ShrinkageTrees is an R package for Bayesian tree ensembles in survival analysis and causal inference. The package implements Bayesian additive regression tree models for right- and interval-censored survival outcomes within an accelerated failure time (AFT) framework, with optional decomposition into prognostic and treatment-effect components for causal inference. Two complementary forms of regularisation are available: regularisation of the tree structure, via depth-penalising priors and Dirichlet splitting priors, and regularisation of the step heights, via global-local shrinkage priors. ShrinkageTrees provides the first implementation of the Horseshoe Forest, which places a horseshoe prior on the step heights. These regularisation strategies extend Bayesian tree ensembles to high-dimensional settings. An efficient Rcpp backend, multi-chain MCMC, and S3 methods support the full workflow: fitting, prediction, causal effect estimation, and convergence diagnostics.

The composite likelihood method reduces the computational cost of parameter estimation in time series by considering several subsets of observations instead of all observations at once. The asymptotic properties of this method are related to the Godambe information, an extension of the Fisher information that accounts for the dependence between subsets of observations. We aim to apply this method to linear Gaussian models, in particular fractional Brownian motion and fractional Gaussian noise. We derive theoretical expressions for their Fisher information and their Godambe information and deduce a subset selection design that sequentially maximizes the Godambe information. The size of the subsets then allows us to control the trade-off between estimation accuracy and computational cost. Through simulations, we compare this method with the method of moments and maximum likelihood estimation, and we apply it to real data, namely volatility series of a stock index and a wind speed time series.

We prove that optimally weighted second-order least squares (SLS) and the degree-two generalized polynomial maximization method (PMM) are the same population estimating equation for linear regression with conditionally homoskedastic non-Gaussian errors: they choose the same optimal linear combination of the first two centered residual moments, solve one population normal system, share one influence function, and attain the common asymptotic variance $c_2g_2/N$ -- the ordinary-least-squares slope-variance factor $c_2$ scaled by the PMM variance-reduction coefficient $g_2=1-\gamma_3^2/(2+\gamma_4)$ (with $\gamma_3,\gamma_4$ the error skewness and excess kurtosis). Feasible plug-in implementations are therefore first-order equivalent, with only higher-order finite-sample differences. The identity is sharp: under heteroskedasticity the unconditional PMM body and the conditional SLS weighting separate, costing efficiency for symmetric errors and consistency for asymmetric errors. Beyond degree two, PMM holds an efficiency reserve that SLS cannot reach within its second-moment span. For symmetric platykurtic errors SLS collapses to ordinary least squares for the slope, while degree-three PMM exploits kurtosis information outside the SLS moment span through a closed-form coefficient $g_3$; for canonical asymmetric laws this reserve is $30$--$50\%$ within the degree-three polynomial moment class. The Lean 4 development machine-checks the degree-specific algebraic core -- the closed forms for $g_2$ and $g_3$, the $g_2\le1$ result, the design cancellations, and the symmetric collapse -- while the general monotonicity $g_{S+1}\le g_S\le1$ is proved analytically by nesting. A Monte Carlo study illustrates the equivalence, the reserve, and the heteroskedastic boundary at finite samples.

Gaussian processes are a powerful tool for modeling continuous fields, but their naive $\mathcal{O}(N^3)$ computational cost and $\mathcal{O}(N^2)$ memory requirement often limit their practical use. Vecchia's approximation is a sparse precision matrix approximation for stationary, decaying kernels that conditions each point only on its $k$ nearest neighbors. We present GraphGP, a GPU algorithm for Vecchia's approximation that scales to nearly a billion parameters with linear time and memory requirements, handling arbitrary point distributions over a large dynamic range. Our key contributions are (1) a bit-reversed k-d tree ordering that allows efficient neighbor searches while also maximizing batch parallelism, and (2) a differentiable CUDA implementation, which is substantially faster and more memory efficient than our pure JAX baseline. GraphGP provides the building blocks for inference, including forward generation, inverse application, log-determinant, and kernel parameter derivatives.

Generalized partially linear single-index additive models (GPLSIAMs) have been increasingly applied across diverse areas due to their versatility in integrating functional flexibility with parametric dimension reduction while maintaining interpretability. However, the estimation presents severe computational challenges. This paper introduces a novel stable method that uses the model matrix for each single-index effect, defined by its single-index coefficients, and the penalized complete Fisher information matrix to dynamically update the boundaries of the single-index covariates within a unified iterative framework. The derived model matrices enable the fast computation of the estimated effective degrees of freedom and pointwise confidence bands for the single-index effects. The smoothing parameter updates are integrated into the iterative process via the generalized Fellner-Schall method, which recycles the derived matrix decompositions, thereby providing an efficient approximation to the global penalized optimization problem. Simulation studies with moderate sample sizes under non-Gaussian distributions confirm the empirical consistency of the estimation across multiple scenarios. Notably, the proposed approach remains stable where state-of-the-art competitive methods fail to recover true single-index coefficients and nonlinear functions, and is 80.13 times faster than the usual two-step method in the most computationally intensive scenario. The modeling advantage is illustrated through an application to Capital Bike Sharing data, where we deal with a single-index interaction effect for each year, with distinct single-index coefficients, a complex structure that makes competitive methods inapplicable. The proposed method is implemented in R, with functions available for reproducibility and transparency in comparisons.

Computer-use agents are increasingly capable of operating on real operating systems, but this capability has also increased the risks posed by prompt injection, indirect instructions, and visual attacks. Existing defenses typically rely on analyzing the prompt or each potentially malicious input with a second large model at inference time, which can limit coverage or increase deployment cost. We propose ProjGuard, an alternative based on behavioral trajectory monitoring. At each step, we derive a lightweight scalar risk signal from the agent's accumulated interaction history and evaluate, online, whether execution is beginning to drift toward an unsafe region. This enables early warnings before the trajectory reaches a potentially harmful action. When an alert is raised, we selectively activate an auxiliary vision-language model to propose a corrected next step and steer execution back toward task completion. Experiments on OS-Harm show that monitoring with on-demand correction reduces the unsafe rate from 16 percent to 3 percent while improving task completion from 59 percent to 65 percent. We further evaluate transfer to RiosWorld, where the method remains competitive, reaching 4 percent unsafe and 64 percent completion. Overall, these results support a hierarchical safety strategy in which always-on monitoring anticipates deviations and activates correction only when needed.

To address the common problem of high dimensionality in tensor regressions, we introduce a generalized tensor random projection method that embeds high-dimensional tensor-valued covariates into low-dimensional subspaces with minimal loss of information about the responses. The method is flexible, allowing for tensor-wise, mode-wise, or combined random projections as special cases. A Bayesian inference framework is provided featuring the use of a hierarchical prior distribution and a low-rank representation of the parameter. Strong theoretical support is provided for the concentration properties of the random projection and posterior consistency of the Bayesian inference. An efficient Gibbs sampler is developed to perform inference on the compressed data. To mitigate the sensitivity introduced by random projections, Bayesian model averaging is employed, with normalising constants estimated using reverse logistic regression. An extensive simulation study is conducted to examine the effects of different tuning parameters. Simulations indicate, and the real data application confirms, that compressed Bayesian tensor regression can achieve better out-of-sample prediction while significantly reducing computational cost compared to standard Bayesian tensor regression.

Diffusion-weighted magnetic resonance imaging (D-MRI) is a noninvasive in vivo technique for probing the microstructural architecture of biological tissues. At each voxel, the fiber orientation distribution (FOD) characterizes local fiber configurations and orientations and is therefore a central object of estimation in D-MRI analysis. We propose the Nearest-Neighbor Adaptive Regression Model (NARM), a spatially adaptive framework for FOD estimation that performs weighted local likelihood estimation over nested spatial neighborhoods, where the weights jointly encode spatial proximity and similarity among neighboring FODs, measured by either the optimal transport or Hellinger distance. To prevent over-smoothing while preserving structural heterogeneity, we introduce a voxel-wise rescaling scheme and a data-driven stopping rule based on minimum nearest-neighbor dissimilarity. We further develop a configuration-aware strategy for selecting the similarity-smoothing parameter, allowing the smoothing strength to adapt to local fiber complexity. Simulation studies demonstrate that NARM improves FOD estimation accuracy relative to voxel-wise methods and the existing spatial smoothing approach PMARM. Application to test-retest data from the Human Connectome Project additionally shows that NARM yields more reproducible FOD estimates. Implementation details and scripts for the simulation and real data analyses are available at this https URL