Understanding causality in medical research is essential for developing effective interventions and diagnostic tools. Mendelian Randomization (MR) is a pivotal method for inferring causality through genetic data. However, MR analysis often requires pre-identification of exposure-outcome pairs from clinical experience or literature, which can be challenging to obtain. This poses difficulties for clinicians investigating causal factors of specific diseases. To address this, we introduce MRAgent, an innovative automated agent leveraging Large Language Models (LLMs) to enhance causal knowledge discovery in disease research. MRAgent autonomously scans scientific literature, discovers potential exposure-outcome pairs, and performs MR causal inference using extensive Genome-Wide Association Study data. We conducted both automated and human evaluations to compare different LLMs in operating MRAgent and provided a proof-of-concept case to demonstrate the complete workflow. MRAgent's capability to conduct large-scale causal analyses represents a significant advancement, equipping researchers and clinicians with a robust tool for exploring and validating causal relationships in complex diseases. Our code is public at https://github.com/xuwei1997/MRAgent.

Hard Thresholding Pursuit (HTP) has aroused increasing attention for its robust theoretical guarantees and impressive numerical performance in non-convex optimization. This paper consider a high-dimensional linear regression model withnobservations,ppredictors, and an unknowns∗-sparse signal β∗∈ Rpcorrupted by noise of magnitude σ.We introduce a novel tuning-free procedure, namely Full-Adaptive HTP (FAHTP), that simultaneously adapts to both the unknown sparsity and signal strength of the underlying model. Our theoretical analysis rigorously characterizes the iterative thresholding dynamics of FAHTP, offering refined theoretical insights. In specific, under the beta-min condition min{i:β∗i̸=0}|β∗i| ≥ Cσ(logp/n)1/2, FAHTP achieves oracle estimation rate σ(s∗/n)1/2, highlighting its theoretical superiority over convex competitors such as LASSO and SLOPE, and recovers the true support set exactly. More importantly, even without the beta-min condition, FAHTP achieves a tighter error bound than the classical minimax rate with high probability. The comprehensive numerical experiments substantiate our theoretical findings, underscoring the effectiveness and robustness of the proposed FAHTP.

Kernel methods are widely used in machine learning, especially for classification problems. However, the theoretical analysis of kernel classification is still limited. This paper investigates the statistical performances of kernel classifiers. With some mild assumptions on the conditional probability $\eta(x)=\mathbb{P}(Y=1\mid X=x)$, we derive an upper bound on the classification excess risk of a kernel classifier using recent advances in the theory of kernel regression. We also obtain a minimax lower bound for Sobolev spaces, which shows the optimality of the proposed classifier. Our theoretical results can be extended to the generalization error of overparameterized neural network classifiers. To make our theoretical results more applicable in realistic settings, we also propose a simple method to estimate the interpolation smoothness of $2\eta(x)-1$ and apply the method to real datasets.

In this paper, we focus our attention on the high-dimensional double sparse linear regression, that is, a combination of element-wise and group-wise sparsity. To address this problem, we propose an IHT-style (iterative hard thresholding) procedure that dynamically updates the threshold at each step. We establish the matching upper and lower bounds for parameter estimation, showing the optimality of our proposal in the minimax sense. More importantly, we introduce a fully adaptive optimal procedure designed to address unknown sparsity and noise levels. Our adaptive procedure demonstrates optimal statistical accuracy with fast convergence. Additionally, we elucidate the significance of the element-wise sparsity level $s_0$ as the trade-off between IHT and group IHT, underscoring the superior performance of our method over both. Leveraging the beta-min condition, we establish that our IHT-style procedure can attain the oracle estimation rate and achieve almost full recovery of the true support set at both the element level and group level. Finally, we demonstrate the superiority of our method by comparing it with several state-of-the-art algorithms on both synthetic and real-world datasets.

In this paper, we focus on the high-dimensional double sparse structures, where the parameter of interest simultaneously encourages group-wise and element-wise sparsity. By combining the Gilbert-Varshamov bound and its variants, we develop a novel lower bound technique for the metric entropy of the parameter space, specifically tailored for the double sparse structure over$\ell _{u}(\ell _{q})$-balls with$u,q \in [0,2$). We give lower bounds on the estimation error using an information-theoretic approach, leveraging the proposed technique and Fano’s inequality. To complement the lower bounds, we establish matching upper bounds through a direct analysis of constrained least-squares estimators and utilizing results from empirical processes. A significant discovery is that a phase transition phenomenon exists on the minimax rates for$u,q \in (0, 2)$. Furthermore, we extend the theoretical findings to the double sparse regression models and determine the minimax rates for estimation error. A novel Double Sparse Iterative Hard Thresholding (DSIHT) procedure is developed, with minimax optimality guaranteed. Finally, we demonstrate the superiority of the proposed method through numerical experiments.

The droop control and virtual synchronous generator control are currently the two most popular inverter control strategies, but both of these control strategies cannot be satisfied at the same time: (1) Frequency stability in stand-alone (SA) mode. (2) In the grid-connected (GC) mode, the output active power quickly follows the input power command. (3) Anti-interference ability of inverter output frequency in gridconnected mode. In response to these deficiencies, this paper proposes an improved droop control based on multi-stage leadlag compensation. This control strategy adds a lag link to the frequency output link of the traditional droop control to provide virtual inertia for the system; multi-stage lead lag compensation is added to the active power output section to improve the dynamic characteristics in the grid-connected mode. In the GC state, the improved droop control effectively reduces the power impact when the power command changes, and accelerates the power response speed. Enhanced the anti-interference ability of output frequency. In SA state, improved droop control can provide sufficient inertia and damping characteristics. Finally, the simulation results verify the effectiveness of the proposed improved droop control.