--Nonnegative matrix factorization (NMF) is a known unsupervised data-reduction method. The principle of the common cause (PCC) is a basic methodological approach in probabilistic causality, which seeks an independent mixture model for the joint probability of two dependent random variables. It turns out that these two concepts are closely related. This relationship is explored reciprocally for several datasets of gray-scale images, which are conveniently mapped into probability models. On one hand, PCC provides a predictability tool that leads to a robust estimation of the effective rank of NMF . Unlike other estimates (e.g., those based on the Bayesian Information Criteria), our estimate of the rank is stable against weak noise. We show that NMF implemented around this rank produces features (basis images) that are also stable against noise and against seeds of local optimization, thereby effectively resolving the NMF nonidentifiability problem. On the other hand, NMF provides an interesting possibility of implementing PCC in an approximate way, where larger and positively correlated joint probabilities tend to be explained better via the independent mixture model. We work out a clustering method, where data points with the same common cause are grouped into the same cluster . We also show how NMF can be employed for data denoising. Nonnegative matrix factorization (NMF) was proposed and developed in data science [1]-[3].

While queueing network models are powerful tools for analyzing service systems, they traditionally require substantial human effort and domain expertise to construct. To make this modeling approach more scalable and accessible, we propose a data-driven framework for queueing network modeling and simulation based on autoregressive sequence models trained on event-stream data. Instead of explicitly specifying arrival processes, service mechanisms, or routing logic, our approach learns the conditional distributions of event types and event times, recasting the modeling task as a problem of sequence distribution learning. We show that Transformer-style architectures can effectively parameterize these distributions, enabling automated construction of high-fidelity simulators. As a proof of concept, we validate our framework on event tables generated from diverse queueing networks, showcasing its utility in simulation, uncertainty quantification, and counterfactual evaluation. Leveraging advances in artificial intelligence and the growing availability of data, our framework takes a step toward more automated, data-driven modeling pipelines to support broader adoption of queueing network models across service domains.

Detecting whether an LLM hallucinates is an important research challenge. One promising way of doing so is to estimate the semantic entropy (Farquhar et al., 2024) of the distribution of generated sequences. We propose a new algorithm for doing that, with two main advantages. First, due to us taking the Bayesian approach, we achieve a much better quality of semantic entropy estimates for a given budget of samples from the LLM. Second, we are able to tune the number of samples adaptively so that `harder' contexts receive more samples. We demonstrate empirically that our approach systematically beats the baselines, requiring only 53% of samples used by Farquhar et al. (2024) to achieve the same quality of hallucination detection as measured by AUROC. Moreover, quite counterintuitively, our estimator is useful even with just one sample from the LLM.

Large Language Models are increasingly used to simulate human opinion dynamics, yet the effect of genuine interaction is often obscured by systematic biases. We present a Bayesian framework to disentangle and quantify three such biases: (i) a topic bias toward prior opinions in the training data; (ii) an agreement bias favoring agreement irrespective of the question; and (iii) an anchoring bias toward the initiating agent's stance. Applying this framework to multi-step dialogues reveals that opinion trajectories tend to quickly converge to a shared attractor, with the influence of the interaction fading over time, and the impact of biases differing between LLMs. In addition, we fine-tune an LLM on different sets of strongly opinionated statements (incl. misinformation) and demonstrate that the opinion attractor shifts correspondingly. Exposing stark differences between LLMs and providing quantitative tools to compare them to human subjects in the future, our approach highlights both chances and pitfalls in using LLMs as proxies for human behavior.

Transductive conformal prediction addresses the simultaneous prediction for multiple data points. Given a desired confidence level, the objective is to construct a prediction set that includes the true outcomes with the prescribed confidence. We demonstrate a fundamental trade-off between confidence and efficiency in transductive methods, where efficiency is measured by the size of the prediction sets. Specifically, we derive a strict finite-sample bound showing that any non-trivial confidence level leads to exponential growth in prediction set size for data with inherent uncertainty. The exponent scales linearly with the number of samples and is proportional to the conditional entropy of the data. Additionally, the bound includes a second-order term, dispersion, defined as the variance of the log conditional probability distribution. We show that this bound is achievable in an idealized setting. Finally, we examine a special case of transductive prediction where all test data points share the same label. We show that this scenario reduces to the hypothesis testing problem with empirically observed statistics and provide an asymptotically optimal confidence predictor, along with an analysis of the error exponent.

Here, we show emergent tactile behaviors resulting from the proposed contact-aware Fisher information maximization method that results in human-like tactile behaviors for learning (a) mass and weight, (b) friction and textures, (c) stiffness, and (d) shape [20]. Abstract--Contact dynamics hold immense amounts of information that can improve a robot's ability to characterize and learn about objects in their environment through interactions. However, collecting information-rich contact data is challenging due to its inherent sparsity and non-smooth nature, requiring an active approach to maximize the utility of contacts for learning. In this work, we investigate an optimal experimental design approach to synthesize robot behaviors that produce contact-rich data for learning. Our approach derives a contact-aware Fisher information measure that characterizes information-rich contact behaviors that improve parameter learning. We observe emergent robot behaviors that are able to excite contact interactions that efficiently learns object parameters across a range of parameter learning examples. Last, we demonstrate the utility of contact-awareness for learning parameters through contact-seeking behaviors on several robotic experiments. Contact dynamics are commonly used in robotics to manipulate the robot itself, e.g., through locomotion, or manipulate objects in its environment. However, the utility of contacts goes beyond just manipulation, and instead, contact can be seen as a medium to transmit information that can help a robot learn about its environment. In fact, prior work has demonstrated the information-richness of contact as a means to improve parameter estimation problems [8, 21, 27]. The underlying challenge is enabling robot behaviors that can actively acquire contact data for learning.

Differential privacy (DP) is the standard for privacy-preserving analysis, and introduces a fundamental trade-off between privacy guarantees and model performance. Selecting the optimal balance is a critical challenge that can be framed as a multi-objective optimization (MOO) problem where one first discovers the set of optimal trade-offs (the Pareto front) and then learns a decision-maker's preference over them. While a rich body of work on interactive MOO exists, the standard approach -- modeling the objective functions with generic surrogates and learning preferences from simple pairwise feedback -- is inefficient for DP because it fails to leverage the problem's unique structure: a point on the Pareto front can be generated directly by maximizing accuracy for a fixed privacy level. Motivated by this property, we first derive the shape of the trade-off theoretically, which allows us to model the Pareto front directly and efficiently. To address inefficiency in preference learning, we replace pairwise comparisons with a more informative interaction. In particular, we present the user with hypothetical trade-off curves and ask them to pick their preferred trade-off. Our experiments on differentially private logistic regression and deep transfer learning across six real-world datasets show that our method converges to the optimal privacy-accuracy trade-off with significantly less computational cost and user interaction than baselines.

We formulate the inverse problem in a Bayesian framework and aim to train a generative model that allows us to simulate (i.e., sample from the likelihood) and do inference (i.e., sample from the posterior). We review the use of triangular normalizing flows for conditional sampling in this context and show how to combine two such triangular maps (an upper and a lower one) in to one invertible mapping that can be used for simulation and inference. We work out several useful properties of this invertible generative model and propose a possible training loss for training the map directly. We illustrate the workings of this new approach to conditional generative modeling numerically on a few stylized examples.

Stein variational gradient descent (SVGD) is a kernel-based and non-parametric particle method for sampling from a target distribution, such as in Bayesian inference and other machine learning tasks. Different from other particle methods, SVGD does not require estimating the score, which is the gradient of the log-density. However, in practice, SVGD can be slow compared to score-estimation-based sampling algorithms. To design a fast and efficient high-dimensional sampling algorithm with the advantages of SVGD, we introduce accelerated SVGD (ASVGD), based on an accelerated gradient flow in a metric space of probability densities following Nesterov's method. We then derive a momentum-based discrete-time sampling algorithm, which evolves a set of particles deterministically. To stabilize the particles' position update, we also include a Wasserstein metric regularization. This paper extends the conference version \cite{SL2025}. For the bilinear kernel and Gaussian target distributions, we study the kernel parameter and damping parameters with an optimal convergence rate of the proposed dynamics. This is achieved by analyzing the linearized accelerated gradient flows at the equilibrium. Interestingly, the optimal parameter is a constant, which does not depend on the covariance of the target distribution. For the generalized kernel functions, such as the Gaussian kernel, numerical examples with varied target distributions demonstrate the effectiveness of ASVGD compared to SVGD and other popular sampling methods. Furthermore, we show that in the setting of Bayesian neural networks, ASVGD outperforms SVGD significantly in terms of log-likelihood and total iteration times.

Simulation-based inference (SBI) enables Bayesian analysis when the likelihood is intractable but model simulations are available. Recent advances in statistics and machine learning, including Approximate Bayesian Computation and deep generative models, have expanded the applicability of SBI, yet these methods often face challenges in moderate to high-dimensional parameter spaces. Motivated by the success of gradient-based Monte Carlo methods in Bayesian sampling, we propose a novel SBI method that integrates score matching with Langevin dynamics to explore complex posterior landscapes more efficiently in such settings. Our approach introduces tailored score-matching procedures for SBI, including a localization scheme that reduces simulation costs and an architectural regularization that embeds the statistical structure of log-likelihood scores to improve score-matching accuracy. We provide theoretical analysis of the method and illustrate its practical benefits on benchmark tasks and on more challenging problems in moderate to high dimensions, where it performs favorably compared to existing approaches.