Related papers: Introduction to the signature method

Machine learning has been widely applied to clearly defined problems of astronomy and astrophysics. However, deep learning and its conceptual differences to classical machine learning have been largely overlooked in these fields. The broad…

Searches for statistically significant correlations between arrival directions of ultra-high energy cosmic rays and classes of astrophysical objects are common in astroparticle physics. We present a method to test potential correlation…

Recent innovations from machine learning allow for data unfolding, without binning and including correlations across many dimensions. We describe a set of known, upgraded, and new methods for ML-based unfolding. The performance of these…

Regression is a fundamental prediction task common in data-centric engineering applications that involves learning mappings between continuous variables. In many engineering applications (e.g.\ structural health monitoring), feature-label…

Adaptive cognition requires structured internal models of objects and their relations. Predictive neural networks are often proposed to learn such world models, but how these are instantiated and how they support prediction remain unclear.…

Central to rough path theory is the signature transform of a path, an infinite series of tensors given by the iterated integrals of the underlying path. The signature poses an effective way to capture sequentially ordered information,…

In the field of machine learning, data understanding is the practice of getting initial insights in unknown datasets. Such knowledge-intensive tasks require a lot of documentation, which is necessary for data scientists to grasp the meaning…

Connecting multiple machine learning models into a pipeline is effective for handling complex problems. By breaking down the problem into steps, each tackled by a specific component model of the pipeline, the overall solution can be made…

An increasing number of scientific applications are making use of irregular data access patterns. An important class of such patterns involve subscripted-subscripts, wherein an array value appears in the index expression of another array.…

Many, if not most, systems of interest in science are naturally described as nonlinear dynamical systems. Empirically, we commonly access these systems through time series measurements. Often such time series may consist of discrete random…

In this paper, we present an algorithm that computes the topological signature for a given periodic motion sequence. Such signature consists of a vector obtained by persistent homology which captures the topological and geometric changes of…

Data assimilation is a method that combines observations (that is, real world data) of a state of a system with model output for that system in order to improve the estimate of the state of the system and thereby the model output. The model…

The sequence of moments of a vector-valued random variable can characterize its law. We study the analogous problem for path-valued random variables, that is stochastic processes, by using so-called robust signature moments. This allows us…

Historical maps are valuable resources that capture detailed geographical information from the past. However, these maps are typically available in printed formats, which are not conducive to modern computer-based analyses. Digitizing these…

The use of patterns in predictive models is a topic that has received a lot of attention in recent years. Pattern mining can help to obtain models for structured domains, such as graphs and sequences, and has been proposed as a means to…

Despite the fact that nonlinear subspace learning techniques (e.g. manifold learning) have successfully applied to data representation, there is still room for improvement in explainability (explicit mapping), generalization…

The signature of a parametric curve is a sequence of tensors whose entries are iterated integrals. This construction is central to the theory of rough paths in stochastic analysis. It is here examined through the lens of algebraic geometry.…

We address the problem of merging graph and feature-space information while learning a metric from structured data. Existing algorithms tackle the problem in an asymmetric way, by either extracting vectorized summaries of the graph…

Unravelling hidden patterns in datasets is a classical problem with many potential applications. In this paper, we present a challenge whose objective is to discover nonlinear relationships in noisy cloud of points. If a set of point…

Symbolic equations are at the core of scientific discovery. The task of discovering the underlying equation from a set of input-output pairs is called symbolic regression. Traditionally, symbolic regression methods use hand-designed…