Related papers: Using Shape Constraints for Improving Symbolic Reg…

We study generalised additive models, with shape restrictions (e.g. monotonicity, convexity, concavity) imposed on each component of the additive prediction function. We show that this framework facilitates a nonparametric estimator of each…

Regression splines are smooth, flexible, and parsimonious nonparametric function estimators. They are known to be sensitive to knot number and placement, but if assumptions such as monotonicity or convexity may be imposed on the regression…

We consider the problem of nonparametric regression under shape constraints. The main examples include isotonic regression (with respect to any partial order), unimodal/convex regression, additive shape-restricted regression, and…

Evolutionary symbolic regression approaches are powerful tools that can approximate an explicit mapping between input features and observation for various problems. However, ensuring that explored expressions maintain consistency with…

Evolutionary symbolic regression (SR) fits a symbolic equation to data, which gives a concise interpretable model. We explore using SR as a method to propose which data to gather in an active learning setting with physical constraints. SR…

In [1], we have explored the theoretical aspects of feature selection and evolutionary algorithms. In this chapter, we focus on optimization algorithms for enhancing data analytic process, i.e., we propose to explore applications of…

Symbolic Regression (SR) can generate interpretable, concise expressions that fit a given dataset, allowing for more human understanding of the structure than black-box approaches. The addition of background knowledge (in the form of…

Model compression is generally performed by using quantization, low-rank approximation or pruning, for which various algorithms have been researched in recent years. One fundamental question is: what types of compression work better for a…

Neural fields are receiving increased attention as a geometric representation due to their ability to compactly store detailed and smooth shapes and easily undergo topological changes. Compared to classic geometry representations, however,…

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…

A Constraint Satisfaction Problem (CSP) is a framework used for modeling and solving constrained problems. Tree-search algorithms like backtracking try to construct a solution to a CSP by selecting the variables of the problem one after…

Shape and texture are two prominent and complementary cues for recognizing objects. Nonetheless, Convolutional Neural Networks are often biased towards either texture or shape, depending on the training dataset. Our ablation shows that such…

Mechanical product engineering often must comply with manufacturing or geometric constraints related to the shaping process. Mechanical design hence should rely on robust and fast tools to explore complex shapes, typically for design for…

The goal of feature selection is to choose the optimal subset of features for a recognition task by evaluating the importance of each feature, thereby achieving effective dimensionality reduction. Currently, proposed feature selection…

Designing functional materials requires a deep search through multidimensional spaces for system parameters that yield desirable material properties. For cases where conventional parameter sweeps or trial-and-error sampling are impractical,…

Real-world applications of computational fluid dynamics often involve the evaluation of quantities of interest for several distinct geometries that define the computational domain or are embedded inside it. For example, design optimization…

Hypothesis testing procedures are developed to assess linear operator constraints in function-on-scalar regression when incomplete functional responses are observed. The approach enables statistical inferences about the shape and other…

Transfer learning has emerged as a highly sought-after and actively pursued research area within the statistical community. The core concept of transfer learning involves leveraging insights and information from auxiliary datasets to…

This paper focuses on the statistical analysis of shapes of data objects called shape graphs, a set of nodes connected by articulated curves with arbitrary shapes. A critical need here is a constrained registration of points (nodes to…

In the field of parametric partial differential equations, shape optimization represents a challenging problem due to the required computational resources. In this contribution, a data-driven framework involving multiple reduction…