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We introduce a family of multilayer graph kernels and establish new links between graph convolutional neural networks and kernel methods. Our approach generalizes convolutional kernel networks to graph-structured data, by representing…
Belonging to the family of Bayesian nonparametrics, Gaussian process (GP) based approaches have well-documented merits not only in learning over a rich class of nonlinear functions, but also in quantifying the associated uncertainty.…
Deep Bayesian neural networks (BNNs) are a powerful tool, though computationally demanding, to perform parameter estimation while jointly estimating uncertainty around predictions. BNNs are typically implemented using arbitrary…
Neural network models are known to reinforce hidden data biases, making them unreliable and difficult to interpret. We seek to build models that `know what they do not know' by introducing inductive biases in the function space. We show…
Whilst deep neural networks have shown great empirical success, there is still much work to be done to understand their theoretical properties. In this paper, we study the relationship between random, wide, fully connected, feedforward…
Gaussian processes (GPs) produce good probabilistic models of functions, but most GP kernels require $O((n+m)n^2)$ time, where $n$ is the number of data points and $m$ the number of predictive locations. We present a new kernel that allows…
Forecasting in probabilistic time series is a complex endeavor that extends beyond predicting future values to also quantifying the uncertainty inherent in these predictions. Gaussian process regression stands out as a Bayesian machine…
This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using Gaussian processes on the one side, and…
Gaussian process regression networks (GPRN) are powerful Bayesian models for multi-output regression, but their inference is intractable. To address this issue, existing methods use a fully factorized structure (or a mixture of such…
Artificial neural networks (NNs) have become the de facto standard in machine learning. They allow learning highly nonlinear transformations in a plethora of applications. However, NNs usually only provide point estimates without…
Convolutional neural networks (CNNs) work well on large datasets. But labelled data is hard to collect, and in some applications larger amounts of data are not available. The problem then is how to use CNNs with small data -- as CNNs…
This work presents a family of parsimonious Gaussian process models which allow to build, from a finite sample, a model-based classifier in an infinite dimensional space. The proposed parsimonious models are obtained by constraining the…
When constructing a Bayesian Machine Learning model, we might be faced with multiple different prior distributions and thus are required to properly consider them in a sensible manner in our model. While this situation is reasonably well…
Prior-Data Fitted Networks (PFNs) enable amortized Bayesian inference in a single forward pass, yet their internal representations remain opaque. It is unknown whether PFNs encode identifiable Bayesian structure or merely memorize…
Which neural networks are similar is a fundamental question for both machine learning and neuroscience. Here, it is proposed to base comparisons on the predictive distributions of linear readouts from intermediate representations. In…
Bayesian inference and kernel methods are well established in machine learning. The neural network Gaussian process in particular provides a concept to investigate neural networks in the limit of infinitely wide hidden layers by using…
Interpretability is crucial for machine learning in many scenarios such as quantitative finance, banking, healthcare, etc. Symbolic regression (SR) is a classic interpretable machine learning method by bridging X and Y using mathematical…
Deep feedforward neural networks (DFNNs) are a powerful tool for functional approximation. We describe flexible versions of generalized linear and generalized linear mixed models incorporating basis functions formed by a DFNN. The…
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…
Neural networks (NN) have achieved state-of-the-art performance in various applications. Unfortunately in applications where training data is insufficient, they are often prone to overfitting. One effective way to alleviate this problem is…