Modern large scale datasets are often plagued with missing entries. For tabular data with missing values, a flurry of imputation algorithms solve for a complete matrix which minimizes some penalized reconstruction error. However, almost none of them can estimate the uncertainty of its imputations. This paper proposes a probabilistic and scalable framework for missing value imputation with quantified uncertainty.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. Authors propose a method of estimating a graphical model for continuous data that blends the following three, established ideas: 1) assume the data follows a multivariate Gaussian and estimate using the graphical lasso; 2) do not assume the data follows a multivariate Gaussian and instead use a Gaussian copula, the nonparanormal, to allow arbitrary single variable marginals; or 3) assume a specific tree-structured factorization and model arbitrary bivariate marginals along the tree structure. The proposed method introduces the blossom tree, which is a specific factorization of the model into a collection of densely connected blossom components that are connected by a specific set of tree edges. In particular, each blossom is connected (via a pedicel node) to at most one tree edge. The blossom components are modeled as sparse multivariate Gaussians (or using the non-paranormal copula) and the tree edges are modeled as arbitrary bivariate distributions with single variable marginals that are consistent with the marginal of any blossom pedicel to which they are attached.

Multimodal generative models require a unified approach to handle both discrete data (e.g., text and code) and continuous data (e.g., image, audio, video). In this work, we propose Latent Language Modeling (LatentLM), which seamlessly integrates continuous and discrete data using causal Transformers. Specifically, we employ a variational autoencoder (VAE) to represent continuous data as latent vectors and introduce next-token diffusion for autoregressive generation of these vectors. Additionally, we develop $\sigma$-VAE to address the challenges of variance collapse, which is crucial for autoregressive modeling. Extensive experiments demonstrate the effectiveness of LatentLM across various modalities. In image generation, LatentLM surpasses Diffusion Transformers in both performance and scalability. When integrated into multimodal large language models, LatentLM provides a general-purpose interface that unifies multimodal generation and understanding. Experimental results show that LatentLM achieves favorable performance compared to Transfusion and vector quantized models in the setting of scaling up training tokens. In text-to-speech synthesis, LatentLM outperforms the state-of-the-art VALL-E 2 model in speaker similarity and robustness, while requiring 10x fewer decoding steps. The results establish LatentLM as a highly effective and scalable approach to advance large multimodal models.

Bayesian flow networks (BFNs) iteratively refine the parameters, instead of the samples in diffusion models (DMs), of distributions at various noise levels through Bayesian inference. Owing to its differentiable nature, BFNs are promising in modeling both continuous and discrete data, while simultaneously maintaining fast sampling capabilities. This paper aims to understand and enhance BFNs by connecting them with DMs through stochastic differential equations (SDEs). We identify the linear SDEs corresponding to the noise-addition processes in BFNs, demonstrate that BFN's regression losses are aligned with denoise score matching, and validate the sampler in BFN as a first-order solver for the respective reverse-time SDE. Based on these findings and existing recipes of fast sampling in DMs, we propose specialized solvers for BFNs that markedly surpass the original BFN sampler in terms of sample quality with a limited number of function evaluations (e.g., 10) on both image and text datasets. Notably, our best sampler achieves an increase in speed of 5~20 times for free. Our code is available at https://github.com/ML-GSAI/BFN-Solver.

Differential privacy (DP) has been accepted as a rigorous criterion for measuring the privacy protection offered by random mechanisms used to obtain statistics or, as we will study here, synthetic datasets from confidential data. Methods to generate such datasets are increasingly numerous, using varied tools including Bayesian models, deep neural networks and copulas. However, little is still known about how to properly perform statistical inference with these differentially private synthetic (DIPS) datasets. The challenge is for the analyses to take into account the variability from the synthetic data generation in addition to the usual sampling variability. A similar challenge also occurs when missing data is imputed before analysis, and statisticians have developed appropriate inference procedures for this case, which we tend extended to the case of synthetic datasets for privacy. In this work, we study the applicability of these procedures, based on combining rules, to the analysis of DIPS datasets. Our empirical experiments show that the proposed combining rules may offer accurate inference in certain contexts, but not in all cases.

This paper introduces Bayesian Flow Networks (BFNs), a new class of generative model in which the parameters of a set of independent distributions are modified with Bayesian inference in the light of noisy data samples, then passed as input to a neural network that outputs a second, interdependent distribution. Starting from a simple prior and iteratively updating the two distributions yields a generative procedure similar to the reverse process of diffusion models; however it is conceptually simpler in that no forward process is required. Discrete and continuous-time loss functions are derived for continuous, discretised and discrete data, along with sample generation procedures. Notably, the network inputs for discrete data lie on the probability simplex, and are therefore natively differentiable, paving the way for gradient-based sample guidance and few-step generation in discrete domains such as language modelling. The loss function directly optimises data compression and places no restrictions on the network architecture. In our experiments BFNs achieve competitive log-likelihoods for image modelling on dynamically binarized MNIST and CIFAR-10, and outperform all known discrete diffusion models on the text8 character-level language modelling task.

This paper introduces a new neural network model that aims to mimic the biological brain more closely by structuring the network as a complete directed graph that processes continuous data for each timestep. Current neural networks have structures that vaguely mimic the brain structure, such as neurons, convolutions, and recurrence. The model proposed in this paper adds additional structural properties by introducing cycles into the neuron connections and removing the sequential nature commonly seen in other network layers. Furthermore, the model has continuous input and output, inspired by spiking neural networks, which allows the network to learn a process of classification, rather than simply returning the final result.