Time Series Gaussian Chain Graph Models

Time series graphical models have recently received considerable attention for characterizing (conditional) dependence structures in multivariate time series. In many applications, the multivariate series exhibit variable-partitioned blockwise dependence, with distinct patterns within and across blocks. In this paper, we introduce a new class of time series Gaussian chain graph models that represent contemporaneous and lagged causal relations via directed edges across blocks, while capturing within-block conditional dependencies through undirected edges. In the frequency domain, this formulation induces a cross-frequency shared group sparse plus group low-rank decomposition of the inverse spectral density matrices, which we exploit to establish identifiability of the time series chain graph structure. Building on this, we then propose a three-stage learning procedure for estimating the undirected and directed edge sets, which involves optimizing a regularized Whittle likelihood with a group lasso penalty to encourage group sparsity and a novel tensor-unfolding nuclear norm penalty to enforce group low-rank structure. We investigate the asymptotic properties of the proposed method, ensuring its consistency for exact recovery of the chain graph structure. The superior empirical performance of the proposed method is demonstrated through both extensive simulation studies and an application to U.S. macroeconomic data that highlights key monetary policy transmission mechanisms.

Realizing Text-Driven Motion Generation on NAO Robot: A Reinforcement Learning-Optimized Control Pipeline

Human motion retargeting for humanoid robots, transferring human motion data to robots for imitation, presents significant challenges but offers considerable potential for real-world applications. Traditionally, this process relies on human demonstrations captured through pose estimation or motion capture systems. In this paper, we explore a text-driven approach to mapping human motion to humanoids. To address the inherent discrepancies between the generated motion representations and the kinematic constraints of humanoid robots, we propose an angle signal network based on norm-position and rotation loss (NPR Loss). It generates joint angles, which serve as inputs to a reinforcement learning-based whole-body joint motion control policy. The policy ensures tracking of the generated motions while maintaining the robot's stability during execution. Our experimental results demonstrate the efficacy of this approach, successfully transferring text-driven human motion to a real humanoid robot NAO.

Two-Dimensional Deep ReLU CNN Approximation for Korobov Functions: A Constructive Approach

This paper investigates approximation capabilities of two-dimensional (2D) deep convolutional neural networks (CNNs), with Korobov functions serving as a benchmark. We focus on 2D CNNs, comprising multi-channel convolutional layers with zero-padding and ReLU activations, followed by a fully connected layer. We propose a fully constructive approach for building 2D CNNs to approximate Korobov functions and provide rigorous analysis of the complexity of the constructed networks. Our results demonstrate that 2D CNNs achieve near-optimal approximation rates under the continuous weight selection model, significantly alleviating the curse of dimensionality. This work provides a solid theoretical foundation for 2D CNNs and illustrates their potential for broader applications in function approximation.