On the Recoverability of Causal Relations from Temporally Aggregated I.I.D. Data

We consider the effect of temporal aggregation on instantaneous (non-temporal) causal discovery in general setting. This is motivated by the observation that the true causal time lag is often considerably shorter than the observational interval. This discrepancy leads to high aggregation, causing time-delay causality to vanish and instantaneous dependence to manifest. Although we expect such instantaneous dependence has consistency with the true causal relation in certain sense to make the discovery results meaningful, it remains unclear what type of consistency we need and when will such consistency be satisfied. We proposed functional consistency and conditional independence consistency in formal way correspond functional causal model-based methods and conditional independence-based methods respectively and provide the conditions under which these consistencies will hold. We show theoretically and experimentally that causal discovery results may be seriously distorted by aggregation especially in complete nonlinear case and we also find causal relationship still recoverable from aggregated data if we have partial linearity or appropriate prior. Our findings suggest community should take a cautious and meticulous approach when interpreting causal discovery results from such data and show why and when aggregation will distort the performance of causal discovery methods.

Learning Discrete Concepts in Latent Hierarchical Models

Learning concepts from natural high-dimensional data (e.g., images) holds potential in building human-aligned and interpretable machine learning models. Despite its encouraging prospect, formalization and theoretical insights into this crucial task are still lacking. In this work, we formalize concepts as discrete latent causal variables that are related via a hierarchical causal model that encodes different abstraction levels of concepts embedded in high-dimensional data (e.g., a dog breed and its eye shapes in natural images). We formulate conditions to facilitate the identification of the proposed causal model, which reveals when learning such concepts from unsupervised data is possible. Our conditions permit complex causal hierarchical structures beyond latent trees and multi-level directed acyclic graphs in prior work and can handle high-dimensional, continuous observed variables, which is well-suited for unstructured data modalities such as images. We substantiate our theoretical claims with synthetic data experiments. Further, we discuss our theory's implications for understanding the underlying mechanisms of latent diffusion models and provide corresponding empirical evidence for our theoretical insights.

From Orthogonality to Dependency: Learning Disentangled Representation for Multi-Modal Time-Series Sensing Signals

Existing methods for multi-modal time series representation learning aim to disentangle the modality-shared and modality-specific latent variables. Although achieving notable performances on downstream tasks, they usually assume an orthogonal latent space. However, the modality-specific and modality-shared latent variables might be dependent on real-world scenarios. Therefore, we propose a general generation process, where the modality-shared and modality-specific latent variables are dependent, and further develop a \textbf{M}ulti-mod\textbf{A}l \textbf{TE}mporal Disentanglement (\textbf{MATE}) model. Specifically, our \textbf{MATE} model is built on a temporally variational inference architecture with the modality-shared and modality-specific prior networks for the disentanglement of latent variables. Furthermore, we establish identifiability results to show that the extracted representation is disentangled. More specifically, we first achieve the subspace identifiability for modality-shared and modality-specific latent variables by leveraging the pairing of multi-modal data. Then we establish the component-wise identifiability of modality-specific latent variables by employing sufficient changes of historical latent variables. Extensive experimental studies on multi-modal sensors, human activity recognition, and healthcare datasets show a general improvement in different downstream tasks, highlighting the effectiveness of our method in real-world scenarios.

On the Identification of Temporally Causal Representation with Instantaneous Dependence

Temporally causal representation learning aims to identify the latent causal process from time series observations, but most methods require the assumption that the latent causal processes do not have instantaneous relations. Although some recent methods achieve identifiability in the instantaneous causality case, they require either interventions on the latent variables or grouping of the observations, which are in general difficult to obtain in real-world scenarios. To fill this gap, we propose an \textbf{ID}entification framework for instantane\textbf{O}us \textbf{L}atent dynamics (\textbf{IDOL}) by imposing a sparse influence constraint that the latent causal processes have sparse time-delayed and instantaneous relations. Specifically, we establish identifiability results of the latent causal process based on sufficient variability and the sparse influence constraint by employing contextual information of time series data. Based on these theories, we incorporate a temporally variational inference architecture to estimate the latent variables and a gradient-based sparsity regularization to identify the latent causal process. Experimental results on simulation datasets illustrate that our method can identify the latent causal process. Furthermore, evaluations on multiple human motion forecasting benchmarks with instantaneous dependencies indicate the effectiveness of our method in real-world settings.

An Efficient Finite Difference Approximation via a Double Sample-Recycling Approach

Estimating stochastic gradients is pivotal in fields like service systems within operations research. The classical method for this estimation is the finite difference approximation, which entails generating samples at perturbed inputs. Nonetheless, practical challenges persist in determining the perturbation and obtaining an optimal finite difference estimator in the sense of possessing the smallest mean squared error (MSE). To tackle this problem, we propose a double sample-recycling approach in this paper. Firstly, pilot samples are recycled to estimate the optimal perturbation. Secondly, recycling these pilot samples again and generating new samples at the estimated perturbation, lead to an efficient finite difference estimator. We analyze its bias, variance and MSE. Our analyses demonstrate a reduction in asymptotic variance, and in some cases, a decrease in asymptotic bias, compared to the optimal finite difference estimator. Therefore, our proposed estimator consistently coincides with, or even outperforms the optimal finite difference estimator. In numerical experiments, we apply the estimator in several examples, and numerical results demonstrate its robustness, as well as coincidence with the theory presented, especially in the case of small sample sizes.

A Conditional Independence Test in the Presence of Discretization

Testing conditional independence has many applications, such as in Bayesian network learning and causal discovery. Different test methods have been proposed. However, existing methods generally can not work when only discretized observations are available. Specifically, consider $X_1$, $\tilde{X}_2$ and $X_3$ are observed variables, where $\tilde{X}_2$ is a discretization of latent variables $X_2$. Applying existing test methods to the observations of $X_1$, $\tilde{X}_2$ and $X_3$ can lead to a false conclusion about the underlying conditional independence of variables $X_1$, $X_2$ and $X_3$. Motivated by this, we propose a conditional independence test specifically designed to accommodate the presence of such discretization. To achieve this, we design the bridge equations to recover the parameter reflecting the statistical information of the underlying latent continuous variables. An appropriate test statistic and its asymptotic distribution under the null hypothesis of conditional independence have also been derived. Both theoretical results and empirical validation have been provided, demonstrating the effectiveness of our test methods.

POMDP-Guided Active Force-Based Search for Robotic Insertion

In robotic insertion tasks where the uncertainty exceeds the allowable tolerance, a good search strategy is essential for successful insertion and significantly influences efficiency. The commonly used blind search method is time-consuming and does not exploit the rich contact information. In this paper, we propose a novel search strategy that actively utilizes the information contained in the contact configuration and shows high efficiency. In particular, we formulate this problem as a Partially Observable Markov Decision Process (POMDP) with carefully designed primitives based on an in-depth analysis of the contact configuration's static stability. From the formulated POMDP, we can derive a novel search strategy. Thanks to its simplicity, this search strategy can be incorporated into a Finite-State-Machine (FSM) controller. The behaviors of the FSM controller are realized through a low-level Cartesian Impedance Controller. Our method is based purely on the robot's proprioceptive sensing and does not need visual or tactile sensors. To evaluate the effectiveness of our proposed strategy and control framework, we conduct extensive comparison experiments in simulation, where we compare our method with the baseline approach. The results demonstrate that our proposed method achieves a higher success rate with a shorter search time and search trajectory length compared to the baseline method. Additionally, we show that our method is robust to various initial displacement errors.

Masked Multi-Domain Network: Multi-Type and Multi-Scenario Conversion Rate Prediction with a Single Model

In real-world advertising systems, conversions have different types in nature and ads can be shown in different display scenarios, both of which highly impact the actual conversion rate (CVR). This results in the multi-type and multi-scenario CVR prediction problem. A desired model for this problem should satisfy the following requirements: 1) Accuracy: the model should achieve fine-grained accuracy with respect to any conversion type in any display scenario. 2) Scalability: the model parameter size should be affordable. 3) Convenience: the model should not require a large amount of effort in data partitioning, subset processing and separate storage. Existing approaches cannot simultaneously satisfy these requirements. For example, building a separate model for each (conversion type, display scenario) pair is neither scalable nor convenient. Building a unified model trained on all the data with conversion type and display scenario included as two features is not accurate enough. In this paper, we propose the Masked Multi-domain Network (MMN) to solve this problem. To achieve the accuracy requirement, we model domain-specific parameters and propose a dynamically weighted loss to account for the loss scale imbalance issue within each mini-batch. To achieve the scalability requirement, we propose a parameter sharing and composition strategy to reduce model parameters from a product space to a sum space. To achieve the convenience requirement, we propose an auto-masking strategy which can take mixed data from all the domains as input. It avoids the overhead caused by data partitioning, individual processing and separate storage. Both offline and online experimental results validate the superiority of MMN for multi-type and multi-scenario CVR prediction. MMN is now the serving model for real-time CVR prediction in UC Toutiao.

Identifiable Latent Neural Causal Models

Causal representation learning seeks to uncover latent, high-level causal representations from low-level observed data. It is particularly good at predictions under unseen distribution shifts, because these shifts can generally be interpreted as consequences of interventions. Hence leveraging {seen} distribution shifts becomes a natural strategy to help identifying causal representations, which in turn benefits predictions where distributions are previously {unseen}. Determining the types (or conditions) of such distribution shifts that do contribute to the identifiability of causal representations is critical. This work establishes a {sufficient} and {necessary} condition characterizing the types of distribution shifts for identifiability in the context of latent additive noise models. Furthermore, we present partial identifiability results when only a portion of distribution shifts meets the condition. In addition, we extend our findings to latent post-nonlinear causal models. We translate our findings into a practical algorithm, allowing for the acquisition of reliable latent causal representations. Our algorithm, guided by our underlying theory, has demonstrated outstanding performance across a diverse range of synthetic and real-world datasets. The empirical observations align closely with the theoretical findings, affirming the robustness and effectiveness of our approach.

Local Causal Discovery with Linear non-Gaussian Cyclic Models

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.