相关论文: Closed Form Variational Objectives For Bayesian Ne…

Bayesian inference for neural networks, or Bayesian deep learning, has the potential to provide well-calibrated predictions with quantified uncertainty and robustness. However, the main hurdle for Bayesian deep learning is its computational…

We prove new upper and lower bounds on the VC-dimension of deep neural networks with the ReLU activation function. These bounds are tight for almost the entire range of parameters. Letting $W$ be the number of weights and $L$ be the number…

This paper re-examines the problem of parameter estimation in Bayesian networks with missing values and hidden variables from the perspective of recent work in on-line learning [Kivinen & Warmuth, 1994]. We provide a unified framework for…

Bayesian optimisation has proven to be a powerful tool for expensive global black-box optimisation problems. In this paper, we propose new Bayesian optimisation variants of the popular Knowledge Gradient acquisition functions for problems…

Based on the tree architecture, the objective of this paper is to design deep neural networks with two or more hidden layers (called deep nets) for realization of radial functions so as to enable rotational invariance for near-optimal…

Recent progress in deep latent variable models has largely been driven by the development of flexible and scalable variational inference methods. Variational training of this type involves maximizing a lower bound on the log-likelihood,…

We study the problem of learning a Bayesian network (BN) of a set of variables when structural side information about the system is available. It is well known that learning the structure of a general BN is both computationally and…

Bayesian neural networks provide a direct and natural way to extend standard deep neural networks to support probabilistic deep learning through the use of probabilistic layers that, traditionally, encode weight (and bias) uncertainty. In…

We characterise the likelihood function computed from a Bayesian network with latent variables as root nodes. We show that the marginal distribution over the remaining, manifest, variables also factorises as a Bayesian network, which we…

In classic papers, Zellner demonstrated that Bayesian inference could be derived as the solution to an information theoretic functional. Below we derive a generalized form of this functional as a variational lower bound of a predictive…

We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often…

Recently, a spate of papers have provided positive theoretical results for training over-parameterized neural networks (where the network size is larger than what is needed to achieve low error). The key insight is that with sufficient…

We propose a new family of optimization criteria for variational auto-encoding models, generalizing the standard evidence lower bound. We provide conditions under which they recover the data distribution and learn latent features, and…

Latent variable models have been playing a central role in psychometrics and related fields. In many modern applications, the inference based on latent variable models involves one or several of the following features: (1) the presence of…

Neural networks are regularly employed in adaptive control of nonlinear systems and related methods of reinforcement learning. A common architecture uses a neural network with a single hidden layer (i.e. a shallow network), in which the…

We make three related contributions motivated by the challenge of training stochastic neural networks, particularly in a PAC-Bayesian setting: (1) we show how averaging over an ensemble of stochastic neural networks enables a new class of…

Recent work on weighted model counting has been very successfully applied to the problem of probabilistic inference in Bayesian networks. The probability distribution is encoded into a Boolean normal form and compiled to a target language,…

Neural networks with piecewise linear activation functions, such as rectified linear units (ReLU) or maxout, are among the most fundamental models in modern machine learning. We make a step towards proving lower bounds on the size of such…

Recent progress in variational inference has paid much attention to the flexibility of variational posteriors. One promising direction is to use implicit distributions, i.e., distributions without tractable densities as the variational…

We extend variational autoencoders (VAEs) to collaborative filtering for implicit feedback. This non-linear probabilistic model enables us to go beyond the limited modeling capacity of linear factor models which still largely dominate…