相关论文: Double Descent Risk and Volume Saturation Effects:…
Model multiplicity is a well-known but poorly understood phenomenon that undermines the generalisation guarantees of machine learning models. It appears when two models with similar training-time performance differ in their predictions and…
In overparameterized logistic regression, gradient descent (GD) iterates diverge in norm while converging in direction to the maximum $\ell_2$-margin solution -- a phenomenon known as the implicit bias of GD. This work investigates…
Bilevel learning has gained prominence in machine learning, inverse problems, and imaging applications, including hyperparameter optimization, learning data-adaptive regularizers, and optimizing forward operators. The large-scale nature of…
Onset of double-component convection due to different boundary conditions is studied in a diversely oriented infinite slot with broken reflection symmetry between the slot conditions for a component. Among other outcomes, the broken…
Recent growing interest in using machine learning for turbulence modelling has led to many proposed data-driven turbulence models in the literature. However, most of these models have not been developed with overcoming non-unique mapping…
Popularly used eigendecomposition-based criteria such as BIC type, ratio estimation and principal component-based criterion often underdetermine model dimensionality for regressions or the number of factors for factor models. This…
The fluid dynamics of liquid droplet impact on surfaces hold significant relevance to various industrial applications. However, high impact velocities introduce compressible effects, leading to material erosion. A gap in understanding and…
In solving a system of $n$ linear equations in $d$ variables $Ax=b$, the condition number of the $n,d$ matrix $A$ measures how much errors in the data $b$ affect the solution $x$. Estimates of this type are important in many inverse…
We analyze gradient descent with randomly weighted data points in a linear regression model, under a generic weighting distribution. This includes various forms of stochastic gradient descent, importance sampling, but also extends to…
This paper investigates the finite-sample prediction risk of the high-dimensional least squares estimator. We derive the central limit theorem for the prediction risk when both the sample size and the number of features tend to infinity.…
We numerically study confined channel foam flow around an obstacle using a two-dimensional bubble model, inspired by experiments performed in the same geometry. We systematically vary the polydispersity, the external driving force, and the…
A key physical quantity during reionization is the size of HII regions. Previous studies found a characteristic bubble size which increases rapidly during reionization, with apparent agreement between simulations and analytic excursion set…
Bilevel optimization is a central tool in machine learning for high-dimensional hyperparameter tuning. Its applications are vast; for instance, in imaging it can be used for learning data-adaptive regularizers and optimizing forward…
Motivated by a bidimensional discrete-time risk model in insurance, we study the second-order asymptotics for two kinds of tail probabilities of the stochastic discounted value of aggregate net losses including two business lines. These are…
In this paper we consider optimization with relaxation, an ample paradigm to make data-driven designs. This approach was previously considered by the same authors of this work in Garatti and Campi (2019), a study that revealed a deep-seated…
Two main concepts studied in machine learning theory are generalization gap (difference between train and test error) and excess risk (difference between test error and the minimum possible error). While information-theoretic tools have…
Stochastic gradient descent (SGD) is a promising method for solving large-scale inverse problems, due to its excellent scalability with respect to data size. The current mathematical theory in the lens of regularization theory predicts that…
When training a machine learning model with observational data, it is often encountered that some values are systemically missing. Learning from the incomplete data in which the missingness depends on some covariates may lead to biased…
(Stochastic) bilevel optimization is a frequently encountered problem in machine learning with a wide range of applications such as meta-learning, hyper-parameter optimization, and reinforcement learning. Most of the existing studies on…
The peculiar velocities of galaxies distort the clustering pattern anisotropically in redshift space. This effect on the statistics of isodensity contours is examined by linear theory. The statistics considered in this paper are the three-…