Multi-task learning is a widely used technique for harnessing information from various tasks. Recently, the sparse orthogonal factor regression (SOFAR) framework, based on the sparse singular value decomposition (SVD) within the coefficient matrix, was introduced for interpretable multi-task learning, enabling the discovery of meaningful latent feature-response association networks across different layers. However, conducting precise inference on the latent factor matrices has remained challenging due to orthogonality constraints inherited from the sparse SVD constraint. In this paper, we suggest a novel approach called high-dimensional manifold-based SOFAR inference (SOFARI), drawing on the Neyman near-orthogonality inference while incorporating the Stiefel manifold structure imposed by the SVD constraints. By leveraging the underlying Stiefel manifold structure, SOFARI provides bias-corrected estimators for both latent left factor vectors and singular values, for which we show to enjoy the asymptotic mean-zero normal distributions with estimable variances. We introduce two SOFARI variants to handle strongly and weakly orthogonal latent factors, where the latter covers a broader range of applications. We illustrate the effectiveness of SOFARI and justify our theoretical results through simulation examples and a real data application in economic forecasting.
We investigate the robustness of the model-X knockoffs framework with respect to the misspecified or estimated feature distribution. We achieve such a goal by theoretically studying the feature selection performance of a practically implemented knockoffs algorithm, which we name as the approximate knockoffs (ARK) procedure, under the measures of the false discovery rate (FDR) and family wise error rate (FWER). The approximate knockoffs procedure differs from the model-X knockoffs procedure only in that the former uses the misspecified or estimated feature distribution. A key technique in our theoretical analyses is to couple the approximate knockoffs procedure with the model-X knockoffs procedure so that random variables in these two procedures can be close in realizations. We prove that if such coupled model-X knockoffs procedure exists, the approximate knockoffs procedure can achieve the asymptotic FDR or FWER control at the target level. We showcase three specific constructions of such coupled model-X knockoff variables, verifying their existence and justifying the robustness of the model-X knockoffs framework.
Epilepsy is one of the most serious neurological diseases, affecting 1-2% of the world's population. The diagnosis of epilepsy depends heavily on the recognition of epileptic waves, i.e., disordered electrical brainwave activity in the patient's brain. Existing works have begun to employ machine learning models to detect epileptic waves via cortical electroencephalogram (EEG). However, the recently developed stereoelectrocorticography (SEEG) method provides information in stereo that is more precise than conventional EEG, and has been broadly applied in clinical practice. Therefore, we propose the first data-driven study to detect epileptic waves in a real-world SEEG dataset. While offering new opportunities, SEEG also poses several challenges. In clinical practice, epileptic wave activities are considered to propagate between different regions in the brain. These propagation paths, also known as the epileptogenic network, are deemed to be a key factor in the context of epilepsy surgery. However, the question of how to extract an exact epileptogenic network for each patient remains an open problem in the field of neuroscience. To address these challenges, we propose a novel model (BrainNet) that jointly learns the dynamic diffusion graphs and models the brain wave diffusion patterns. In addition, our model effectively aids in resisting label imbalance and severe noise by employing several self-supervised learning tasks and a hierarchical framework. By experimenting with the extensive real SEEG dataset obtained from multiple patients, we find that BrainNet outperforms several latest state-of-the-art baselines derived from time-series analysis.
We focus on the weakly-supervised audio-visual video parsing task (AVVP), which aims to identify and locate all the events in audio/visual modalities. Previous works only concentrate on video-level overall label denoising across modalities, but overlook the segment-level label noise, where adjacent video segments (i.e., 1-second video clips) may contain different events. However, recognizing events in the segment is challenging because its label could be any combination of events that occur in the video. To address this issue, we consider tackling AVVP from the language perspective, since language could freely describe how various events appear in each segment beyond fixed labels. Specifically, we design language prompts to describe all cases of event appearance for each video. Then, the similarity between language prompts and segments is calculated, where the event of the most similar prompt is regarded as the segment-level label. In addition, to deal with the mislabeled segments, we propose to perform dynamic re-weighting on the unreliable segments to adjust their labels. Experiments show that our simple yet effective approach outperforms state-of-the-art methods by a large margin.
Large-scale network inference with uncertainty quantification has important applications in natural, social, and medical sciences. The recent work of Fan, Fan, Han and Lv (2022) introduced a general framework of statistical inference on membership profiles in large networks (SIMPLE) for testing the sharp null hypothesis that a pair of given nodes share the same membership profiles. In real applications, there are often groups of nodes under investigation that may share similar membership profiles at the presence of relatively weaker signals than the setting considered in SIMPLE. To address these practical challenges, in this paper we propose a SIMPLE method with random coupling (SIMPLE-RC) for testing the non-sharp null hypothesis that a group of given nodes share similar (not necessarily identical) membership profiles under weaker signals. Utilizing the idea of random coupling, we construct our test as the maximum of the SIMPLE tests for subsampled node pairs from the group. Such technique reduces significantly the correlation among individual SIMPLE tests while largely maintaining the power, enabling delicate analysis on the asymptotic distributions of the SIMPLE-RC test. Our method and theory cover both the cases with and without node degree heterogeneity. These new theoretical developments are empowered by a second-order expansion of spiked eigenvectors under the $\ell_\infty$-norm, built upon our work for random matrices with weak spikes. Our theoretical results and the practical advantages of the newly suggested method are demonstrated through several simulation and real data examples.
Random forests is one of the most widely used machine learning methods over the past decade thanks to its outstanding empirical performance. Yet, because of its black-box nature, the results by random forests can be hard to interpret in many big data applications. Quantifying the usefulness of individual features in random forests learning can greatly enhance its interpretability. Existing studies have shown that some popularly used feature importance measures for random forests suffer from the bias issue. In addition, there lack comprehensive size and power analyses for most of these existing methods. In this paper, we approach the problem via hypothesis testing, and suggest a framework of the self-normalized feature-residual correlation test (FACT) for evaluating the significance of a given feature in the random forests model with bias-resistance property, where our null hypothesis concerns whether the feature is conditionally independent of the response given all other features. Such an endeavor on random forests inference is empowered by some recent developments on high-dimensional random forests consistency. The vanilla version of our FACT test can suffer from the bias issue in the presence of feature dependency. We exploit the techniques of imbalancing and conditioning for bias correction. We further incorporate the ensemble idea into the FACT statistic through feature transformations for the enhanced power. Under a fairly general high-dimensional nonparametric model setting with dependent features, we formally establish that FACT can provide theoretically justified random forests feature p-values and enjoy appealing power through nonasymptotic analyses. The theoretical results and finite-sample advantages of the newly suggested method are illustrated with several simulation examples and an economic forecasting application in relation to COVID-19.
This paper investigates the estimation and inference of the average treatment effect (ATE) using deep neural networks (DNNs) in the potential outcomes framework. Under some regularity conditions, the observed response can be formulated as the response of a mean regression problem with both the confounding variables and the treatment indicator as the independent variables. Using such formulation, we investigate two methods for ATE estimation and inference based on the estimated mean regression function via DNN regression using a specific network architecture. We show that both DNN estimates of ATE are consistent with dimension-free consistency rates under some assumptions on the underlying true mean regression model. Our model assumptions accommodate the potentially complicated dependence structure of the observed response on the covariates, including latent factors and nonlinear interactions between the treatment indicator and confounding variables. We also establish the asymptotic normality of our estimators based on the idea of sample splitting, ensuring precise inference and uncertainty quantification. Simulation studies and real data application justify our theoretical findings and support our DNN estimation and inference methods.
Rain streaks degrade the image quality and seriously affect the performance of subsequent computer vision tasks, such as autonomous driving, social security, etc. Therefore, removing rain streaks from a given rainy images is of great significance. Convolutional neural networks(CNN) have been widely used in image deraining tasks, however, the local computational characteristics of convolutional operations limit the development of image deraining tasks. Recently, the popular transformer has global computational features that can further facilitate the development of image deraining tasks. In this paper, we introduce Swin-transformer into the field of image deraining for the first time to study the performance and potential of Swin-transformer in the field of image deraining. Specifically, we improve the basic module of Swin-transformer and design a three-branch model to implement single-image rain removal. The former implements the basic rain pattern feature extraction, while the latter fuses different features to further extract and process the image features. In addition, we employ a jump connection to fuse deep features and shallow features. In terms of experiments, the existing public dataset suffers from image duplication and relatively homogeneous background. So we propose a new dataset Rain3000 to validate our model. Therefore, we propose a new dataset Rain3000 for validating our model. Experimental results on the publicly available datasets Rain100L, Rain100H and our dataset Rain3000 show that our proposed method has performance and inference speed advantages over the current mainstream single-image rain streaks removal models.The source code will be available at https://github.com/H-tfx/SDNet.
Network data is prevalent in many contemporary big data applications in which a common interest is to unveil important latent links between different pairs of nodes. Yet a simple fundamental question of how to precisely quantify the statistical uncertainty associated with the identification of latent links still remains largely unexplored. In this paper, we propose the method of statistical inference on membership profiles in large networks (SIMPLE) in the setting of degree-corrected mixed membership model, where the null hypothesis assumes that the pair of nodes share the same profile of community memberships. In the simpler case of no degree heterogeneity, the model reduces to the mixed membership model for which an alternative more robust test is also proposed. Both tests are of the Hotelling-type statistics based on the rows of empirical eigenvectors or their ratios, whose asymptotic covariance matrices are very challenging to derive and estimate. Nevertheless, their analytical expressions are unveiled and the unknown covariance matrices are consistently estimated. Under some mild regularity conditions, we establish the exact limiting distributions of the two forms of SIMPLE test statistics under the null hypothesis and contiguous alternative hypothesis. They are the chi-square distributions and the noncentral chi-square distributions, respectively, with degrees of freedom depending on whether the degrees are corrected or not. We also address the important issue of estimating the unknown number of communities and establish the asymptotic properties of the associated test statistics. The advantages and practical utility of our new procedures in terms of both size and power are demonstrated through several simulation examples and real network applications.