Vision-language foundation models (e.g., CLIP) have shown remarkable performance across a wide range of tasks. However, deploying these models may be unreliable when significant distribution gaps exist between the training and test data. The training-free test-time dynamic adapter (TDA) is a promising approach to address this issue by storing representative test samples to guide the classification of subsequent ones. However, TDA only naively maintains a limited number of reference samples in the cache, leading to severe test-time catastrophic forgetting when the cache is updated by dropping samples. In this paper, we propose a simple yet effective method for DistributiOnal Test-time Adaptation (Dota). Instead of naively memorizing representative test samples, Dota continually estimates the distributions of test samples, allowing the model to continually adapt to the deployment environment. The test-time posterior probabilities are then computed using the estimated distributions based on Bayes' theorem for adaptation purposes. To further enhance the adaptability on the uncertain samples, we introduce a new human-in-the-loop paradigm which identifies uncertain samples, collects human-feedback, and incorporates it into the Dota framework. Extensive experiments validate that Dota enables CLIP to continually learn, resulting in a significant improvement compared to current state-of-the-art methods.

Intransitivity is a critical issue in pairwise preference modeling. It refers to the intransitive pairwise preferences between a group of players or objects that potentially form a cyclic preference chain and has been long discussed in social choice theory in the context of the dominance relationship. However, such multifaceted intransitivity between players and the corresponding player representations in high dimensions is difficult to capture. In this paper, we propose a probabilistic model that jointly learns each player's d-dimensional representation (d>1) and a dataset-specific metric space that systematically captures the distance metric in Rd over the embedding space. Interestingly, by imposing additional constraints in the metric space, our proposed model degenerates to former models used in intransitive representation learning. Moreover, we present an extensive quantitative investigation of the vast existence of intransitive relationships between objects in various real-world benchmark datasets. To our knowledge, this investigation is the first of this type. The predictive performance of our proposed method on different real-world datasets, including social choice, election, and online game datasets, shows that our proposed method outperforms several competing methods in terms of prediction accuracy.

Neural simulation-based inference (SBI) describes an emerging family of methods for Bayesian inference with intractable likelihood functions that use neural networks as surrogate models. Here we introduce sbijax, a Python package that implements a wide variety of state-of-the-art methods in neural simulation-based inference using a user-friendly programming interface. sbijax offers high-level functionality to quickly construct SBI estimators, and compute and visualize posterior distributions with only a few lines of code. In addition, the package provides functionality for conventional approximate Bayesian computation, to compute model diagnostics, and to automatically estimate summary statistics. By virtue of being entirely written in JAX, sbijax is extremely computationally efficient, allowing rapid training of neural networks and executing code automatically in parallel on both CPU and GPU.

Causal Graph Discovery (CGD) is the process of estimating the underlying probabilistic graphical model that represents joint distribution of features of a dataset. CGD-algorithms are broadly classified into two categories: (i) Constraint-based algorithms (outcome depends on conditional independence (CI) tests), (ii) Score-based algorithms (outcome depends on optimized score-function). Since, sensitive features of observational data is prone to privacy-leakage, Differential Privacy (DP) has been adopted to ensure user privacy in CGD. Adding same amount of noise in this sequential-natured estimation process affects the predictive performance of the algorithms. As initial CI tests in constraint-based algorithms and later iterations of the optimization process of score-based algorithms are crucial, they need to be more accurate, less noisy. Based on this key observation, we present CURATE (CaUsal gRaph AdapTivE privacy), a DP-CGD framework with adaptive privacy budgeting. In contrast to existing DP-CGD algorithms with uniform privacy budgeting across all iterations, CURATE allows adaptive privacy budgeting by minimizing error probability (for constraint-based), maximizing iterations of the optimization problem (for score-based) while keeping the cumulative leakage bounded. To validate our framework, we present a comprehensive set of experiments on several datasets and show that CURATE achieves higher utility compared to existing DP-CGD algorithms with less privacy-leakage.

Constrained by the lack of model interpretability and a deep understanding of human movement in traditional movement recognition machine learning methods, this study introduces a novel representation learning method based on causal inference to better understand human joint dynamics and complex behaviors. We propose a two-stage framework that combines the Peter-Clark (PC) algorithm and Kullback-Leibler (KL) divergence to identify and quantify causal relationships between joints. Our method effectively captures interactions and produces interpretable, robust representations. Experiments on the EmoPain dataset show that our causal GCN outperforms traditional GCNs in accuracy, F1 score, and recall, especially in detecting protective behaviors. The model is also highly invariant to data scale changes, enhancing its reliability in practical applications. Our approach advances human motion analysis and paves the way for more adaptive intelligent healthcare solutions.

Bayesian networks (BNs) are widely used for modeling complex systems with uncertainty, yet repositories of pre-built BNs remain limited. This paper introduces bnRep, an open-source R package offering a comprehensive collection of documented BNs, facilitating benchmarking, replicability, and education. With over 200 networks from academic publications, bnRep integrates seamlessly with bnlearn and other R packages, providing users with interactive tools for network exploration.

Many applications, including climate-model analysis and stochastic weather generators, require learning or emulating the distribution of a high-dimensional and non-Gaussian spatial field based on relatively few training samples. To address this challenge, a recently proposed Bayesian transport map (BTM) approach consists of a triangular transport map with nonparametric Gaussian-process (GP) components, which is trained to transform the distribution of interest distribution to a Gaussian reference distribution. To improve the performance of this existing BTM, we propose to shrink the map components toward a ``base'' parametric Gaussian family combined with a Vecchia approximation for scalability. The resulting ShrinkTM approach is more accurate than the existing BTM, especially for small numbers of training samples. It can even outperform the ``base'' family when trained on a single sample of the spatial field. We demonstrate the advantage of ShrinkTM though numerical experiments on simulated data and on climate-model output.

Score-based diffusion models, which generate new data by learning to reverse a diffusion process that perturbs data from the target distribution into noise, have achieved remarkable success across various generative tasks. Despite their superior empirical performance, existing theoretical guarantees are often constrained by stringent assumptions or suboptimal convergence rates. In this paper, we establish a fast convergence theory for a popular SDE-based sampler under minimal assumptions. Our analysis shows that, provided $\ell_{2}$-accurate estimates of the score functions, the total variation distance between the target and generated distributions is upper bounded by $O(d/T)$ (ignoring logarithmic factors), where $d$ is the data dimensionality and $T$ is the number of steps. This result holds for any target distribution with finite first-order moment. To our knowledge, this improves upon existing convergence theory for both the SDE-based sampler and another ODE-based sampler, while imposing minimal assumptions on the target data distribution and score estimates. This is achieved through a novel set of analytical tools that provides a fine-grained characterization of how the error propagates at each step of the reverse process.

Artificial intelligence models trained through loss minimization have demonstrated significant success, grounded in principles from fields like information theory and statistical physics. This work explores these established connections through the lens of statistical mechanics, starting from first-principles sample concentration behaviors that underpin AI and machine learning. Our development of statistical mechanics for modeling highlights the key role of exponential families, and quantities of statistics, physics, and information theory.

Abstract: Real-world chemical processes often exhibit stochastic dynamics with non-trivial correlations and state-dependent fluctuations. However, most process models simply add stationary noise terms to a deterministic prediction, which can lead to inaccurate predictions. This work proposes using conditional normalizing flows as discrete-time models (DTMs) to learn the stochastic dynamics of chemical processes. Normalizing flows learn an explicit expression of the system states' probability density function (PDF) given prior states and control inputs. The resulting model naturally allows for formulating stochastic and probabilistic setpoint-tracking objectives and chance constraints. In applications to a continuous reactor and a reactor cascade, the normalizing flow yields stable simulations over long time horizons and high-quality results in stochastic and probabilistic MPC formulation for open-loop control. Furthermore, a chance-constrained optimization finds reliable startup controls for the reactor cascade with stochastic reactions. In conclusion, the conditional normalizing flow presents an excellent choice for modeling nonlinear stochastic dynamics.