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.

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.

-- Social learning constitutes a fundamental framework for studying interactions among rational agents who observe each other's actions but lack direct access to individual beliefs. This paper investigates a specific social learning paradigm known as Word-of-Mouth (WoM), where a series of agents seeks to estimate the state of a dynamical system. The first agent receives noisy measurements of the state, while each subsequent agent relies solely on a degraded version of her predecessor's estimate. A defining feature of WoM is that the final agent's belief is publicly broadcast and subsequently adopted by all agents, in place of their own. We analyze this setting theoretically and through numerical simulations, noting that some agents benefit from using the belief of the last agent, while others experience performance deterioration.

The demand for text classification is growing significantly in web searching, data mining, web ranking, recommendation systems, and so many other fields of information and technology. This paper illustrates the text classification process on different datasets using some standard supervised machine learning techniques. Text documents can be classified through various kinds of classifiers. Labeled text documents are used to classify the text in supervised classifications. This paper applies these classifiers on different kinds of labeled documents and measures the accuracy of the classifiers. An Artificial Neural Network (ANN) model using Back Propagation Network (BPN) is used with several other models to create an independent platform for labeled and supervised text classification process. An existing benchmark approach is used to analyze the performance of classification using labeled documents. Experimental analysis on real data reveals which model works well in terms of classification accuracy.

Traditional budget allocation models struggle with the stochastic and nonlinear nature of real-world financial data. This study proposes a hybrid reinforcement learning (RL) framework for dynamic budget allocation, enhanced with Dirichlet-inspired stochasticity and quantum mutation-based genetic optimization. Using Apple Inc. quarterly financial data (2009 to 2025), the RL agent learns to allocate budgets between Research and Development and Selling, General and Administrative to maximize profitability while adhering to historical spending patterns, with L2 penalties discouraging unrealistic deviations. A Dirichlet distribution governs state evolution to simulate shifting financial contexts. To escape local minima and improve generalization, the trained policy is refined using genetic algorithms with quantum mutation via parameterized qubit rotation circuits. Generation-wise rewards and penalties are logged to visualize convergence and policy behavior. On unseen fiscal data, the model achieves high alignment with actual allocations (cosine similarity 0.9990, KL divergence 0.0023), demonstrating the promise of combining deep RL, stochastic modeling, and quantum-inspired heuristics for adaptive enterprise budgeting.

Recent technological advances have expanded the availability of high-throughput biological datasets, enabling the reliable design of digital twins of biomedical systems or patients. Such computational tools represent key reaction networks driving perturbation or drug response and can guide drug discovery and personalized therapeutics. Yet, their development still relies on laborious data integration by the human modeler, so that automated approaches are critically needed. The success of data-driven system discovery in Physics, rooted in clean datasets and well-defined governing laws, has fueled interest in applying similar techniques in Biology, which presents unique challenges. Here, we reviewed methodologies for automatically inferring digital twins from biological time series, which mostly involve symbolic or sparse regression. We evaluate algorithms according to eight biological and methodological challenges, associated to noisy/incomplete data, multiple conditions, prior knowledge integration, latent variables, high dimensionality, unobserved variable derivatives, candidate library design, and uncertainty quantification. Upon these criteria, sparse regression generally outperformed symbolic regression, particularly when using Bayesian frameworks. We further highlight the emerging role of deep learning and large language models, which enable innovative prior knowledge integration, though the reliability and consistency of such approaches must be improved. While no single method addresses all challenges, we argue that progress in learning digital twins will come from hybrid and modular frameworks combining chemical reaction network-based mechanistic grounding, Bayesian uncertainty quantification, and the generative and knowledge integration capacities of deep learning. To support their development, we further propose a benchmarking framework to evaluate methods across all challenges.