A Subspace-Constrained Tyler's Estimator and its Applications to Structure from Motion

We present the subspace-constrained Tyler's estimator (STE) designed for recovering a low-dimensional subspace within a dataset that may be highly corrupted with outliers. STE is a fusion of the Tyler's M-estimator (TME) and a variant of the fast median subspace. Our theoretical analysis suggests that, under a common inlier-outlier model, STE can effectively recover the underlying subspace, even when it contains a smaller fraction of inliers relative to other methods in the field of robust subspace recovery. We apply STE in the context of Structure from Motion (SfM) in two ways: for robust estimation of the fundamental matrix and for the removal of outlying cameras, enhancing the robustness of the SfM pipeline. Numerical experiments confirm the state-of-the-art performance of our method in these applications. This research makes significant contributions to the field of robust subspace recovery, particularly in the context of computer vision and 3D reconstruction.

Theoretical Guarantees for the Subspace-Constrained Tyler's Estimator

This work analyzes the subspace-constrained Tyler's estimator (STE) designed for recovering a low-dimensional subspace within a dataset that may be highly corrupted with outliers. It assumes a weak inlier-outlier model and allows the fraction of inliers to be smaller than a fraction that leads to computational hardness of the robust subspace recovery problem. It shows that in this setting, if the initialization of STE, which is an iterative algorithm, satisfies a certain condition, then STE can effectively recover the underlying subspace. It further shows that under the generalized haystack model, STE initialized by the Tyler's M-estimator (TME), can recover the subspace when the fraction of iniliers is too small for TME to handle.

A Bi-Pyramid Multimodal Fusion Method for the Diagnosis of Bipolar Disorders

Previous research on the diagnosis of Bipolar disorder has mainly focused on resting-state functional magnetic resonance imaging. However, their accuracy can not meet the requirements of clinical diagnosis. Efficient multimodal fusion strategies have great potential for applications in multimodal data and can further improve the performance of medical diagnosis models. In this work, we utilize both sMRI and fMRI data and propose a novel multimodal diagnosis model for bipolar disorder. The proposed Patch Pyramid Feature Extraction Module extracts sMRI features, and the spatio-temporal pyramid structure extracts the fMRI features. Finally, they are fused by a fusion module to output diagnosis results with a classifier. Extensive experiments show that our proposed method outperforms others in balanced accuracy from 0.657 to 0.732 on the OpenfMRI dataset, and achieves the state of the art.

MusicAOG: an Energy-Based Model for Learning and Sampling a Hierarchical Representation of Symbolic Music

In addressing the challenge of interpretability and generalizability of artificial music intelligence, this paper introduces a novel symbolic representation that amalgamates both explicit and implicit musical information across diverse traditions and granularities. Utilizing a hierarchical and-or graph representation, the model employs nodes and edges to encapsulate a broad spectrum of musical elements, including structures, textures, rhythms, and harmonies. This hierarchical approach expands the representability across various scales of music. This representation serves as the foundation for an energy-based model, uniquely tailored to learn musical concepts through a flexible algorithm framework relying on the minimax entropy principle. Utilizing an adapted Metropolis-Hastings sampling technique, the model enables fine-grained control over music generation. A comprehensive empirical evaluation, contrasting this novel approach with existing methodologies, manifests considerable advancements in interpretability and controllability. This study marks a substantial contribution to the fields of music analysis, composition, and computational musicology.

Hyperparameter Estimation for Sparse Bayesian Learning Models

Sparse Bayesian Learning (SBL) models are extensively used in signal processing and machine learning for promoting sparsity through hierarchical priors. The hyperparameters in SBL models are crucial for the model's performance, but they are often difficult to estimate due to the non-convexity and the high-dimensionality of the associated objective function. This paper presents a comprehensive framework for hyperparameter estimation in SBL models, encompassing well-known algorithms such as the expectation-maximization (EM), MacKay, and convex bounding (CB) algorithms. These algorithms are cohesively interpreted within an alternating minimization and linearization (AML) paradigm, distinguished by their unique linearized surrogate functions. Additionally, a novel algorithm within the AML framework is introduced, showing enhanced efficiency, especially under low signal noise ratios. This is further improved by a new alternating minimization and quadratic approximation (AMQ) paradigm, which includes a proximal regularization term. The paper substantiates these advancements with thorough convergence analysis and numerical experiments, demonstrating the algorithm's effectiveness in various noise conditions and signal-to-noise ratios.

Multi-Dimension-Embedding-Aware Modality Fusion Transformer for Psychiatric Disorder Clasification

Deep learning approaches, together with neuroimaging techniques, play an important role in psychiatric disorders classification. Previous studies on psychiatric disorders diagnosis mainly focus on using functional connectivity matrices of resting-state functional magnetic resonance imaging (rs-fMRI) as input, which still needs to fully utilize the rich temporal information of the time series of rs-fMRI data. In this work, we proposed a multi-dimension-embedding-aware modality fusion transformer (MFFormer) for schizophrenia and bipolar disorder classification using rs-fMRI and T1 weighted structural MRI (T1w sMRI). Concretely, to fully utilize the temporal information of rs-fMRI and spatial information of sMRI, we constructed a deep learning architecture that takes as input 2D time series of rs-fMRI and 3D volumes T1w. Furthermore, to promote intra-modality attention and information fusion across different modalities, a fusion transformer module (FTM) is designed through extensive self-attention of hybrid feature maps of multi-modality. In addition, a dimension-up and dimension-down strategy is suggested to properly align feature maps of multi-dimensional from different modalities. Experimental results on our private and public OpenfMRI datasets show that our proposed MFFormer performs better than that using a single modality or multi-modality MRI on schizophrenia and bipolar disorder diagnosis.

CCOM-HuQin: an Annotated Multimodal Chinese Fiddle Performance Dataset

HuQin is a family of traditional Chinese bowed string instruments. Playing techniques(PTs) embodied in various playing styles add abundant emotional coloring and aesthetic feelings to HuQin performance. The complex applied techniques make HuQin music a challenging source for fundamental MIR tasks such as pitch analysis, transcription and score-audio alignment. In this paper, we present a multimodal performance dataset of HuQin music that contains audio-visual recordings of 11,992 single PT clips and 57 annotated musical pieces of classical excerpts. We systematically describe the HuQin PT taxonomy based on musicological theory and practical use cases. Then we introduce the dataset creation methodology and highlight the annotation principles featuring PTs. We analyze the statistics in different aspects to demonstrate the variety of PTs played in HuQin subcategories and perform preliminary experiments to show the potential applications of the dataset in various MIR tasks and cross-cultural music studies. Finally, we propose future work to be extended on the dataset.

Robust Regularized Low-Rank Matrix Models for Regression and Classification

While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy matrix-valued predictors. To address these issues, this paper proposes a framework of matrix variate regression models based on a rank constraint, vector regularization (e.g., sparsity), and a general loss function with three special cases considered: ordinary matrix regression, robust matrix regression, and matrix logistic regression. We also propose an alternating projected gradient descent algorithm. Based on analyzing our objective functions on manifolds with bounded curvature, we show that the algorithm is guaranteed to converge, all accumulation points of the iterates have estimation errors in the order of $O(1/\sqrt{n})$ asymptotically and substantially attaining the minimax rate. Our theoretical analysis can be applied to general optimization problems on manifolds with bounded curvature and can be considered an important technical contribution to this work. We validate the proposed method through simulation studies and real image data examples.

Symphony Generation with Permutation Invariant Language Model

In this work, we present a symbolic symphony music generation solution, SymphonyNet, based on a permutation invariant language model. To bridge the gap between text generation and symphony generation task, we propose a novel Multi-track Multi-instrument Repeatable (MMR) representation with particular 3-D positional embedding and a modified Byte Pair Encoding algorithm (Music BPE) for music tokens. A novel linear transformer decoder architecture is introduced as a backbone for modeling extra-long sequences of symphony tokens. Meanwhile, we train the decoder to learn automatic orchestration as a joint task by masking instrument information from the input. We also introduce a large-scale symbolic symphony dataset for the advance of symphony generation research. Our empirical results show that our proposed approach can generate coherent, novel, complex and harmonious symphony compared to human composition, which is the pioneer solution for multi-track multi-instrument symbolic music generation.

Vertical Federated Principal Component Analysis and Its Kernel Extension on Feature-wise Distributed Data

Despite enormous research interest and rapid application of federated learning (FL) to various areas, existing studies mostly focus on supervised federated learning under the horizontally partitioned local dataset setting. This paper will study the unsupervised FL under the vertically partitioned dataset setting. Accordingly, we propose the federated principal component analysis for vertically partitioned dataset (VFedPCA) method, which reduces the dimensionality across the joint datasets over all the clients and extracts the principal component feature information for downstream data analysis. We further take advantage of the nonlinear dimensionality reduction and propose the vertical federated advanced kernel principal component analysis (VFedAKPCA) method, which can effectively and collaboratively model the nonlinear nature existing in many real datasets. In addition, we study two communication topologies. The first is a server-client topology where a semi-trusted server coordinates the federated training, while the second is the fully-decentralized topology which further eliminates the requirement of the server by allowing clients themselves to communicate with their neighbors. Extensive experiments conducted on five types of real-world datasets corroborate the efficacy of VFedPCA and VFedAKPCA under the vertically partitioned FL setting. Code is available at: https://github.com/juyongjiang/VFedPCA-VFedAKPCA