0.80 for TopK SAEs on LLM activations) with appropriate architectural choices.Our contributions include: (i) theoretical grounding for strong consistency in the idealized setting of TopK SAEs; (ii) synthetic validation using a model organism, which verifies PW-MCC as a reliable proxy for ground-truth recovery; and (iii) empirical analysis on LLM activations, where PW-MCC correlates with the similarity of automatically generated natural-language feature explanations.

Knowledge graphs serve as critical resources supporting intelligent systems, but they can be noisy due to imperfect automatic generation processes. Existing approaches to noise detection often rely on external facts, logical rule constraints, or structural embeddings. These methods are often challenged by imperfect entity alignment, flexible knowledge graph construction, and overfitting on structures. In this paper, we propose to exploit the consistency between entity and relation type information for noise detection, resulting a novel self-supervised knowledge graph denoising method that avoids those problems. We formalize \textit{type inconsistency} noise as triples that deviate from the majority with respect to type-dependent reasoning along the topological structure. Specifically, we first extract a compact representation of a given knowledge graph via an encoder that models the type dependencies of triples. Then, the decoder reconstructs the original input knowledge graph based on the compact representation. It is worth noting that, our proposal has the potential to address the problems of knowledge graph compression and completion, although this is not our focus. For the specific task of noise detection, the discrepancy between the reconstruction results and the input knowledge graph provides an opportunity for denoising, which is facilitated by the type consistency embedded in our method. Experimental validation demonstrates the effectiveness of our approach in detecting potential noise in real-world data.

Nearly all identifiability results in unsupervised representation learning inspired by, e.g., independent component analysis, factor analysis, and causal representation learning, rely on assumptions of additive independent noise or noiseless regimes. In contrast, we study the more general case where noise can take arbitrary forms, depend on latent variables, and be non-invertibly entangled within a nonlinear function. We propose a general framework for identifying latent variables in the nonparametric noisy settings. We first show that, under suitable conditions, the generative model is identifiable up to certain submanifold indeterminacies even in the presence of non-negligible noise. Furthermore, under the structural or distributional variability conditions, we prove that latent variables of the general nonlinear models are identifiable up to trivial indeterminacies. Based on the proposed theoretical framework, we have also developed corresponding estimation methods and validated them in various synthetic and real-world settings. Interestingly, our estimate of the true GDP growth from alternative measurements suggests more insightful information on the economies than official reports. We expect our framework to provide new insight into how both researchers and practitioners deal with latent variables in real-world scenarios.

Contrastive Language-Image Pre-training (CLIP) [37] has emerged as a pivotal model in computer vision and multimodal learning, achieving state-of-the-art performance at aligning visual and textual representations through contrastive learning. However, CLIP struggles with potential information misalignment in many image-text datasets and suffers from entangled representation. On the one hand, short captions for a single image in datasets like MSCOCO may describe disjoint regions in the image, leaving the model uncertain about which visual features to retain or disregard. On the other hand, directly aligning long captions with images can lead to the retention of entangled details, preventing the model from learning disentangled, atomic concepts – ultimately limiting its generalization on certain downstream tasks involving short prompts.In this paper, we establish theoretical conditions that enable flexible alignment between textual and visual representations across varying levels of granularity. Specifically, our framework ensures that a model can not only preserve cross-modal semantic information in its entirety but also disentangle visual representations to capture finegrained textual concepts. Building on this foundation, we introduce SmartCLIP, a novel approach that identifies and aligns the most relevant visual and textual representations in a modular manner. Superior performance across various tasks demonstrates its capability to handle information misalignment and supports our identification theory. The code is available at https://github.com/MidPush/SmartCLIP.

Disentangled representation learning aims to uncover the latent variables underlying observed data, yet identifying these variables under mild assumptions remains challenging. Some methods rely on sufficient changes in the distribution of latent variables indicated by auxiliary variables, such as domain indices, but acquiring enough domains is often impractical. Alternative approaches exploit the structural sparsity assumption on mixing processes, but this constraint may not hold in practice. Interestingly, we find that these two seemingly unrelated assumptions can actually complement each other. Specifically, when conditioned on auxiliary variables, the sparse mixing process induces independence between latent and observed variables, which simplifies the mapping from estimated to true latent variables and hence compensates for deficiencies of auxiliary variables. Building on this insight, we propose an identifiability theory with less restrictive constraints regarding the auxiliary variables and the sparse mixing process, enhancing applicability to real-world scenarios. Additionally, we develop a generative model framework incorporating a domain encoding network and a sparse mixing constraint and provide two implementations based on variational autoencoders and generative adversarial networks. Experiment results on synthetic and real-world datasets support our theoretical results.

Identifying time-delayed latent causal process is crucial for understanding temporal dynamics and enabling downstream reasoning. While recent methods have made progress in identifying latent time-delayed causal processes, they cannot address the dynamics in which the influence of some latent factors on both the subsequent latent states and the observed data can become inactive or irrelevant at different time steps. Therefore, we introduce intermittent temporal latent processes, where: (1) any subset of latent factors may be missing during nonlinear data generation at any time step, and (2) the active latent factors at each step are unknown. This framework encompasses both nonstationary and stationary transitions, accommodating changing or consistent active factors over time. Our work shows that under certain assumptions, the latent causal variables are block-wise identifiable. With further conditional independence assumption, each latent variable can even be recovered up to component-wise transformations. Using this identification theory, we propose an unsupervised approach, InterLatent, to reliably uncover the representations of the intermittent temporal latent process. The experimental findings on both synthetic and real-world datasets verify our theoretical claims.

Prevalent in biomedical applications (e.g., human phenotype research), multimodal datasets can provide valuable insights into the underlying physiological mechanisms. However, current machine learning (ML) models designed to analyze these datasets often lack interpretability and identifiability guarantees, which are essential for biomedical research. Recent advances in causal representation learning have shown promise in identifying interpretable latent causal variables with formal theoretical guarantees. Unfortunately, most current work on multimodal distributions either relies on restrictive parametric assumptions or yields only coarse identification results, limiting their applicability to biomedical research that favors a detailed understanding of the mechanisms. In this work, we aim to develop flexible identification conditions for multimodal data and principled methods to facilitate the understanding of biomedical datasets. Theoretically, we consider a nonparametric latent distribution (c.f., parametric assumptions in previous work) that allows for causal relationships across potentially different modalities. We establish identifiability guarantees for each latent component, extending the subspace identification results from previous work. Our key theoretical contribution is the structural sparsity of causal connections between modalities, which, as we will discuss, is natural for a large collection of biomedical systems. Empirically, we present a practical framework to instantiate our theoretical insights. We demonstrate the effectiveness of our approach through extensive experiments on both numerical and synthetic datasets. Results on a real-world human phenotype dataset are consistent with established biomedical research, validating our theoretical and methodological framework.

We are born with the ability to learn concepts by comparing diverse observations. This helps us to understand the new world in a compositional manner and facilitates extrapolation, as objects naturally consist of multiple concepts. In this work, we argue that the cognitive mechanism of comparison, fundamental to human learning, is also vital for machines to recover true concepts underlying the data. This offers correctness guarantees for the field of concept learning, which, despite its impressive empirical successes, still lacks general theoretical support. Specifically, we aim to develop a theoretical framework for the identifiability of concepts with multiple classes of observations. We show that with sufficient diversity across classes, hidden concepts can be identified without assuming specific concept types, functional relations, or parametric generative models. Interestingly, even when conditions are not globally satisfied, we can still provide alternative guarantees for as many concepts as possible based on local comparisons, thereby extending the applicability of our theory to more flexible scenarios. Moreover, the hidden structure between classes and concepts can also be identified nonparametrically. We validate our theoretical results in both synthetic and real-world settings.

A central problem in unsupervised domain adaptation is determining what to transfer from labeled source domains to an unlabeled target domain. To handle high-dimensional observations (e.g., images), a line of approaches use deep learning to learn latent representations of the observations, which facilitate knowledge transfer in the latent space. However, existing approaches often rely on restrictive assumptions to establish identifiability of the joint distribution in the target domain, such as independent latent variables or invariant label distributions, limiting their real-world applicability. In this work, we propose a general domain adaptation framework that learns compact latent representations to capture distribution shifts relative to the prediction task and address the fundamental question of what representations should be learned and transferred. Notably, we first demonstrate that learning representations based on all the predictive information, i.e., the label's Markov blanket in terms of the learned representations, is often underspecified in general settings. Instead, we show that, interestingly, general domain adaptation can be achieved by partitioning the representations of Markov blanket into those of the label's parents, children, and spouses. Moreover, its identifiability guarantee can be established. Building on these theoretical insights, we develop a practical, nonparametric approach for domain adaptation in a general setting, which can handle different types of distribution shifts.

Concept learning seeks to extract semantic and interpretable representations of atomic concepts from high-dimensional data such as images and text, which can be instrumental to a variety of downstream tasks (e.g., image generation/editing). Despite its importance, the theoretical foundations for learning atomic concepts and their interactions, especially from multimodal distributions, remain underexplored. In this work, we establish fundamental conditions for learning atomic multimodal concepts and their underlying interactions With identfiability guarantees. We formulate concept learning as a latent variable identification problem, representing atomic concepts in each modality as latent variables, with a graphical model to specify their interactions across modalities. Our theoretical contribution is to provide component-wise identifiability of atomic concepts under flexible, nonparametric conditions that accommodate both continuous and discrete modalities. Building on these theoretical insights, we demonstrate the practical utility of our theory in a downstream task text-to-image (T2I) generation. We develop a principled T2I model that explicitly learns atomic textual and visual concepts with sparse connections between them, allowing us to achieve image generation and editing at the atomic concept level. Empirical evaluations show that our model outperforms existing methods in T2I generation tasks, offering superior controllability and interpretability.

Revealing the underlying causal mechanisms in the real world is critical for scientific and technical progress. Despite advancements over the past decades, the lack of high-quality data and the inability of traditional causal discovery algorithms (TCDA) to fully comprehend the exact semantics of variables have long been major obstacles to the broader application of causal discovery. To address this issue, this paper proposes a novel causal modeling framework, LLM-CD, which integrates the metadata-based reasoning capabilities of large language models (LLMs) with the data-driven modeling abilities of TCDA for causal discovery. LLM-CD deeply couples the reasoning abilities of LLMs at various stages of TCDA, and enhances causal discovery through an iterative process. Due to the issues of overconfidence and hallucination in LLMs, LLM-CD quantifies and analyzes its uncertainty by incorporating evidence-based deep learning theory with the assumptions of TCDA. We utilize a large-scale de-identified real patient dataset provided by a hospital, a new dataset extracted from MIMIC-IV about the same disease (lung cancer), and two benchmark datasets to comprehensively evaluate LLM-CD. Extensive experimental results confirm the effectiveness and reliability of LLM-CD, with the highest improvement of 403.93% in the Recall and 25.77% in the Ratio metric across four datasets.

Despite Large Language Models' remarkable capabilities, understanding their internal representations remains challenging. Mechanistic interpretability tools such as sparse autoencoders (SAEs) were developed to extract interpretable features from LLMs but lack temporal dependency modeling, instantaneous relation representation, and more importantly theoretical guarantees—undermining both the theoretical foundations and the practical confidence necessary for subsequent analyses. While causal representation learning (CRL) offers theoretically-grounded approaches for uncovering latent concepts, existing methods cannot scale to LLMs' rich conceptual space due to inefficient computation. To bridge the gap, we introduce an identifiable temporal causal representation learning framework specifically designed for LLMs' high-dimensional concept space, capturing both time-delayed and instantaneous causal relations. Our approach provides theoretical guarantees and demonstrates efficacy on synthetic datasets scaled to match real-world complexity. By extending SAE techniques with our temporal causal framework, we successfully discover meaningful concept relationships in LLM activations. Our findings show that modeling both temporal and instantaneous conceptual relationships advances the interpretability of LLMs.

Natural language has long enabled human cooperation, but its lossy, ambiguous, and indirect nature limits the potential of collective intelligence. While machines are not subject to these constraints, most LLM-based multi-agent systems still rely solely on natural language, exchanging tokens or their embeddings. To go beyond language, we introduce a new paradigm, *thought communication*, which enables agents to interact directly mind-to-mind, akin to telepathy. To uncover these latent thoughts in a principled way, we formalize the process as a general latent variable model, where agent states are generated by an unknown function of underlying thoughts. We prove that, in a nonparametric setting without auxiliary information, both shared and private latent thoughts between any pair of agents can be identified. Moreover, the global structure of thought sharing, including which agents share which thoughts and how these relationships are structured, can also be recovered with theoretical guarantees. Guided by the established theory, we develop a framework that extracts latent thoughts from all agents prior to communication and assigns each agent the relevant thoughts, along with their sharing patterns. This paradigm naturally extends beyond LLMs to all modalities, as most observational data arise from hidden generative processes. Experiments on both synthetic and real-world benchmarks validate the theory and demonstrate the collaborative advantages of thought communication. We hope this work illuminates the potential of leveraging the hidden world, as many challenges remain unsolvable through surface-level observation alone, regardless of compute or data scale.

Local causal discovery is of great practical significance, as there are often situations where the discovery of the global causal structure is unnecessary, and the interest lies solely on a single target variable. Most existing local methods utilize conditional independence relations, providing only a partially directed graph, and assume acyclicity for the ground-truth structure, even though real-world scenarios often involve cycles like feedback mechanisms. In this work, we present a general, unified local causal discovery method with linear non-Gaussian models, whether they are cyclic or acyclic. We extend the application of independent component analysis from the global context to independent subspace analysis, enabling the exact identification of the equivalent local directed structures and causal strengths from the Markov blanket of the target variable. We also propose an alternative regression-based method in the particular acyclic scenarios. Our identifiability results are empirically validated using both synthetic and real-world datasets.

Most existing causal discovery methods rely on the assumption of no latent confounders, limiting their applicability in solving real-life problems. In this paper, we introduce a novel, versatile framework for causal discovery that accommodates the presence of causally-related hidden variables almost everywhere in the causal network (for instance, they can be effects of measured variables), based on rank information of covariance matrix over measured variables. We start by investigating the efficacy of rank in comparison to conditional independence and, theoretically, establish necessary and sufficient conditions for the identifiability of certain latent structural patterns. Furthermore, we develop a Rank-based Latent Causal Discovery algorithm, RLCD, that can efficiently locate hidden variables, determine their cardinalities, and discover the entire causal structure over both measured and hidden ones. We also show that, under certain graphical conditions, RLCD correctly identifies the Markov Equivalence Class of the whole latent causal graph asymptotically. Experimental results on both synthetic and real-world personality data sets demonstrate the efficacy of the proposed approach in finite-sample cases. Our code will be publicly available.

In many problems, the measured variables (e.g., image pixels) are just mathematical functions of the latent causal variables (e.g., the underlying concepts or objects). For the purpose of making predictions in changing environments or making proper changes to the system, it is helpful to recover the latent causal variables $Z_i$ and their causal relations represented by graph $\mathcal{G}_Z$. This problem has recently been known as causal representation learning. This paper is concerned with a general, completely nonparametric setting of causal representation learning from multiple distributions (arising from heterogeneous data or nonstationary time series), without assuming hard interventions behind distribution changes. We aim to develop general solutions in this fundamental case; as a by product, this helps see the unique benefit offered by other assumptions such as parametric causal models or hard interventions. We show that under the sparsity constraint on the recovered graph over the latent variables and suitable sufficient change conditions on the causal influences, interestingly, one can recover the moralized graph of the underlying directed acyclic graph, and the recovered latent variables and their relations are related to the underlying causal model in a specific, nontrivial way. In some cases, most latent variables can even be recovered up to component-wise transformations. Experimental results verify our theoretical claims.

We argue that the selective inclusion of data points based on latent objectives is common in practical situations, such as music sequences. Since this selection process often distorts statistical analysis, previous work primarily views it as a bias to be corrected and proposes various methods to mitigate its effect. However, while controlling this bias is crucial, selection also offers an opportunity to provide a deeper insight into the hidden generation process, as it is a fundamental mechanism underlying what we observe. In particular, overlooking selection in sequential data can lead to an incomplete or overcomplicated inductive bias in modeling, such as assuming a universal autoregressive structure for all dependencies. Therefore, rather than merely viewing it as a bias, we explore the causal structure of selection in sequential data to delve deeper into the complete causal process. Specifically, we show that selection structure is identifiable without any parametric assumptions or interventional experiments. Moreover, even in cases where selection variables coexist with latent confounders, we still establish the nonparametric identifiability under appropriate structural conditions. Meanwhile, we also propose a provably correct algorithm to detect and identify selection structures as well as other types of dependencies. The framework has been validated empirically on both synthetic data and real-world music.

When solving long-horizon tasks, it is intriguing to decompose the high-level task into subtasks. Decomposing experiences into reusable subtasks can improve data efficiency, accelerate policy generalization, and in general provide promising solutions to multi-task reinforcement learning and imitation learning problems. However, the concept of subtasks is not sufficiently understood and modeled yet, and existing works often overlook the true structure of the data generation process: subtasks are the results of a *selection* mechanism on actions, rather than possible underlying confounders or intermediates. Specifically, we provide a theory to identify, and experiments to verify the existence of selection variables in such data. These selections serve as subgoals that indicate subtasks and guide policy. In light of this idea, we develop a sequential non-negative matrix factorization (seq- NMF) method to learn these subgoals and extract meaningful behavior patterns as subtasks. Our empirical results on a challenging Kitchen environment demonstrate that the learned subtasks effectively enhance the generalization to new tasks in multi-task imitation learning scenarios. The codes are provided at this [*link*](https://anonymous.4open.science/r/Identifying\_Selections\_for\_Unsupervised\_Subtask\_Discovery/README.md).

Causal Temporal Representation Learning (Ctrl) methods aim to identify the temporal causal dynamics of complex nonstationary temporal sequences. Despite the success of existing Ctrl methods, they require either directly observing the domain variables or assuming a Markov prior on them. Such requirements limit the application of these methods in real-world scenarios when we do not have such prior knowledge of the domain variables. To address this problem, this work adopts a sparse transition assumption, aligned with intuitive human understanding, and presents identifiability results from a theoretical perspective. In particular, we explore under what conditions on the significance of the variability of the transitions we can build a model to identify the distribution shifts. Based on the theoretical result, we introduce a novel framework, *Causal Temporal Representation Learning with Nonstationary Sparse Transition* (CtrlNS), designed to leverage the constraints on transition sparsity and conditional independence to reliably identify both distribution shifts and latent factors. Our experimental evaluations on synthetic and real-world datasets demonstrate significant improvements over existing baselines, highlighting the effectiveness of our approach.

Graph Neural Networks (GNNs) have achieved great success on a variety of tasks with graph-structural data, among which node classification is an essential one. Unsupervised Graph Domain Adaptation (UGDA) shows its practical value of reducing the labeling cost for node classification. It leverages knowledge from a labeled graph (i.e., source domain) to tackle the same task on another unlabeled graph (i.e., target domain). Most existing UGDA methods heavily rely on the labeled graph in the source domain. They utilize labels from the source domain as the supervision signal and are jointly trained on both the source graph and the target graph. However, in some real-world scenarios, the source graph is inaccessible because of privacy issues. Therefore, we propose a novel scenario named Source Free Unsupervised Graph Domain Adaptation (SFUGDA). In this scenario, the only information we can leverage from the source domain is the well-trained source model, without any exposure to the source graph and its labels. As a result, existing UGDA methods are not feasible anymore. To address the non-trivial adaptation challenges in this practical scenario, we propose a model-agnostic algorithm called SOGA for domain adaptation to fully exploit the discriminative ability of the source model while preserving the consistency of structural proximity on the target graph. We prove the effectiveness of the proposed algorithm both theoretically and empirically. The experimental results on four cross-domain tasks show consistent improvements in the Macro-F1 score and Macro-AUC.

The page presentation biases in the information retrieval system, especially on the click behavior, is a well-known challenge that hinders improving ranking models' performance with implicit user feedback. Unbiased Learning to Rank~(ULTR) algorithms are then proposed to learn an unbiased ranking model with biased click data. However, most existing algorithms are specifically designed to mitigate position-related bias, e.g., trust bias, without considering biases induced by other features in search result page presentation(SERP), e.g. attractive bias induced by the multimedia. Unfortunately, those biases widely exist in industrial systems and may lead to an unsatisfactory search experience. Therefore, we introduce a new problem, i.e., whole-page Unbiased Learning to Rank(WP-ULTR), aiming to handle biases induced by whole-page SERP features simultaneously. It presents tremendous challenges: (1) a suitable user behavior model (user behavior hypothesis) can be hard to find; and (2) complex biases cannot be handled by existing algorithms. To address the above challenges, we propose a Bias Agnostic whole-page unbiased Learning to rank algorithm, named BAL, to automatically find the user behavior model with causal discovery and mitigate the biases induced by multiple SERP features with no specific design. Experimental results on a real-world dataset verify the effectiveness of the BAL.

Causal discovery aims at revealing causal relations from observational data, which is a fundamental task in science and engineering. We describe causal-learn, an open-source Python library for causal discovery. This library focuses on bringing a comprehensive collection of causal discovery methods to both practitioners and researchers. It provides easy-to-use APIs for non-specialists, modular building blocks for developers, detailed documentation for learners, and comprehensive methods for all. Different from previous packages in R or Java, causal-learn is fully developed in Python, which could be more in tune with the recent preference shift in programming languages within related communities. The library is available at https://github.com/py-why/causal-learn.

Independent component analysis (ICA) is a fundamental statistical tool used to reveal hidden generative processes from observed data. However, traditional ICA approaches struggle with the rotational invariance inherent in Gaussian distributions, often necessitating the assumption of non-Gaussianity in the underlying sources. This may limit their applicability in broader contexts. To accommodate Gaussian sources, we develop an identifiability theory that relies on second-order statistics without imposing further preconditions on the distribution of sources, by introducing novel assumptions on the connective structure from sources to observed variables. Different from recent work that focuses on potentially restrictive connective structures, our proposed assumption of structural variability is both considerably less restrictive and provably necessary. Furthermore, we propose two estimation methods based on second-order statistics and sparsity constraint. Experimental results are provided to validate our identifiability theory and estimation methods.

Nonlinear independent component analysis (ICA) aims to uncover the true latent sources from their observable nonlinear mixtures. Despite its significance, the identifiability of nonlinear ICA is known to be impossible without additional assumptions. Recent advances have proposed conditions on the connective structure from sources to observed variables, known as Structural Sparsity, to achieve identifiability in an unsupervised manner. However, the sparsity constraint may not hold universally for all sources in practice. Furthermore, the assumptions of bijectivity of the mixing process and independence among all sources, which arise from the setting of ICA, may also be violated in many real-world scenarios. To address these limitations and generalize nonlinear ICA, we propose a set of new identifiability results in the general settings of undercompleteness, partial sparsity and source dependence, and flexible grouping structures. Specifically, we prove identifiability when there are more observed variables than sources (undercomplete), and when certain sparsity and/or source independence assumptions are not met for some changing sources. Moreover, we show that even in cases with flexible grouping structures (e.g., part of the sources can be divided into irreducible independent groups with various sizes), appropriate identifiability results can also be established. Theoretical claims are supported empirically on both synthetic and real-world datasets.

Functional magnetic resonance imaging (fMRI) has become one of the most common imaging modalities for brain function analysis. Recently, graph neural networks (GNN) have been adopted for fMRI analysis with superior performance. Unfortunately, traditional functional brain networks are mainly constructed based on similarities among region of interests (ROI), which are noisy and agnostic to the downstream prediction tasks and can lead to inferior results for GNN-based models. To better adapt GNNs for fMRI analysis, we propose TBDS, an end-to-end framework based on Task-aware Brain connectivity DAG (short for Directed Acyclic Graph) Structure generation for fMRI analysis. The key component of TBDS is the brain network generator which adopts a DAG learning approach to transform the raw time-series into task-aware brain connectivities. Besides, we design an additional contrastive regularization to inject task-specific knowledge during the brain network generation process. Comprehensive experiments on two fMRI datasets, namely Adolescent Brain Cognitive Development (ABCD) and Philadelphia Neuroimaging Cohort (PNC) datasets demonstrate the efficacy of TBDS. In addition, the generated brain networks also highlight the prediction-related brain regions and thus provide unique interpretations of the prediction results. Our implementation will be published upon acceptance.

Unsupervised domain adaptation is critical to many real-world applications where label information is unavailable in the target domain. In general, without further assumptions, the joint distribution of the features and the label is not identifiable in the target domain. To address this issue, we rely on a property of minimal changes of causal mechanisms across domains to minimize unnecessary influences of domain shift. To encode this property, we first formulate the data generating process using a latent variable model with two partitioned latent subspaces: invariant components whose distributions stay the same across domains, and sparse changing components that vary across domains. We further constrain the domain shift to have a restrictive influence on the changing components. Under mild conditions, we show that the latent variables are partially identifiable, from which it follows that the joint distribution of data and labels in the target domain is also identifiable. Given the theoretical insights, we propose a practical domain adaptation framework, called iMSDA. Extensive experimental results reveal that iMSDA outperforms state-of-the-art domain adaptation algorithms on benchmark datasets, demonstrating the effectiveness of our framework.

Nonlinear independent component analysis (ICA) aims to recover the underlying independent latent sources from their observable nonlinear mixtures. How to make the nonlinear ICA model identifiable up to certain trivial indeterminacies is a long-standing problem in unsupervised learning. Recent breakthroughs reformulate the standard independence assumption of sources as conditional independence given some auxiliary variables (e.g., class labels and/or domain/time indexes) as weak supervision or inductive bias. However, nonlinear ICA with unconditional priors cannot benefit from such developments. We explore an alternative path and consider only assumptions on the mixing process, such as Structural Sparsity. We show that under specific instantiations of such constraints, the independent latent sources can be identified from their nonlinear mixtures up to a permutation and a component-wise transformation, thus achieving nontrivial identifiability of nonlinear ICA without auxiliary variables. We provide estimation methods and validate the theoretical results experimentally. The results on image data suggest that our conditions may hold in a number of practical data generating processes.

This paper explores meta-learning in sequential recommendation to alleviate the item cold-start problem. Sequential recommendation aims to capture user's dynamic preferences based on historical behavior sequences and acts as a key component of most online recommendation scenarios. However, most previous methods have trouble recommending cold-start items, which are prevalent in those scenarios. As there is generally no side information in sequential recommendation task, previous cold-start methods could not be applied when only user-item interactions are available. Thus, we propose a Meta-learning-based Cold-Start Sequential Recommendation Framework, namely Mecos, to mitigate the item cold-start problem in sequential recommendation. This task is non-trivial as it targets at an important problem in a novel and challenging context. Mecos effectively extracts user preference from limited interactions and learns to match the target cold-start item with the potential user. Besides, our framework can be painlessly integrated with neural network-based models. Extensive experiments conducted on three real-world datasets verify the superiority of Mecos, with the average improvement up to 99%, 91%, and 70% in HR@10 over state-of-the-art baseline methods.

In today's context, deploying data-driven services like recommendation on edge devices instead of cloud servers becomes increasingly attractive due to privacy and network latency concerns. A common practice in building compact on-device recommender systems is to compress their embeddings which are normally the cause of excessive parameterization. However, despite the vast variety of devices and their associated memory constraints, existing memory-efficient recommender systems are only specialized for a fixed memory budget in every design and training life cycle, where a new model has to be retrained to obtain the optimal performance while adapting to a smaller/larger memory budget. In this paper, we present a novel lightweight recommendation paradigm that allows a well-trained recommender to be customized for arbitrary device-specific memory constraints without retraining. The core idea is to compose elastic embeddings for each item, where an elastic embedding is the concatenation of a set of embedding blocks that are carefully chosen by an automated search function. Correspondingly, we propose an innovative approach, namely recommendation with universally learned elastic embeddings (RULE). To ensure the expressiveness of all candidate embedding blocks, RULE enforces a diversity-driven regularization when learning different embedding blocks. Then, a performance estimator-based evolutionary search function is designed, allowing for efficient specialization of elastic embeddings under any memory constraint for on-device recommendation. Extensive experiments on real-world datasets reveal the superior performance of RULE under tight memory budgets.

Many of the causal discovery methods rely on the faithfulness assumption to guarantee asymptotic correctness. However, the assumption can be approximately violated in many ways, leading to sub-optimal solutions. Although there is a line of research in Bayesian network structure learning that focuses on weakening the assumption, such as exact search methods with well-defined score functions, they do not scale well to large graphs. In this work, we introduce several strategies to improve the scalability of exact score-based methods in the linear Gaussian setting. In particular, we develop a super-structure estimation method based on the support of inverse covariance matrix which requires assumptions that are strictly weaker than faithfulness, and apply it to restrict the search space of exact search. We also propose a local search strategy that performs exact search on the local clusters formed by each variable and its neighbors within two hops in the super-structure. Numerical experiments validate the efficacy of the proposed procedure, and demonstrate that it scales up to hundreds of nodes with a high accuracy.

Session-based recommendation focuses on the prediction of user actions based on anonymous sessions and is a necessary method in the lack of user historical data. However, none of the existing session-based recommendation methods explicitly takes the long-tail recommendation into consideration, which plays an important role in improving the diversity of recommendation and producing the serendipity. As the distribution of items with long-tail is prevalent in session-based recommendation scenarios (e.g., e-commerce, music, and TV program recommendations), more attention should be put on the long-tail session-based recommendation. In this paper, we propose a novel network architecture, namely TailNet, to improve long-tail recommendation performance, while maintaining competitive accuracy performance compared with other methods. We start by classifying items into short-head (popular) and long-tail (niche) items based on click frequency. Then a novel preference mechanism is proposed and applied in TailNet to determine user preference between two types of items, so as to softly adjust and personalize recommendations. Extensive experiments on two real-world datasets verify the superiority of our method compared with state-of-the-art works.