scCDCG: Efficient Deep Structural Clustering for single-cell RNA-seq via Deep Cut-informed Graph Embedding

Single-cell RNA sequencing (scRNA-seq) is essential for unraveling cellular heterogeneity and diversity, offering invaluable insights for bioinformatics advancements. Despite its potential, traditional clustering methods in scRNA-seq data analysis often neglect the structural information embedded in gene expression profiles, crucial for understanding cellular correlations and dependencies. Existing strategies, including graph neural networks, face challenges in handling the inefficiency due to scRNA-seq data's intrinsic high-dimension and high-sparsity. Addressing these limitations, we introduce scCDCG (single-cell RNA-seq Clustering via Deep Cut-informed Graph), a novel framework designed for efficient and accurate clustering of scRNA-seq data that simultaneously utilizes intercellular high-order structural information. scCDCG comprises three main components: (i) A graph embedding module utilizing deep cut-informed techniques, which effectively captures intercellular high-order structural information, overcoming the over-smoothing and inefficiency issues prevalent in prior graph neural network methods. (ii) A self-supervised learning module guided by optimal transport, tailored to accommodate the unique complexities of scRNA-seq data, specifically its high-dimension and high-sparsity. (iii) An autoencoder-based feature learning module that simplifies model complexity through effective dimension reduction and feature extraction. Our extensive experiments on 6 datasets demonstrate scCDCG's superior performance and efficiency compared to 7 established models, underscoring scCDCG's potential as a transformative tool in scRNA-seq data analysis. Our code is available at: https://github.com/XPgogogo/scCDCG.

Robust Distributed Learning Against Both Distributional Shifts and Byzantine Attacks

In distributed learning systems, robustness issues may arise from two sources. On one hand, due to distributional shifts between training data and test data, the trained model could exhibit poor out-of-sample performance. On the other hand, a portion of working nodes might be subject to byzantine attacks which could invalidate the learning result. Existing works mostly deal with these two issues separately. In this paper, we propose a new algorithm that equips distributed learning with robustness measures against both distributional shifts and byzantine attacks. Our algorithm is built on recent advances in distributionally robust optimization as well as norm-based screening (NBS), a robust aggregation scheme against byzantine attacks. We provide convergence proofs in three cases of the learning model being nonconvex, convex, and strongly convex for the proposed algorithm, shedding light on its convergence behaviors and endurability against byzantine attacks. In particular, we deduce that any algorithm employing NBS (including ours) cannot converge when the percentage of byzantine nodes is 1/3 or higher, instead of 1/2, which is the common belief in current literature. The experimental results demonstrate the effectiveness of our algorithm against both robustness issues. To the best of our knowledge, this is the first work to address distributional shifts and byzantine attacks simultaneously.

QC-ODKLA: Quantized and Communication-Censored Online Decentralized Kernel Learning via Linearized ADMM

This paper focuses on online kernel learning over a decentralized network. Each agent in the network receives continuous streaming data locally and works collaboratively to learn a nonlinear prediction function that is globally optimal in the reproducing kernel Hilbert space with respect to the total instantaneous costs of all agents. In order to circumvent the curse of dimensionality issue in traditional online kernel learning, we utilize random feature (RF) mapping to convert the non-parametric kernel learning problem into a fixed-length parametric one in the RF space. We then propose a novel learning framework named Online Decentralized Kernel learning via Linearized ADMM (ODKLA) to efficiently solve the online decentralized kernel learning problem. To further improve the communication efficiency, we add the quantization and censoring strategies in the communication stage and develop the Quantized and Communication-censored ODKLA (QC-ODKLA) algorithm. We theoretically prove that both ODKLA and QC-ODKLA can achieve the optimal sublinear regret $\mathcal{O}(\sqrt{T})$ over $T$ time slots. Through numerical experiments, we evaluate the learning effectiveness, communication, and computation efficiencies of the proposed methods.

COKE: Communication-Censored Kernel Learning for Decentralized Non-parametric Learning

This paper studies the decentralized optimization and learning problem where multiple interconnected agents aim to learn an optimal decision function defined over a reproducing kernel Hilbert (RKH) space by jointly minimizing a global objective function, with access to locally observed data only. As a non-parametric approach, kernel learning faces a major challenge in distributed implementation: the decision variables of local objective functions are data-dependent with different sizes and thus cannot be optimized under the decentralized consensus framework without any raw data exchange among agents. To circumvent this major challenge and preserve data privacy, we leverage the random feature (RF) approximation approach to map the large-volume data represented in the RKH space into a smaller RF space, which facilitates the same-size parameter exchange and enables distributed agents to reach consensus on the function decided by the parameters in the RF space. For fast convergent implementation, we design an iterative algorithm for Decentralized Kernel Learning via Alternating direction method of multipliers (DKLA). Further, we develop a COmmunication-censored KErnel learning (COKE) algorithm to reduce the communication load in DKLA. To do so, we apply a communication-censoring strategy, which prevents an agent from transmitting at every iteration unless its local updates are deemed informative. Theoretical results in terms of linear convergence guarantee and generalization performance analysis of DKLA and COKE are provided. Comprehensive tests with both synthetic and real datasets are conducted to verify the communication efficiency and learning effectiveness of COKE.

Variational Quantum Circuits for Quantum State Tomography

We propose a hybrid quantum-classical algorithm for quantum state tomography. Given an unknown quantum state, a quantum machine learning algorithm is used to maximize the fidelity between the output of a variational quantum circuit and this state. The number of parameters of the variational quantum circuit grows linearly with the number of qubits and the circuit depth. After that, a subsequent classical algorithm is used to reconstruct the unknown quantum state. We demonstrate our method by performing numerical simulations to reconstruct the ground state of a one-dimensional quantum spin chain, using a variational quantum circuit simulator. Our method is suitable for near-term quantum computing platforms, and could be used for relatively large-scale quantum state tomography for experimentally relevant quantum states.