At its core, the package implements an efficient Mode Jumping Markov Chain Monte Carlo (MJMCMC) algorithm, designed to improve mixing in multi-modal posterior landscapes within Bayesian generalized linear models. In addition, it provides a genetically modified MJMCMC (GMJMCMC) algorithm that introduces nonlinear feature generation, thereby enabling the estimation of Bayesian generalized nonlinear models (BGNLMs). Within this framework, the algorithm maintains and updates populations of transformed features, computes their posterior probabilities, and evaluates the posteriors of models constructed from them. We demonstrate the effective use of FBMS for both inferential and predictive modeling in Gaussian regression, focusing on different instances of the BGNLM class of models. Furthermore, through a broad set of applications, we illustrate how the methodology can be extended to increasingly complex modeling scenarios, extending to other response distributions and mixed effect models.

Accurate disease risk prediction based on genomic and clinical data can lead to more effective disease screening, early prevention, and personalized treatment strategies. However, despite the identifications of hundreds of disease-associated genomic and molecular features for many disease traits through genome-wide studies in the past two decades, drug resistance often causes the targeted therapies to fail in cancer patients, which is largely due to tumor heterogeneity (Zhang et al., 2022). For advanced cancers, tumor heterogeneity encompasses both the malignant cells and their microenvironment, which makes it challenging to develop accurate prediction models for personalized treatment strategies that account for intratumor heterogeneity. Single-cell technologies provide an unprecedented opportunity for dissecting the interplay between the cancer cells and the associated tumor microenvironment (TME), and the produced high-dimensional omics data should also augment existing survival modeling approaches for identifying tumor cell type-specific genes predictive of cancer patient survival.

Bayesian inference is useful to obtain a predictive distribution with a small generalization error. However, since posterior distributions are rarely evaluated analytically, we employ the variational Bayesian inference or sampling method to approximate posterior distributions. When we obtain samples from a posterior distribution, Hamiltonian Monte Carlo (HMC) has been widely used for the continuous variable part and Markov chain Monte Carlo (MCMC) for the discrete variable part. Another sampling method, the bouncy particle sampler (BPS), has been proposed, which combines uniform linear motion and stochastic reflection to perform sampling. BPS was reported to have the advantage of being easier to set simulation parameters than HMC. To accelerate the convergence to a posterior distribution, we introduced parallel tempering (PT) to BPS, and then proposed an algorithm when the inverse temperature exchange rate is set to infinity. We performed numerical simulations and demonstrated its effectiveness for multimodal distribution.

The chromatin folding and the spatial arrangement of chromosomes in the cell play a crucial role in DNA replication and genes expression. An improper chromatin folding could lead to malfunctions and, over time, diseases. For eukaryotes, centromeres are essential for proper chromosome segregation and folding. Despite extensive research using de novo sequencing of genomes and annotation analysis, centromere locations in yeasts remain difficult to infer and are still unknown in most species. Recently, genome-wide chromosome conformation capture coupled with next-generation sequencing (Hi-C) has become one of the leading methods to investigate chromosome structures. Some recent studies have used Hi-C data to give a point estimate of each centromere, but those approaches highly rely on a good pre-localization. Here, we present a novel approach that infers in a stochastic manner the locations of all centromeres in budding yeast based on both the experimental Hi-C map and simulated contact maps.

Probabilities of causation provide principled ways to assess causal relationships but face computational challenges due to partial identifiability and latent confounding. This paper introduces both algorithmic simplifications, significantly reducing the computational complexity of calculating tighter bounds for these probabilities, and a novel methodological framework for Root Cause Analysis that systematically employs these causal metrics to rank entire causal paths.

We study the problem of experimental design for accurately identifying the causal graph structure of a simple structural causal model (SCM), where the underlying graph may include both cycles and bidirected edges induced by latent confounders. The presence of cycles renders it impossible to recover the graph skeleton using observational data alone, while confounding can further invalidate traditional conditional independence (CI) tests in certain scenarios. To address these challenges, we establish lower bounds on both the maximum number of variables that can be intervened upon in a single experiment and the total number of experiments required to identify all directed edges and non-adjacent bidirected edges. Leveraging both CI tests and do see tests, and accounting for $d$ separation and $σ$ separation, we develop two classes of algorithms, i.e., bounded and unbounded, that can recover all causal edges except for double adjacent bidirected edges. We further show that, up to logarithmic factors, the proposed algorithms are tight with respect to the derived lower bounds.

We consider sampling from a Gibbs distribution by evolving finitely many particles. We propose a preconditioned version of a recently proposed noise-free sampling method, governed by approximating the score function with the numerically tractable score of a regularized Wasserstein proximal operator. This is derived by a Cole--Hopf transformation on coupled anisotropic heat equations, yielding a kernel formulation for the preconditioned regularized Wasserstein proximal. The diffusion component of the proposed method is also interpreted as a modified self-attention block, as in transformer architectures. For quadratic potentials, we provide a discrete-time non-asymptotic convergence analysis and explicitly characterize the bias, which is dependent on regularization and independent of step-size. Experiments demonstrate acceleration and particle-level stability on various log-concave and non-log-concave toy examples to Bayesian total-variation regularized image deconvolution, and competitive/better performance on non-convex Bayesian neural network training when utilizing variable preconditioning matrices.

This paper investigates the expected excess risk of In-Context Learning (ICL) for multi-class classification. We model each task as a sequence of labeled prompt samples and a query input, where a pre-trained model estimates the conditional class probabilities of the query. The expected excess risk is defined as the average truncated Kullback-Leibler (KL) divergence between the predicted and ground-truth conditional class distributions, averaged over a specified family of tasks. We establish a new oracle inequality for the expected excess risk based on KL divergence in multiclass classification. This allows us to derive tight upper and lower bounds for the expected excess risk in transformer-based models, demonstrating that the ICL estimator achieves the minimax optimal rate--up to a logarithmic factor--for conditional probability estimation. From a technical standpoint, our results introduce a novel method for controlling generalization error using the uniform empirical covering entropy of the log-likelihood function class. Furthermore, we show that multilayer perceptrons (MLPs) can also perform ICL and achieve this optimal rate under specific assumptions, suggesting that transformers may not be the exclusive architecture capable of effective ICL.

Gradient-based causal discovery shows great potential for deducing causal structure from data in an efficient and scalable way. Those approaches however can be susceptible to distributional biases in the data they are trained on. We identify two such biases: Marginal Distribution Asymmetry, where differences in entropy skew causal learning toward certain factorizations, and Marginal Distribution Shift Asymmetry, where repeated interventions cause faster shifts in some variables than in others. For the bivariate categorical setup with Dirichlet priors, we illustrate how these biases can occur even in controlled synthetic data. To examine their impact on gradient-based methods, we employ two simple models that derive causal factorizations by learning marginal or conditional data distributions - a common strategy in gradient-based causal discovery. We demonstrate how these models can be susceptible to both biases. We additionally show how the biases can be controlled. An empirical evaluation of two related, existing approaches indicates that eliminating competition between possible causal factorizations can make models robust to the presented biases.

We introduce bandit importance sampling (BIS), a new class of importance sampling methods designed for settings where the target density is expensive to evaluate. In contrast to adaptive importance sampling, which optimises a proposal distribution, BIS directly designs the samples through a sequential strategy that combines space-filling designs with multi-armed bandits. Our method leverages Gaussian process surrogates to guide sample selection, enabling efficient exploration of the parameter space with minimal target evaluations. We establish theoretical guarantees on convergence and demonstrate the effectiveness of the method across a broad range of sampling tasks. BIS delivers accurate approximations with fewer target evaluations, outperforming competing approaches across multimodal, heavy-tailed distributions, and real-world applications to Bayesian inference of computationally expensive models.