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Learning uncertain dynamics models using Gaussian process~(GP) regression has been demonstrated to enable high-performance and safety-aware control strategies for challenging real-world applications. Yet, for computational tractability,…

Surface registration is a technique that is used in various areas such as object recognition and 3D model reconstruction. Problem of surface registration can be analyzed as an optimization problem of seeking a rigid motion between two…

Stochastic bilevel optimization (SBO) has been integrated into many machine learning paradigms recently, including hyperparameter optimization, meta learning, and reinforcement learning. Along with the wide range of applications, there have…

Score-based generative modeling (SGM) is a highly successful approach for learning a probability distribution from data and generating further samples. We prove the first polynomial convergence guarantees for the core mechanic behind SGM:…

Automated scientific discovery aims to improve scientific understanding through machine learning. A central approach in this field is symbolic regression, which uses genetic programming or sparse regression to learn interpretable…

This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…

Genetic Programming (GP) is known to suffer from the burden of being computationally expensive by design. While, over the years, many techniques have been developed to mitigate this issue, data vectorization, in particular, is arguably…

The optimization of structural parameters, such as mass(m), stiffness(k), and damping coefficient(c), is critical for designing efficient, resilient, and stable structures. Conventional numerical approaches, including Finite Element Method…

Manifold learning methods are an invaluable tool in today's world of increasingly huge datasets. Manifold learning algorithms can discover a much lower-dimensional representation (embedding) of a high-dimensional dataset through non-linear…

In this paper, we consider a general stochastic optimization problem which is often at the core of supervised learning, such as deep learning and linear classification. We consider a standard stochastic gradient descent (SGD) method with a…

Graph Structure Learning (GSL) has recently garnered considerable attention due to its ability to optimize both the parameters of Graph Neural Networks (GNNs) and the computation graph structure simultaneously. Despite the proliferation of…

Recently there are a considerable amount of work devoted to the study of the algorithmic stability and generalization for stochastic gradient descent (SGD). However, the existing stability analysis requires to impose restrictive assumptions…

Stochastic gradient descent (SGD) holds as a classical method to build large scale machine learning models over big data. A stochastic gradient is typically calculated from a limited number of samples (known as mini-batch), so it…

We introduce a new scalable approximation for Gaussian processes with provable guarantees which hold simultaneously over its entire parameter space. Our approximation is obtained from an improved sample complexity analysis for sparse…

The paper uses statistical and differential geometric motivation to acquire prior information about the learning capability of an artificial neural network on a given dataset. The paper considers a broad class of neural networks with…

Data-driven methods are widely used to develop physical models, but there still exist limitations that affect their performance, generalizability and robustness. By combining gene expression programming (GEP) with artificial neural network…

A framework previously introduced in [3] for solving a sequence of stochastic optimization problems with bounded changes in the minimizers is extended and applied to machine learning problems such as regression and classification. The…

State-of-the-art methods for data-driven modelling of non-linear dynamical systems typically involve interactions with an expert user. In order to partially automate the process of modelling physical systems from data, many EA-based…

We study the modeling and prediction of dynamical systems based on conventional models derived from measurements. Such algorithms are highly desirable in situations where the underlying dynamics are hard to model from physical principles or…

Score-based graph generative models (SGGMs) have proven effective in critical applications such as drug discovery and protein synthesis. However, their theoretical behavior, particularly regarding convergence, remains underexplored. Unlike…