Deriving Compact Laws Based on Algebraic Formulation of a Data Set
In various subjects, there exist compact and consistent relationships between input and output parameters. Discovering the relationships, or namely compact laws, in a data set is of great interest in many fields, such as physics, chemistry, and finance. While data discovery has made great progress in practice thanks to the success of machine learning in recent years, the development of analytical approaches in finding the theory behind the data is relatively slow. In this paper, we develop an innovative approach in discovering compact laws from a data set. By proposing a novel algebraic equation formulation, we convert the problem of deriving meaning from data into formulating a linear algebra model and searching for relationships that fit the data. Rigorous proof is presented in validating the approach. The algebraic formulation allows the search of equation candidates in an explicit mathematical manner. Searching algorithms are also proposed for finding the governing equations with improved efficiency. For a certain type of compact theory, our approach assures convergence and the discovery is computationally efficient and mathematically precise.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Resolving Kirchhoff's laws for state-estimator design of Li-ion battery packs connected in parallel
A state-space model for Li-ion battery packs with parallel connected cells is introduced. The key feature of this model is an explicit solution to Kirchhoff's laws for parallel connected packs, which expresses the branch…
Pick-and-Mix Information Operators for Probabilistic ODE Solvers
Probabilistic numerical solvers for ordinary differential equations compute posterior distributions over the solution of an initial value problem via Bayesian inference. In this paper, we leverage their probabilistic for…
Bayesian InferenceTransport of Algebraic Structure to Latent Embeddings
Machine learning often aims to produce latent embeddings of inputs which lie in a larger, abstract mathematical space. For example, in the field of 3D modeling, subsets of Euclidean space can be embedded as vectors using…
P3P Made Easy
We revisit the classical Perspective-Three-Point (P3P) problem, which aims to recover the absolute pose of a calibrated camera from three 2D-3D correspondences. It has long been known that P3P can be reduced to a quartic…
P(Expression|Grammar): Probability of deriving an algebraic expression with a probabilistic context-free grammar
Probabilistic context-free grammars have a long-term record of use as generative models in machine learning and symbolic regression. When used for symbolic regression, they generate algebraic expressions. We define the l…
regressionSymbolic Regression