Cyclical MCMC is a novel MCMC framework recently proposed by Zhang et al. (2019) to address the challenge posed by high-dimensional multimodal posterior distributions like those arising in deep learning. The algorithm works by generating a nonhomogeneous Markov chain that tracks - cyclically in time - tempered versions of the target distribution. We show in this work that cyclical MCMC converges to the desired probability distribution in settings where the Markov kernels used are fast mixing, and sufficiently long cycles are employed. However in the far more common settings of slow mixing kernels, the algorithm may fail to produce samples from the desired distribution. In particular, in a simple mixture example with unequal variance where powering is known to produce slow mixing kernels, we show by simulation that cyclical MCMC fails to converge to the desired limit. Finally, we show that cyclical MCMC typically estimates well the local shape of the target distribution around each mode, even when we do not have convergence to the target.

In recent years, denoising problems have become intertwined with the development of deep generative models. In particular, diffusion models are trained like denoisers, and the distribution they model coincide with denoising priors in the Bayesian picture. However, denoising through diffusion-based posterior sampling requires the noise level and covariance to be known, preventing blind denoising. We overcome this limitation by introducing Gibbs Diffusion (GDiff), a general methodology addressing posterior sampling of both the signal and the noise parameters. Assuming arbitrary parametric Gaussian noise, we develop a Gibbs algorithm that alternates sampling steps from a conditional diffusion model trained to map the signal prior to the family of noise distributions, and a Monte Carlo sampler to infer the noise parameters. Our theoretical analysis highlights potential pitfalls, guides diagnostic usage, and quantifies errors in the Gibbs stationary distribution caused by the diffusion model. We showcase our method for 1) blind denoising of natural images involving colored noises with unknown amplitude and spectral index, and 2) a cosmology problem, namely the analysis of cosmic microwave background data, where Bayesian inference of "noise" parameters means constraining models of the evolution of the Universe.

Modeling count-valued time series has been receiving increasing attention since count time series naturally arise in physical and social domains. Poisson gamma dynamical systems (PGDSs) are newly-developed methods, which can well capture the expressive latent transition structure and bursty dynamics behind count sequences. In particular, PGDSs demonstrate superior performance in terms of data imputation and prediction, compared with canonical linear dynamical system (LDS) based methods. Despite these advantages, PGDS cannot capture the heterogeneous overdispersed behaviours of the underlying dynamic processes. To mitigate this defect, we propose a negative-binomial-randomized gamma Markov process, which not only significantly improves the predictive performance of the proposed dynamical system, but also facilitates the fast convergence of the inference algorithm. Moreover, we develop methods to estimate both factor-structured and graph-structured transition dynamics, which enable us to infer more explainable latent structure, compared with PGDSs. Finally, we demonstrate the explainable latent structure learned by the proposed method, and show its superior performance in imputing missing data and forecasting future observations, compared with the related models.

Drawing inspiration from the remarkable This paper introduces diffusion protein language progress in NLP achieved by language models (LMs; Devlin model (DPLM), a versatile protein language et al., 2019; Radford et al., 2018; OpenAI, 2023) thanks to model that demonstrates strong generative and the scalability of Transformers (Vaswani et al., 2017) and predictive capabilities for protein sequences. We the existence of large-scale text data, recent explorations in first pre-train scalable DPLMs from evolutionaryscale protein has also demonstrated the impressive capabilities of protein sequences within a generative selfsupervised protein language models (Rives et al., 2019; Lin et al., 2022; discrete diffusion probabilistic framework, Hu et al., 2022), learned from the universe of evolutionaryscale which generalizes language modeling for protein sequences. As a result, protein LMs have proteins in a principled way. After pre-training, become one of the most important cornerstones in AI for DPLM exhibits the ability to generate structurally protein research, serving a pivotal role not only in predictive plausible, novel and diverse protein sequences tasks (e.g., probing functional properties, and predicting for unconditional generation. We further protein structures from single sequences without explicit demonstrate the proposed diffusion generative evolutionary homologs) but also in generative tasks (e.g., pre-training make DPLM possess a better redesigning sequences given protein backbone structures, or understanding of proteins, making it a superior synthesizing completely new protein sequences).

Human knowledge is largely implicit and relational -- do we have a friend in common? can I walk from here to there? In this work, we leverage the combinatorial structure of graphs to quantify human priors over such relational data. Our experiments focus on two domains that have been continuously relevant over evolutionary timescales: social interaction and spatial navigation. We find that some features of the inferred priors are remarkably consistent, such as the tendency for sparsity as a function of graph size. Other features are domain-specific, such as the propensity for triadic closure in social interactions. More broadly, our work demonstrates how nonclassical statistical analysis of indirect behavioral experiments can be used to efficiently model latent biases in the data.

Reinforcement learning (RL) [43] has emerged as a powerful framework for sequential decision-making in dynamic and uncertain environments. While traditional RL methods, predominantly focused on maximizing the expected return, have seen significant advancements through approaches such as Q-learning [37, 25] and policy gradients [28, 10], they often fall short in real-world scenarios demanding strict risk control, such as financial investment [9], medical treatment [16], and automous driving [11]. The significance of comprehending risk management in RL has led to the emergence of Risk-Sensitive RL (RSRL). Unlike risk-neutral RL, which primarily focuses on maximizing expected returns, RSRL seeks to optimize risk metrics, such as entropy risk measures (ERM) [17, 18] or conditional value-at-risk (CVaR) [46], of the possible cumulative reward which emphasizes its distributional characteristics. However, traditional RL framework based on Q-learning which typically considers the mean of reward-to-go and corresponding Bellman equation, cannot efficiently capture the characteristics of the cumulative reward's distribution. Therefore, there has been an upsurge of interest in Distributional RL (DisRL) due to its capacity to understand the intrinsic distributional attributes of cumulative rewards, which has already achieved significant empirical success in risk-sensitive tasks [8, 14, 30, 45, 34].

Bayesian optimal experimental design (OED) seeks to conduct the most informative experiment under budget constraints to update the prior knowledge of a system to its posterior from the experimental data in a Bayesian framework. Such problems are computationally challenging because of (1) expensive and repeated evaluation of some optimality criterion that typically involves a double integration with respect to both the system parameters and the experimental data, (2) suffering from the curse-of-dimensionality when the system parameters and design variables are high-dimensional, (3) the optimization is combinatorial and highly non-convex if the design variables are binary, often leading to non-robust designs. To make the solution of the Bayesian OED problem efficient, scalable, and robust for practical applications, we propose a novel joint optimization approach. This approach performs simultaneous (1) training of a scalable conditional normalizing flow (CNF) to efficiently maximize the expected information gain (EIG) of a jointly learned experimental design (2) optimization of a probabilistic formulation of the binary experimental design with a Bernoulli distribution. We demonstrate the performance of our proposed method for a practical MRI data acquisition problem, one of the most challenging Bayesian OED problems that has high-dimensional (320 $\times$ 320) parameters at high image resolution, high-dimensional (640 $\times$ 386) observations, and binary mask designs to select the most informative observations.

Tremendous breakthroughs have been developed in Semi-Supervised Semantic Segmentation (S4) through contrastive learning. However, due to limited annotations, the guidance on unlabeled images is generated by the model itself, which inevitably exists noise and disturbs the unsupervised training process. To address this issue, we propose a robust contrastive-based S4 framework, termed the Probabilistic Representation Contrastive Learning (PRCL) framework to enhance the robustness of the unsupervised training process. We model the pixel-wise representation as Probabilistic Representations (PR) via multivariate Gaussian distribution and tune the contribution of the ambiguous representations to tolerate the risk of inaccurate guidance in contrastive learning. Furthermore, we introduce Global Distribution Prototypes (GDP) by gathering all PRs throughout the whole training process. Since the GDP contains the information of all representations with the same class, it is robust from the instant noise in representations and bears the intra-class variance of representations. In addition, we generate Virtual Negatives (VNs) based on GDP to involve the contrastive learning process. Extensive experiments on two public benchmarks demonstrate the superiority of our PRCL framework.

A common network inference problem, arising from real-world data constraints, is how to infer a dynamic network from its time-aggregated adjacency matrix and time-varying marginals (i.e., row and column sums). Prior approaches to this problem have repurposed the classic iterative proportional fitting (IPF) procedure, also known as Sinkhorn's algorithm, with promising empirical results. However, the statistical foundation for using IPF has not been well understood: under what settings does IPF provide principled estimation of a dynamic network from its marginals, and how well does it estimate the network? In this work, we establish such a setting, by identifying a generative network model whose maximum likelihood estimates are recovered by IPF. Our model both reveals implicit assumptions on the use of IPF in such settings and enables new analyses, such as structure-dependent error bounds on IPF's parameter estimates. When IPF fails to converge on sparse network data, we introduce a principled algorithm that guarantees IPF converges under minimal changes to the network structure. Finally, we conduct experiments with synthetic and real-world data, which demonstrate the practical value of our theoretical and algorithmic contributions.

Inferring the causal structure underlying stochastic dynamical systems from observational data holds great promise in domains ranging from science and health to finance. Such processes can often be accurately modeled via stochastic differential equations (SDEs), which naturally imply causal relationships via "which variables enter the differential of which other variables". In this paper, we develop a kernel-based test of conditional independence (CI) on "path-space" -- solutions to SDEs -- by leveraging recent advances in signature kernels. We demonstrate strictly superior performance of our proposed CI test compared to existing approaches on path-space. Then, we develop constraint-based causal discovery algorithms for acyclic stochastic dynamical systems (allowing for loops) that leverage temporal information to recover the entire directed graph. Assuming faithfulness and a CI oracle, our algorithm is sound and complete. We empirically verify that our developed CI test in conjunction with the causal discovery algorithm reliably outperforms baselines across a range of settings.