Related papers: Random walk kernels and learning curves for Gaussi…

Many applications in speech, robotics, finance, and biology deal with sequential data, where ordering matters and recurrent structures are common. However, this structure cannot be easily captured by standard kernel functions. To model such…

We propose a model of random walks on weighted graphs where the weights are interval valued, and connect it to reversible imprecise Markov chains. While the theory of imprecise Markov chains is now well established, this is a first attempt…

In recent years, new neural network architectures designed to operate on graph-structured data have pushed the state-of-the-art in the field. A large set of these architectures utilize a form of classical random walks to diffuse…

Gaussian processes are rich distributions over functions, with generalization properties determined by a kernel function. When used for long-range extrapolation, predictions are particularly sensitive to the choice of kernel parameters. It…

We investigate iterated compositions of weighted sums of Gaussian kernels and provide an interpretation of the construction that shows some similarities with the architectures of deep neural networks. On the theoretical side, we show that…

A device called a 'Gaussian Boson Sampler' has initially been proposed as a near-term demonstration of classically intractable quantum computation. As recently shown, it can also be used to decide whether two graphs are isomorphic. Based on…

Bayesian nonparametric models, such as Gaussian processes, provide a compelling framework for automatic statistical modelling: these models have a high degree of flexibility, and automatically calibrated complexity. However, automating…

We study the relationship between online Gaussian process (GP) regression and kernel least mean squares (KLMS) algorithms. While the latter have no capacity of storing the entire posterior distribution during online learning, we discover…

We revisit widely used preferential Gaussian processes by Chu et al.(2005) and challenge their modelling assumption that imposes rankability of data items via latent utility function values. We propose a generalisation of pgp which can…

Graphs are often used to organize data because of their simple topological structure, and therefore play a key role in machine learning. And it turns out that the low-dimensional embedded representation obtained by graph representation…

Various methods in statistical learning build on kernels considered in reproducing kernel Hilbert spaces. In applications, the kernel is often selected based on characteristics of the problem and the data. This kernel is then employed to…

We are interested in a framework of online learning with kernels for low-dimensional but large-scale and potentially adversarial datasets. We study the computational and theoretical performance of online variations of kernel Ridge…

Kernel methods are one of the mainstays of machine learning, but the problem of kernel learning remains challenging, with only a few heuristics and very little theory. This is of particular importance in methods based on estimation of…

We present a unified framework to study graph kernels, special cases of which include the random walk graph kernel \citep{GaeFlaWro03,BorOngSchVisetal05}, marginalized graph kernel \citep{KasTsuIno03,KasTsuIno04,MahUedAkuPeretal04}, and…

We investigate the use of discrete-time quantum walks to sample from an almost-uniform distribution, in the absence of any external source of randomness. Integers are encoded on the vertices of a cycle graph, and a quantum walker evolves…

Random walks are at the heart of many existing deep learning algorithms for graph data. However, such algorithms have many limitations that arise from the use of random walks, e.g., the features resulting from these methods are unable to…

Kernel methods give powerful, flexible, and theoretically grounded approaches to solving many problems in machine learning. The standard approach, however, requires pairwise evaluations of a kernel function, which can lead to scalability…

Gaussian processes have become a popular tool for nonparametric regression because of their flexibility and uncertainty quantification. However, they often use stationary kernels, which limit the expressiveness of the model and may be…

Bayesian computational strategies for inference can be inefficient in approximating the posterior distribution in models that exhibit some form of periodicity. This is because the probability mass of the marginal posterior distribution of…

Feature learning in neural networks is crucial for their expressive power and inductive biases, motivating various theoretical approaches. Some approaches describe network behavior after training through a change in kernel scale from…