Related papers: The Poisson Gamma Belief Network
To reduce the curse of dimensionality for Gaussian processes (GP), they can be decomposed into a Gaussian Process Network (GPN) of coupled subprocesses with lower dimensionality. In some cases, intermediate observations are available within…
This work studies the global convergence and implicit bias of Gauss Newton's (GN) when optimizing over-parameterized one-hidden layer networks in the mean-field regime. We first establish a global convergence result for GN in the…
We consider the problem of learning high dimensional polynomial transformations of Gaussians. Given samples of the form $p(x)$, where $x\sim N(0, \mathrm{Id}_r)$ is hidden and $p: \mathbb{R}^r \to \mathbb{R}^d$ is a function where every…
It has been proposed by many researchers that combining deep neural networks with graphical models can create more efficient and better regularized composite models. The main difficulties in implementing this in practice are associated with…
The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability…
In regression analysis of counts, a lack of simple and efficient algorithms for posterior computation has made Bayesian approaches appear unattractive and thus underdeveloped. We propose a lognormal and gamma mixed negative binomial (NB)…
Training deep graph neural networks (GNNs) poses a challenging task, as the performance of GNNs may suffer from the number of hidden message-passing layers. The literature has focused on the proposals of {over-smoothing} and…
Deep learning is a hierarchical inference method formed by subsequent multiple layers of learning able to more efficiently describe complex relationships. In this work, Deep Gaussian Mixture Models are introduced and discussed. A Deep…
The Dirichlet Belief Network~(DirBN) has been recently proposed as a promising approach in learning interpretable deep latent representations for objects. In this work, we leverage its interpretable modelling architecture and propose a deep…
The Gaussian-radial-basis function neural network (GRBFNN) has been a popular choice for interpolation and classification. However, it is computationally intensive when the dimension of the input vector is high. To address this issue, we…
A low-energy hardware implementation of deep belief network (DBN) architecture is developed using near-zero energy barrier probabilistic spin logic devices (p-bits), which are modeled to realize an intrinsic sigmoidal activation function. A…
Deep conditional generative models are developed to simultaneously learn the temporal dependencies of multiple sequences. The model is designed by introducing a three-way weight tensor to capture the multiplicative interactions between side…
The graph structure is a commonly used data storage mode, and it turns out that the low-dimensional embedded representation of nodes in the graph is extremely useful in various typical tasks, such as node classification, link prediction ,…
Neural networks often struggle with high-dimensional but small sample-size tabular datasets. One reason is that current weight initialisation methods assume independence between weights, which can be problematic when there are insufficient…
Recent years have seen a growing interest in the use of belief propagation - an algorithm originally introduced for performing statistical inference on graphical models - for approximate, but highly efficient, tensor network contraction.…
Count-weighted temporal networks often exhibit unequal dispersion in the edge weights, which cannot be fully explained by modelling observational heterogeneity through latent factors in the conditional mean. Therefore, we propose new…
Bayesian neural networks (BNNs) augment deep networks with uncertainty quantification by Bayesian treatment of the network weights. However, such models face the challenge of Bayesian inference in a high-dimensional and usually…
Learned neural solvers have successfully been used to solve combinatorial optimization and decision problems. More general counting variants of these problems, however, are still largely solved with hand-crafted solvers. To bridge this gap,…
We propose a new computationally efficient method for quantizing the weights of pre- trained neural networks that is general enough to handle both multi-layer perceptrons and convolutional neural networks. Our method deterministically…
Gradient Boosting Machines (GBM) are hugely popular for solving tabular data problems. However, practitioners are not only interested in point predictions, but also in probabilistic predictions in order to quantify the uncertainty of the…