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Found 23 papers, 15 papers with code
Neural SDEs as Infinite-Dimensional GANs
Stochastic differential equations (SDEs) are a staple of mathematical modelling of temporal dynamics.
Bayesian Learning from Sequential Data using Gaussian Processes with Signature Covariances
We develop a Bayesian approach to learning from sequential data by using Gaussian processes (GPs) with so-called signature kernels as covariance functions.
Ranked #1 on
Time Series Classification
on DigitShapes
Seq2Tens: An Efficient Representation of Sequences by Low-Rank Tensor Projections
Sequential data such as time series, video, or text can be challenging to analyse as the ordered structure gives rise to complex dependencies.
Ranked #1 on
Time Series Classification
on KickvsPunch
Signature moments to characterize laws of stochastic processes
This allows us to derive a metric of maximum mean discrepancy type for laws of stochastic processes and study the topology it induces on the space of laws of stochastic processes.
Fast Bayesian Inference with Batch Bayesian Quadrature via Kernel Recombination
Empirically, we find that our approach significantly outperforms the sampling efficiency of both state-of-the-art BQ techniques and Nested Sampling in various real-world datasets, including lithium-ion battery analytics.
SOBER: Highly Parallel Bayesian Optimization and Bayesian Quadrature over Discrete and Mixed Spaces
Batch Bayesian optimisation and Bayesian quadrature have been shown to be sample-efficient methods of performing optimisation and quadrature where expensive-to-evaluate objective functions can be queried in parallel.
Random Fourier Signature Features
Tensor algebras give rise to one of the most powerful measures of similarity for sequences of arbitrary length called the signature kernel accompanied with attractive theoretical guarantees from stochastic analysis.
Nonlinear Independent Component Analysis for Discrete-Time and Continuous-Time Signals
We study the classical problem of recovering a multidimensional source signal from observations of nonlinear mixtures of this signal.
Positively Weighted Kernel Quadrature via Subsampling
We study kernel quadrature rules with convex weights.
Sampling-based Nyström Approximation and Kernel Quadrature
We analyze the Nystr\"om approximation of a positive definite kernel associated with a probability measure.
Capturing Graphs with Hypo-Elliptic Diffusions
This results in a novel tensor-valued graph operator, which we call the hypo-elliptic graph Laplacian.
A Randomized Algorithm to Reduce the Support of Discrete Measures
Given a discrete probability measure supported on $N$ atoms and a set of $n$ real-valued functions, there exists a probability measure that is supported on a subset of $n+1$ of the original $N$ atoms and has the same mean when integrated against each of the $n$ functions.
Adaptive Batch Sizes for Active Learning A Probabilistic Numerics Approach
Active learning parallelization is widely used, but typically relies on fixing the batch size throughout experimentation.
Persistence paths and signature features in topological data analysis
We introduce a new feature map for barcodes that arise in persistent homology computation.
Probabilistic supervised learning
Predictive modelling and supervised learning are central to modern data science.
Kernels for sequentially ordered data
We present a novel framework for kernel learning with sequential data of any kind, such as time series, sequences of graphs, or strings.
Carathéodory Sampling for Stochastic Gradient Descent
Various flavours of Stochastic Gradient Descent (SGD) replace the expensive summation that computes the full gradient by approximating it with a small sum over a randomly selected subsample of the data set that in turn suffers from a high variance.
Neural SDEs Made Easy: SDEs are Infinite-Dimensional GANs
Several authors have introduced \emph{Neural Stochastic Differential Equations} (Neural SDEs), often involving complex theory with various limitations.
Tangent Space and Dimension Estimation with the Wasserstein Distance
Consider a set of points sampled independently near a smooth compact submanifold of Euclidean space.
HADES: Fast Singularity Detection with Local Measure Comparison
We introduce Hades, an unsupervised algorithm to detect singularities in data.
A Quadrature Approach for General-Purpose Batch Bayesian Optimization via Probabilistic Lifting
Parallelisation in Bayesian optimisation is a common strategy but faces several challenges: the need for flexibility in acquisition functions and kernel choices, flexibility dealing with discrete and continuous variables simultaneously, model misspecification, and lastly fast massive parallelisation.
