Diffusion models are state-of-the-art deep learning generative models that are trained on the principle of learning forward and backward diffusion processes via the progressive addition of noise and denoising. In this paper, we seek to trick audio-based DNN models, such as those in the Hugging Face framework, for example, those that focus on audio, in particular transformer-based artificial intelligence models, which are powerful machine learning models that save time and deliver faster, more efficient results. We demonstrate the feasibility of backdoor attacks (called `BacKBayDiffMod`) on audio transformers derived from Hugging Face, a popular framework in the world of artificial intelligence (AI) research. The backdoor attack developed in this paper is based on poisoning the model's training data by incorporating backdoor diffusion sampling and a Bayesian approach to the distribution of poisoned data.

The \textit{local learning coefficient} (LLC) is a principled way of quantifying model complexity, originally derived in the context of Bayesian statistics using singular learning theory (SLT). Several methods are known for numerically estimating the local learning coefficient, but so far these methods have not been extended to the scale of modern deep learning architectures or data sets. Using a method developed in {\tt arXiv:2308.12108 [stat.ML]} we empirically show how the LLC may be measured accurately and self-consistently for deep linear networks (DLNs) up to 100M parameters. We also show that the estimated LLC has the rescaling invariance that holds for the theoretical quantity.

Probabilistic circuits (PCs) such as sum-product networks efficiently represent large multi-variate probability distributions. They are preferred in practice over other probabilistic representations such as Bayesian and Markov networks because PCs can solve marginal inference (MAR) tasks in time that scales linearly in the size of the network. Unfortunately, the maximum-a-posteriori (MAP) and marginal MAP (MMAP) tasks remain NP-hard in these models. Inspired by the recent work on using neural networks for generating near-optimal solutions to optimization problems such as integer linear programming, we propose an approach that uses neural networks to approximate (M)MAP inference in PCs. The key idea in our approach is to approximate the cost of an assignment to the query variables using a continuous multilinear function, and then use the latter as a loss function. The two main benefits of our new method are that it is self-supervised and after the neural network is learned, it requires only linear time to output a solution. We evaluate our new approach on several benchmark datasets and show that it outperforms three competing linear time approximations, max-product inference, max-marginal inference and sequential estimation, which are used in practice to solve MMAP tasks in PCs.

We study the problem of automatically discovering Granger causal relations from observational multivariate time-series data. Vector autoregressive (VAR) models have been time-tested for this problem, including Bayesian variants and more recent developments using deep neural networks. Most existing VAR methods for Granger causality use sparsity-inducing penalties/priors or post-hoc thresholds to interpret their coefficients as Granger causal graphs. Instead, we propose a new Bayesian VAR model with a hierarchical graph prior over binary Granger causal graphs, separately from the VAR coefficients. We develop an efficient algorithm to infer the posterior over binary Granger causal graphs. Our method provides better uncertainty quantification, has less hyperparameters, and achieves better performance than competing approaches, especially on sparse multivariate time-series data.

Variable importance plays a pivotal role in interpretable machine learning as it helps measure the impact of factors on the output of the prediction model. Model agnostic methods based on the generation of "null" features via permutation (or related approaches) can be applied. Such analysis is often utilized in pharmaceutical applications due to its ability to interpret black-box models, including tree-based ensembles. A major challenge and significant confounder in variable importance estimation however is the presence of between-feature correlation. Recently, several adjustments to marginal permutation utilizing feature knockoffs were proposed to address this issue, such as the variable importance measure known as conditional predictive impact (CPI). Assessment and evaluation of such approaches is the focus of our work. We first present a comprehensive simulation study investigating the impact of feature correlation on the assessment of variable importance. We then theoretically prove the limitation that highly correlated features pose for the CPI through the knockoff construction. While we expect that there is always no correlation between knockoff variables and its corresponding predictor variables, we prove that the correlation increases linearly beyond a certain correlation threshold between the predictor variables. Our findings emphasize the absence of free lunch when dealing with high feature correlation, as well as the necessity of understanding the utility and limitations behind methods in variable importance estimation.

In online randomized experiments or A/B tests, accurate predictions of participant inclusion rates are of paramount importance. These predictions not only guide experimenters in optimizing the experiment's duration but also enhance the precision of treatment effect estimates. In this paper we present a novel, straightforward, and scalable Bayesian nonparametric approach for predicting the rate at which individuals will be exposed to interventions within the realm of online A/B testing. Our approach stands out by offering dual prediction capabilities--it forecasts both the quantity of new customers expected in future time windows and, unlike available alternative methods, the number of times they will be observed. We derive closedform expressions for the posterior distributions of the quantities needed to form predictions about future user activity, thereby bypassing the need for numerical algorithms such as Markov chain Monte Carlo. After a comprehensive exposition of our model, we test its performance on experiments on real and simulated data, where we show its superior performance with respect to existing alternatives in the literature. 1 Introduction The problem of predicting the size of a population from which random samples are drawn has a long history in the statistics literature. Originally motivated by applications in ecology, where the goal is typically to determine the number of distinct species of animals within a population (Fisher et al., 1943; Good, 1953; Burnham and Overton, 1979), a variation of this problem has recently received considerable attention also in the genomics literature, where scientists are interested in predicting the number of future rare variants to be observed within a genomic study (Ionita-Laza et al., 2009; Zou et al., 2016; Chakraborty et al., 2019; Masoero et al., 2022).

In this paper, we introduce a Bayesian learning model to understand the behavior of Large Language Models (LLMs). We explore the optimization metric of LLMs, which is based on predicting the next token, and develop a novel model grounded in this principle. Our approach involves constructing an ideal generative text model represented by a multinomial transition probability matrix with a prior, and we examine how LLMs approximate this matrix. We discuss the continuity of the mapping between embeddings and multinomial distributions, and present the Dirichlet approximation theorem to approximate any prior. Additionally, we demonstrate how text generation by LLMs aligns with Bayesian learning principles and delve into the implications for in-context learning, specifically explaining why in-context learning emerges in larger models where prompts are considered as samples to be updated. Our findings indicate that the behavior of LLMs is consistent with Bayesian Learning, offering new insights into their functioning and potential applications.

The inadequate mixing of conventional Markov Chain Monte Carlo (MCMC) methods for multi-modal distributions presents a significant challenge in practical applications such as Bayesian inference and molecular dynamics. Addressing this, we propose Diffusive Gibbs Sampling (DiGS), an innovative family of sampling methods designed for effective sampling from distributions characterized by distant and disconnected modes. DiGS integrates recent developments in diffusion models, leveraging Gaussian convolution to create an auxiliary noisy distribution that bridges isolated modes in the original space and applying Gibbs sampling to alternately draw samples from both spaces. Our approach exhibits a better mixing property for sampling multi-modal distributions than state-of-the-art methods such as parallel tempering. We demonstrate that our sampler attains substantially improved results across various tasks, including mixtures of Gaussians, Bayesian neural networks and molecular dynamics.

We introduce a variational inference interpretation for models of "posterior flows" - generalizations of "probability flows" to a broader class of stochastic processes not necessarily diffusion processes. We coin the resulting models as "Variational Flow Models". Additionally, we propose a systematic training-free method to transform the posterior flow of a "linear" stochastic process characterized by the equation Xt = at * X0 + st * X1 into a straight constant-speed (SC) flow, reminiscent of Rectified Flow. This transformation facilitates fast sampling along the original posterior flow without training a new model of the SC flow. The flexibility of our approach allows us to extend our transformation to inter-convert two posterior flows from distinct "linear" stochastic processes. Moreover, we can easily integrate high-order numerical solvers into the transformed SC flow, further enhancing sampling accuracy and efficiency. Rigorous theoretical analysis and extensive experimental results substantiate the advantages of our framework.

In numerous healthcare and other contemporary applications, the variables of primary interest are obtained through indirect measurements, such as in the case of Magnetic Resonance Imaging (MRI) and Computed Tomography (CT). For some of these applications, the reliability of the results is of particular importance. The accuracy and trustworthiness of the outcomes obtained through indirect measurements are significantly influenced by two critical factors: the degree of uncertainty associated with the measuring instrument and the appropriateness of the (forward) model used for the reconstruction of the parameters of interest (measurand). In this paper, we consider Bayesian inversion to obtain the measurand from signals measured by the instrument and a noise model that mimics both the instrument noise and the error of the forward model.