Related papers: Asymptotic Properties for Bayesian Neural Network …

We investigate the asymptotic properties of the L\'evy Adaptive B-spline (LABS) regression model, a Bayesian nonparametric method that incorporates B-spline kernels into the L\'evy Adaptive Regression Kernel (LARK) model. LABS applies…

In this article, we propose a novel spatial global-local spike-and-slab selection prior for image-on-scalar regression. We consider a Bayesian hierarchical Gaussian process model for image smoothing, that uses a flexible Inverse-Wishart…

Sparse deep learning aims to address the challenge of huge storage consumption by deep neural networks, and to recover the sparse structure of target functions. Although tremendous empirical successes have been achieved, most sparse deep…

There is increasing interest in learning how human brain networks vary as a function of a continuous trait, but flexible and efficient procedures to accomplish this goal are limited. We develop a Bayesian semiparametric model, which…

Advances in neuroscience have enabled researchers to measure the activities of large numbers of neurons simultaneously in behaving animals. We have access to the fluorescence of each of the neurons which provides a first-order approximation…

While Bayesian neural networks have many appealing characteristics, current priors do not easily allow users to specify basic properties such as expected lengthscale or amplitude variance. In this work, we introduce Poisson Process Radial…

Uncertainty in biological neural systems appears to be computationally beneficial rather than detrimental. However, in neuromorphic computing systems, device variability often limits performance, including accuracy and efficiency. In this…

In this work we explore a straightforward variational Bayes scheme for Recurrent Neural Networks. Firstly, we show that a simple adaptation of truncated backpropagation through time can yield good quality uncertainty estimates and superior…

While Bayesian neural networks (BNNs) hold the promise of being flexible, well-calibrated statistical models, inference often requires approximations whose consequences are poorly understood. We study the quality of common variational…

Analysing statistical properties of neural networks is a central topic in statistics and machine learning. However, most results in the literature focus on the properties of the neural network minimizing the training error. The goal of this…

We present asymptotic results for the regression-adjusted version of approximate Bayesian computation introduced by Beaumont(2002). We show that for an appropriate choice of the bandwidth, regression adjustment will lead to a posterior…

The application of deep neural networks in geospatial data has become a trending research problem in the present day. A significant amount of statistical research has already been introduced, such as generalized least square optimization by…

In many domains, we are interested in analyzing the structure of the underlying distribution, e.g., whether one variable is a direct parent of the other. Bayesian model-selection attempts to find the MAP model and use its structure to…

Much is now known about the consistency of Bayesian updating on infinite-dimensional parameter spaces with independent or Markovian data. Necessary conditions for consistency include the prior putting enough weight on the correct…

Recently, there has been a significant focus on exploring the theoretical aspects of deep learning, especially regarding its performance in classification tasks. Bayesian deep learning has emerged as a unified probabilistic framework,…

Bayesian density deconvolution using nonparametric prior distributions is a useful alternative to the frequentist kernel based deconvolution estimators due to its potentially wide range of applicability, straightforward uncertainty…

The massively parallel nature of biological information processing plays an important role for its superiority to human-engineered computing devices. In particular, it may hold the key to overcoming the von Neumann bottleneck that limits…

An increasing body of evidence suggests that the trial-to-trial variability of spiking activity in the brain is not mere noise, but rather the reflection of a sampling-based encoding scheme for probabilistic computing. Since the precise…

We study posterior contraction rates for sparse Bayesian Kolmogorov-Arnold networks (KANs) over anisotropic Besov spaces, providing a statistical foundation of KANs from a Bayesian point of view. We show that sparse Bayesian KANs equipped…

Although Bayesian variable selection methods have been intensively studied, their routine use in practice has not caught up with their non-Bayesian counterparts such as Lasso, likely due to difficulties in both computations and…